Patent Publication Number: US-2015076030-A1

Title: Non-toxic liquid impregnated surfaces

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application claims priority to U.S. Provisional Application No. 61/878,481, entitled “Non-Toxic Liquid-Impregnated Surfaces.” filed Sep. 16, 2013, the disclosure of which is incorporated herein by reference in its entirety. 
    
    
     BACKGROUND 
     The advent of micro/nano-engineered surfaces in the last decade has opened up new techniques for enhancing a wide variety of physical phenomena in thermofluids sciences. For example, the use of micro/nano surface textures has provided non-wetting surfaces capable of achieving less viscous drag, reduced adhesion to ice and other materials, self-cleaning, water repellency, and other useful properties. These improvements result generally from diminished contact (i.e., less wetting) between the solid surfaces, and adjacent liquids. One type of non-wetting surface of interest is a super hydrophobic surface. In general, a super hydrophobic surface includes micro/nano-scale roughness on an intrinsically hydrophobic surface, such as a hydrophobic coating. Super hydrophobic surfaces resist contact with water by virtue of an air-water interface within the micro/nano surface textures. 
     One of the drawbacks of existing non-wetting surfaces (e.g., superhydrophobic, superoleophobic, and supermetallophobic surfaces) is that they are susceptible to evaporation and partial entrainment of constituents therein (e.g., in the presence of water and/or a product in contact with the surface), which can degrade the hydrophobicity, and in a consumer products context may lead to concerns about materials toxicity (i.e., as they degrade and/or dissociate). Thus, there is a need for non-wetting surfaces that are more robust. In particular, there is a need for non-wetting surfaces that are non-toxic, are more durable, and can maintain super hydrophobicity even after repeated use. 
     SUMMARY 
     Embodiments described herein relate generally to containers having liquid-impregnated surfaces disposed on their interior surfaces. The liquid-impregnated surfaces may compose an arrangement of solid and/or semi-solid features, defining one or more interstitial regions therebetween, and an impregnating liquid preferentially wetted to those regions. The containers may be designed to contain a product that is intended for human or animal consumption. The solid and/or semi-solid features and the impregnating liquid collectively define a secondary surface (e.g., substantially parallel to the interior surface on which the liquid-impregnated surfaces are disposed) and may include materials which are non-toxic. In particular, non-toxic liquid-impregnated surfaces of the disclosure may be configured for use in food, drug, health and/or beauty product applications, and industrial applications where people make contact with the coating materials, or where fumes or vapors in the manufacturing of coating materials or products made in the industrial applications poses a safety concerns for workers. 
     In some embodiments, the interstitial regions are dimensioned and configured such that the impregnating liquid is retained within the interstitial regions by capillary forces. The impregnating liquid disposed in the interstitial regions and the solid features collectively defines a secondary surface having a second roll off angle less than a first roll off angle of the initial/interior surface. The liquid-impregnated surface, in use, is in contact with at least one of a food product, drug, or health and beauty product, and the impregnating liquid included in the liquid-impregnated surface is non-toxic. In some embodiments, the solid features included in the liquid-impregnated surface can also be formed from materials that are non-toxic. In some embodiments, at least one of the impregnating liquid and the solid features included in the liquid-impregnated surface can include: materials that are approved by the U.S. Food and Drug Administration (FDA) for use as a food additive, an FDA approved food contact substance, an FDA “Generally Regarded as Safe” (GRAS) material, an FDA approved drug ingredient, and/or or an FDA approved health and beauty product ingredient. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1A  is a schematic cross-section view of a product contacting a conventional super-hydrophobic surface, and  FIG. 1B  shows the conventional non-wetting surface after a product has impaled the surface. 
         FIG. 2  shows a schematic cross-section of a liquid-impregnated surface according to an embodiment. 
         FIG. 3  is a scanning electron microscope (SEM) micrograph of a surface including semi-solid features according, to an embodiment. 
         FIG. 4  is a SEM micrograph of a surface including hierarchical semi-solid features, according to an embodiment. 
         FIG. 5  is a SEM micrograph of the surface of  FIG. 3  partially impregnated with an impregnating liquid. 
         FIG. 6  is an enlarged higher-magnification view of the region of the liquid-impregnated surface indicated by arrow A in  FIG. 5 . 
         FIGS. 7A and 7B  are schematic diagrams of liquid droplets placed on a liquid-impregnated surfaces (having a low surface energy lubricant, and a having moderate surface energy lubricant, respectively) according to an embodiment. 
         FIGS. 7C and 7D  show photographs of water droplets on the liquid-impregnated surfaces of  FIGS. 7A and 7B , respectively. 
         FIGS. 7E and 7F  are photographs of water droplets on the liquid-impregnated surfaces of  FIGS. 7A and 7B , taken under a fluorescent light, where the liquid includes a fluorescent dye. 
         FIGS. 7G and 7H  are LCFM images of liquid-impregnated surfaces (having a low surface energy lubricant, and a having moderate surface energy lubricant, respectively) according to an embodiment. 
         FIGS. 7I and 7J  are environmental scanning electron microscope (ESEM) images of liquid-impregnated surfaces (having a low surface energy lubricant, and a having moderate surface energy lubricant, respectively) according to an embodiment. 
         FIG. 8  is a table of schematics and characteristic equations for wetting surface configurations having an oil-solid-air interface (top three rows) and at an oil-solid-water interface (bottom three rows), where the subscript “o” denotes the impregnating liquid (e.g. oil). 
         FIG. 9  shows possible thermodynamic states of a water droplet (or other external phase) on liquid-impregnated surfaces. 
         FIG. 10A  is a plot of measured roll off angles for liquid-impregnated surfaces, according to an embodiment. 
         FIG. 10B  is a SEM image of a liquid-impregnated surface with solid features, according to an embodiment. 
         FIG. 10C  is a SEM image of a liquid-impregnated surface having hierarchical solid features, according to an embodiment. 
         FIG. 10D  is a non-dimensional plot of scaled gravitational force at the instant of roll-off, as a function of the relevant pinning force of the liquid-impregnated and non-impregnated surfaces of  FIG. 9 . 
         FIG. 11A  is a plot of measured velocities of water droplets as a function of substrate tilt angle, according to an embodiment. 
         FIG. 11B  shows a schematic of a liquid droplet moving on a lubricant-impregnated surface, showing the various parameters considered in the scaling model, according to an embodiment. 
         FIG. 11C  shows trajectories of a number of coffee particles measured relative to a water droplet on a liquid-impregnated surface, according to an embodiment. 
         FIG. 11D  shows a non-dimensional plot obtained from a model described herein. 
         FIG. 12  shows a SEM micrograph (at 500× magnification) of a textured substrate formed by spraying a mixture of 0.5 grams carnauba wax and 40 ml ethanol onto a substrate, according to an embodiment. 
         FIG. 13  is a higher-magnification (15,000×) SEM micrograph of the textured substrate shown in  FIG. 12 . 
         FIG. 14  shows a scanning electron microscope (SEM) micrograph of a textured substrate formed by spraying a mixture of 4 grams carnauba wax and 40 ml ethanol onto a substrate, according to an embodiment. 
         FIG. 15  is a higher-magnification (15,000×) SEM micrograph of the textured substrate shown in  FIG. 14 . 
         FIG. 16  is a SEM micrograph (at 500× magnification) of a textured substrate formed by spraying an aerosol wax on a substrate, according to an embodiment. 
         FIG. 17  is a higher-magnification (15,000×) SEM micrograph of the textured substrate shown in  FIG. 16 . 
         FIGS. 18-23  are a sequence of images of a volume of ketchup disposed on a liquid impregnated surface that includes aerosol wax as the solid and ethyl oleate as the impregnating liquid, such that the volume of ketchup slides on the liquid impregnated surface as the liquid impregnated surface is inclined at an angle. 
     
    
    
     DETAILED DESCRIPTION 
     Embodiments described herein relate generally to containers having liquid-impregnated surfaces disposed on their interior surfaces. The liquid-impregnated surfaces may compose an arrangement of solid and/or semi-solid features, defining one or more interstitial regions therebetween, and an impregnating liquid preferentially wetted to those regions. The containers may be designed to contain a product that is intended for human or animal use and/or consumption. The solid and/or semi-solid features and the impregnating liquid collectively define a secondary surface (e.g., substantially parallel to the interior surface on which the liquid-impregnated surfaces are disposed) and may include materials which are non-toxic. In particular, non-toxic liquid-impregnated surfaces of the disclosure may be configured for use in food, drugs, health and/or beauty product applications. 
     In some embodiments, the interstitial regions are dimensioned and configured such that the impregnating liquid is retained within the interstitial regions by capillary forces. The secondary surface may have a second roll off angle less than a first roll off angle of the initial/interior surface. The liquid-impregnated surface, in use, is in contact with at least one of a food product, drug, or health and beauty product, and the impregnating liquid included in the liquid-impregnated surface is non-toxic. In some embodiments, the solid features included in the liquid-impregnated surface can also be formed from materials that are non-toxic. In some embodiments, at least one of the impregnating liquid and the solid features included in the liquid-impregnated surface can include: materials that are approved by the U.S. Food and Drug Administration (FDA) for use as a food additive, an FDA approved food contact substance, an FDA “Generally Regarded as Safe” (GRAS) material, an FDA approved drug ingredient, and/or or an FDA approved health and beauty product ingredient. 
     Some surfaces with designed chemistry and roughness possess substantial non-wetting (hydrophobic) properties, which can be extremely useful in a wide variety of commercial and technological applications. Inspired by nature, such hydrophobic surfaces include air pockets trapped within a microtexture or nanotexture of the surface which diminishes the contact angle between such hydrophobic surfaces and a liquid thereon, or example, water, an aqueous liquid, or any other aqueous product. As long as the air pockets are stable, the surface continues to exhibit hydrophobic behavior. Such hydrophobic surfaces that include air pockets, however, present certain limitations including, for example: i) the air pockets can be collapsed by external wetting pressures, ii) the air pockets can diffuse away into the surrounding liquid, iii) the surface can lose robustness upon damage to the texture, iv) the air pockets may be displaced by low surface tension liquids unless special texture design is implemented, and v) condensation or frost nuclei, which can form at the nanoscale throughout the texture, can completely transform the wetting properties and render the textured surface highly wetting. 
     Non-toxic liquid-impregnated surface coatings described herein include impregnating liquids that are impregnated into a surface that includes an arrangement or “matrix” of solid features defining one or more interstitial regions (i.e., between individual features and/or between groupings of features), such that the interstitial regions include volumes or “pockets” of impregnating liquid. The impregnating liquid is configured to wet the solid surface preferentially, and it adheres to the micro-textured surface with strong capillary forces, enabling an extremely low roll-off angle of a droplet and/or aqueous solution (referred to as contact liquid) that is in contact with the surface. For example, in some embodiments, the roll-off angle of the contact liquid in contact with the surface is about 1 degree. This enables the contact liquid to displace, travel, slide, roll off, etc., with substantial ease on the liquid-impregnated surface. Therefore, the non-toxic liquid-impregnated surfaces described herein, provide certain significant advantages over conventional super hydrophobic surfaces including: (i) low hysteresis, (ii) self cleaning properties, (iii) ability to withstand high drop impact pressure (i.e., are wear resistant), (iv) ability to self heal by capillary wicking upon damage; (v) ability to enhance condensation; and (vi) in the event of evaporation and/or entrainment, toxicity is avoided due to the non-toxic composition of the materials employed. The non-toxic liquid-impregnated surfaces described herein, which may include solids and/or impregnating liquids that are non-toxic, can be used in applications requiring contact with a variety of products destined for human use or consumption, such as, for example; (a) food products such as, for example ketchup, catsup, mustard, mayonnaise, syrup, honey, jelly, etc.; (b) drugs, for example Food and Drug Administration (FDA) approved drugs; and (c) consumer products, for example toothpaste, shampoo, conditioner, hair gel, etc. Furthermore, methods described herein, can enhance the durability of liquid-impregnated surfaces, such that the surface does not wear, wears more slowly, and/or replenishes itself after single and/or repeated use. Examples of liquid-impregnated surfaces, methods of making liquid-impregnated surfaces, and applications thereof, are described in U.S. Pat. No. 8,574,704 (also referred to as “the &#39;704 patent”), entitled “Liquid-Impregnated Surfaces, Methods of Making, and Devices Incorporating the Same,” issued Nov. 5, 2013, and International Publication Number WO2014/078867, entitled “Apparatus and Methods for Employing Liquid-Impregnated Surfaces,” published May 22, 2014, the contents of which are hereby incorporated herein by reference in their entirety. Examples of materials used for forming the solid features on the surface, impregnating liquids, and applications involving edible contact liquids, are described in U.S. Patent Application Publication No. 2013/0251952 (also referred to as “the &#39;952 publication), entitled “Self-Lubricating Surfaces for Food Packaging and Food Processing Equipment,” published Sep. 26, 2013, the content of which is hereby incorporated herein by reference in its entirety. 
     As used herein, the terms “about” and “approximately” generally mean plus or minus 10% of the value stated, for example “about 250 μm” would include any value from 225 μm to 275 μm, and “approximately 1,000 μm” (or “1 mm”) would include any value from 900 μm to 1,100 μm. 
     As used herein, the phrase “contact liquid” and the terms “fluid” and “product” may refer to a solid or liquid that flows, for example a non-Newtonian fluid, a Bingham fluid, or a thixotropic fluid. A “contact liquid” is any such material that is in contact with a liquid-impregnated surface, unless otherwise stated. 
     As used herein, “emerged area fraction” (also “non-submerged area fraction”), or “,” is defined as a representative fraction of the surface area of a liquid-impregnated surface corresponding with non-submerged solid (i.e., solid that is not covered up by the impregnating liquid, and hence may be in direct contact with an adjacent product material) at room temperature. 
     Referring now to  FIGS. 1A and 1B , a conventional non-wetting surface  10  is a textured surface configured such that the non-wetting surface  10  includes a plurality of solid features  12  disposed on the surface  10 . The solid features  12  define interstitial regions between each of the plurality of solid features which are impregnated by a gas, for example, air. A product P (e.g., a non-Newtonian fluid, a Bingham fluid or a thixotropic fluid) is disposed on the conventional non-wetting surface such that the product contacts a top portion of the solid features at a gas-product interface  14 , and the interface  14  is configured such that it prevents or delays the product from wetting the entire surface  10 . Under certain conditions, the product P can displace and/or dissolve the impregnating gas and “impales” the interstitial regions between the features  12  of the surface  10  (it may also be said that the product P is “impaled” by the features). Such impalement may occur, for example, when a droplet of the product P impinges the surface  10  at a high velocity. When impalement occurs, the gas occupying the regions between the solid features  12  is replaced with the product P, either partially or completely, and the surface  10  may lose its non-wetting capabilities as a consequence. 
     Referring now to  FIG. 2 , in some embodiments a liquid-impregnated surface  130  includes a solid surface  110  that includes a plurality of solid features  112  disposed on the solid surface  110  (e.g., the solid features projecting therefrom, adhered thereon/thereto, or comprising projections between recessed regions in the surface, and/or the like) such that the plurality of solid features  112  define interstitial regions between each (individual) of the plurality of solid features and/or between clusters of such solid features. An impregnating liquid  120  is “impregnated” (e.g., introduced, pumped, brushed, applied, injected, rolled, sprayed, poured, etc.) into the interstitial regions defined by the plurality of solid features  112 . A product P is disposed on the liquid-impregnated surface  100  such that a liquid-product interface  124  separates the product P from the surface  110  and prevents the product P from entirely wetting the surface  110 . The liquid-impregnating surface  130  having a product disposed thereon is collectively indicated by reference numeral  100 . 
     The product P can be any product, for example, a non-Newtonian fluid, a Bingham fluid, a thixotropic fluid, a high viscosity fluid, a high zero shear rate viscosity fluid (shear-thinning fluid), a shear-thickening fluid, and/or a fluid having a high surface tension. The product P can include, for example a food product, a drug, a health and/or beauty product, and/or any other product described herein, or a combination thereof. 
     The surface  110  can be any surface that has a first roll off angle or no roll-off angle (e.g. a really sticky surface), for example a roll off angle of a product in contact with the surface  110  (e.g., water, food products, drugs, health or beauty products, or any other products described herein) under a specified environmental condition (e.g., temperature, pressure, etc.). The surface  110  can be a flat surface, for example, a silicon wafer, a plastic sheet stock, a metal sheet stock, a glass wafer, a ceramic substrate, a table top, a wall, a wind shield, a ski goggle screen, etc. The surface  110  can also be a contoured surface, for example a container, a propeller, a pipe, etc. 
     In some embodiments, the surface  110  can include an interior surface of a container for housing the product P, and the container may be any of the following exemplary containers: tube, bottle, hopper, tray, vial, flask, mold, jar, cup, glass, pitcher, barrel, bin, tote, tank, keg, tub, syringe, tin, pouch, box (e.g., a lined box), hose, cylinder, and can (e.g., a tin can). The container can be constructed in almost any desirable shape. In some embodiments, the surface  110  can be an interior surface of a hose, a pipe, a conduit, a nozzle, a paint applicator (e.g., a paint sprayer), a syringe needle, a dispensing tip, a lid, a pump, and/or a surface of any other apparatus for containing, transporting, and/or dispensing a product P. The surface  110 , for example comprising the interior surface of a container, can be constructed of any suitable material, including plastic, glass, metal (including metal meshes and metallic containers lined with linen), Styrofoam, ceramic, coated fibers, and combinations thereof. Suitable surfaces can also include, for example, polystyrene, nylon, polypropylene, wax, polyethylene terephthalate, polypropylene, polyethylene (e.g., low-density polyethylene, LDPE; high-density polyethylene, HDPE; polyethylene terephthalate, PET), polyurethane, polysulphone, polyethersulfone, polytetrafluoroethylene (PTFE), tetrafluoroethylene (TFE), fluorinated ethylenepropylene copolymer (FEP), polyvinylidene fluoride (PVDF), perfluoroalkoxytetrafluoroethylene copolymer (PFA), perfluoromethyl vinylether copolymer (MFA), ethylenechlorotrifluoroethylene copolymer (ECTFE), ethylene-tetrafluoroethylene copolymer (ETFE), perfluoropolyether, Tecnoflon cellulose acetate, and polycarbonate. The container  110  can be constructed of rigid or flexible materials. Foil-lined and polymer-lined cardboard, corrugated, and/or paper boxes can also form suitable containers. In some embodiments, the surface can be solid, smooth, textured, rough, and/or porous. 
     The solid features  112  can be disposed on the surface  110  using any suitable method. For example, the solid features  112  can be applied to the inside of a container (e.g., a bottle or other food container), or they can be integral to the surface itself (e.g., the textures of a polycarbonate bottle may be made of polycarbonate). In some embodiments, the solid features  112  may be formed of a collection or coating of particles, for example edible solid particles. Examples of solid, non-toxic and/or edible materials include (but are not limited to): insoluble fibers (e.g., purified wood cellulose, micro-crystalline cellulose, and/or oat bran fiber), wax (e.g., carnauba wax, japan wax, beeswax, candelilla wax), pulp, zein, dextrin, cellulose, cellulose ethers (e.g., Hydroxyethyl cellulose, Hydroxypropyl cellulose (HPC), Hydroxyethyl methyl cellulose, Hydroxypropyl methyl cellulose (HPMC), Ethyl hydroxyethyl cellulose), ferric oxide, iron oxide, sodium formate, sodium oleate, sodium palmitate, sodium sulfate, gelatin, pectin, gluten, starch alginate, carrageenan, whey and/or any other edible solid particles described herein, or any combination thereof. 
     In some embodiments, the solid features may comprise a material having a melting point of about 75° C. In other embodiments, the solid features may comprise a material having a melting point of as high as 330° C., as high as 240° C. (e.g., for polyurethanes), as high as 60° C., as high as 50° C., between about 40° C. and about 50° C. In other embodiments, the solid features may comprise a material having a melting point of at least about 60° C. In still other embodiments, the solid features may comprise a material having a melting point may be as high as about 2,000° C. 
     In some embodiments, the solid features may comprise materials that are safe for contact with skin, such as a silicone, fluoropolymers (e.g., polytetrafluoroethylene, polychlorotrifluoroethylene, poly(vinylidene difluoride)), nitrile and silicone rubbers, fluorosilicone, polyurethane, fluoropolyurethane, polyvinylpyrrolidone, fluoroacrylates and halocarbons in general, and their corresponding copolymers with hydrocarbons, silicones, acrylates, methacrylates, urethanes and other fluoropolymers (e.g. poly(vinylidene fluoride-o-hexafluoropropylene)). In some embodiments, the solid features may comprise particles including: halocarbons (e.g., polytetrafluoroethylene, polyvinylidene fluoride, chlorotrifluoroethylene, ethylene chlorotrifluoroethylene), ceramics (e.g., surface modified), and metal oxides (e.g., surface modified). 
     In some embodiments, the solid features may comprise one or more of the following substances: Japan wax, beeswax, carnauba wax, rice bran wax, a mineral wax, paraffin wax, candelilla wax, zein, shellac, methyl cellulose, stearic acid, cetyl alcohol, stearic alcohol, calcium stearate, zinc stearate, magnesium stearate, titanium oxide, sodium oleate, sodium palmitate, polydimethylsiloxane (PDMS), and silicone-based sealant, silicone wax, and silicone-based sealant. In some embodiments, materials employed in the formulation of the solid features may have a solubility in an impregnating liquid of the disclosure of not more than 1% (w/w). 
     In some embodiments, the solid features  112  can be formed by exposing the surface  110  (e.g., polycarbonate) to a solvent (e.g., acetone) (i.e., chemical roughening). For example, the solvent may impart texture by inducing crystallization (e.g., polycarbonate may recrystallize when exposed to acetone). In some embodiments, the solid features  112  can be disposed by dissolving, etching, melting, milling, laser rastering, oxidizing (e.g. by boiling in water) and/or evaporating away a portion of a surface, leaving behind a textured, porous, and/or rough surface that includes a plurality of the solid features  112 . In some embodiments, the solid features  112  can be defined by mechanical roughening (e.g., tumbling with an abrasive or sand-blasting), spray-coating, polymer spinning, deposition of particles from solution (e.g., layer-by-layer deposition, evaporating away liquid from a liquid/particle suspension), and/or extrusion or blow-molding of a foam, or foam-forming material (for example a polyurethane foam). In some embodiments, the solid features  112  can also be formed by deposition of a polymer from a solution (e.g., the polymer forms a rough, porous, or textured surface); extrusion or blow-molding of a material that expands upon cooling, leaving behind a wrinkled surface; and application of a layer of a material onto a surface that is under tension or compression, and subsequently relaxing the tension or compression of surface beneath, resulting in a textured surface. 
     In some embodiments, the solid features  112  are formed by non-solvent induced phase separation of a polymer, resulting in a sponge-like porous structure. For example, a solution of polysulfone, poly(vinylpyrrolidone), and dimethylacetamide (DMAc). may be cast onto a substrate and then immersed in a bath of water. Upon immersion in water, the solvent and non-solvent exchange, and the polysulfone precipitates and hardens. 
     In some embodiments, the solid features  112  may be formed by a self-assembly process, for example the co-deposition of solid and liquid. The self-assembly process may involve the use of molecules such as: alkylthiols, alhyldisulfides, alkylselenols, organosilanes, organophosphonates, organophosphates, alkylcarboxilate, among others, for example including different terminal groups configured to modify the chemistry of the surface. 
     The solid features  112  can include micro-scale features such as, for example posts, spheres, nano needles, pores, cavities, interconnected pores, grooves, ridges, interconnected cavities, or any other random geometry that provides a micro and/or nano surface roughness (for example, a roughness averaged over 5 peaks, “S5P,” of less than about 25 μm, 10 μm, e.g., 3 μm), 1 μm, 500 nm. In some embodiments, the solid features  112  can include particles that have micro-scale dimensions that can be randomly or uniformly dispersed on a surface. Characteristic spacing between the solid features  112  can be about 200 μm, about 100 μm, about 90 μm, about 80 μm, about 70 μm, about 60 μm, about 50 μm, about 40 μm, about 30 μm, about 20 μm, about 10 μm, about 5 μm, between about 2 μm and about 5 μm, about 1 μm, or about 100 nm. The characteristic spacing may be uniform or non-uniform (ordered changes in spacing, linearly varying spacing, random spacing, and/or the like). In some embodiments the spacing is nonuniform provided that the spacing between features on over 99% of the surface does not exceed 200 μm, about 100 μm, about 90 μm, about 80 μm, about 70 μm, about 60 μm, about 50 μm, about 40 μm, about 30 μm, about 20 μm, about 10 μm, about 5 μm, between about 2 μm and about 5 μm, about 1 μm, or about 100 nm. Here 99% is only important because it means that there are few defect spots where there could be a larger separation between features consequent pinning of the product in those regions. In some embodiments, the characteristic spacing between the solid features  112  can be (e.g., on average) in the range of about 100 μm to about 100 nm, about 30 μm to about 1 μm, or about 10 μm to about 1 μm. In some embodiments, characteristic spacing between solid features  112  can be (e.g., on average) in the range of about 100 μm to about 80 μm, about 80 μm to about 50 μm, about 50 μm to about 30 μm, or about 30 μm to about 10 μm, inclusive of all ranges therebetween. 
     In some embodiments, the solid features  112 , for example solid “particles,” can have an average dimension (e.g., corresponding to a height, width, diameter, length, and/or the like) of about 200 μm, about 100 μm, about 90 μm, about 80 μm, about 70 μm, about 60 μm, about 50 μm, about 40 μm, about 30 μm, about 20 μm, about 10 μm, about 5 μm, about 1 μm, about 0.5 μm, between 0.5 μm and 10 μm, or about 100 nm. In some embodiments, the average dimension of the solid features  112  can be in a range of about 100 μm to about 100 nm, about 30 μm to about 10 μm, or about 20 μm to about 1 μm. In some embodiments, the average dimension of the solid features  112  can be in a range of about 10 nm to about 50 μm. In some embodiments, the average dimension of the solid features  112  can be in the range of about 100 μm to about 80 μm, about 80 μm to about 50 μm, about 50 μm to about 30 μm, or about 30 μm to about 10 μm, or 10 μm to 100 nm, inclusive of all ranges therebetween. In some embodiments, the height of the solid features  112  can be substantially uniform. In some embodiments, the surface  110  can have hierarchical features, for example micro-scale features that further include nano-scale features disposed thereupon (e.g., etched therein, adhered thereto, etc.). 
     In some embodiments, the solid features  112  (e.g., particles) can be porous. The characteristic pore size (e.g., pore width or length) of particles can be (e.g., on average) about 5,000 nm, about 3,000 nm, about 2,000 nm, about 1,000 nm, about 500 nm, about 400 nm, about 300 nm, about 200 nm, about 100 nm, about 80 nm, about 50, about 10 nm. In some embodiments, the characteristic pore size can be in the range of about 200 nm to about 2 μm, or about 50 nm to about 1 μm, inclusive of all ranges therebetween. 
     The impregnating liquid  120  is disposed on the surface  110  such that the impregnating liquid  120  impregnates substantially all of the interstitial regions defined by the plurality of solid features  112  (the solid features comprising, for example, pores, cavities, or otherwise inter-feature spacing defined by the surface  110 ), such that no air remains in the interstitial regions. The interstitial regions can be dimensioned and configured such that capillary forces retain part of the impregnating liquid  120  in the interstitial regions. The impregnating liquid  120  disposed in the interstitial regions of the plurality of solid features  112  is configured such that the liquid-impregnated surface  130  defines a second roll off angle that is less than the first roll of angle (i.e., the roll of angle of the un-impregnated liquid surface  110 ). In some embodiments, the impregnating liquid  120  can have a viscosity at room temperature of less than about 1,000 cP, for example about 8 cP, between about 1 cP and about 10 cP, between about 10 cP and about 20 cP, about 50 cP about 30 cP, between about 8 cP and about 30 cP, about 50 cP, about 80 cP, between about 20 cP and about 100 cP, about 100 cP, between about 100 cP and about 10 P, about 150 cP, about 200 cP, about 300 cP, about 350 cP, about 400 cP, about 500 cP, about 600 cP, about 700 cP, about 800 cP, about 900 cP, between about 10 P and about 100 P, about 1,000 cP, or between about 100 P and about 1,000 P, inclusive of all ranges therebetween. In some embodiments, the impregnating liquid  120  can have a viscosity of about 8 cP or less. In some embodiments, the impregnating liquid  120  can have a viscosity of about 1,000 cP or less. In some embodiments, the impregnating liquid  120  can have a vapor pressure at room temperature of less than about 20 mmHg. In some embodiments, the impregnating liquid  120  can have a vapor pressure at room temperature of as low as 4×100 −7  mmHg. In some embodiments, the impregnating liquid  120  can have a surface tension of as low as 14 dyn/cm. In some embodiments, the impregnating liquid  120  can fill the interstitial regions defined by the solid features  112  and form a layer of at least about 5 nm thick above the plurality of solid features  112  disposed on the surface  110 . In some embodiments, the impregnating liquid  120  forms a layer of at least about 1 μm of excess mobile liquid (easily moved by external forces such as those resulting from shearing or gravity) above the plurality of solid features  112  disposed on the surface  110  on some regions of the surface. 
     The impregnating liquid  120  may be disposed in the interstitial spaces defined by the solid features  112  using any suitable means. For example, the impregnating liquid  120  can be sprayed or brushed onto the textured surface  110  (e.g., a texture on an inner surface of a bottle). In some embodiments, the impregnating liquid  120  can be applied to the textured surface  110  by filling or partially filling a container that includes the textured surface  110 . The excess impregnating liquid  120  is then removed from the container. In some embodiments, the excess impregnating liquid  120  can be removed by adding a wash liquid (e.g., water) to the container to collect or extract the excess liquid from the container. In some embodiments, the excess impregnating liquid may be mechanically removed (e.g., pushed off the surface with a solid object or fluid), absorbed or wicked off of the surface  110  using another porous material, and/or removed via gravity or centrifugal forces. In some embodiments, the impregnating liquid  120  can be disposed by spinning the surface  110  (e.g., a container) in contact with the liquid (e.g., a spin coating process), and condensing the impregnating liquid  120  onto the surface  110 . In some embodiments, the impregnating liquid  120  is applied by depositing a solution comprising the impregnating liquid and one or more volatile liquids (e.g., depositing via any of the previously described methods) and subsequently evaporating away one or more of the volatile liquids. 
     In some embodiments, the impregnating liquid  120  can be applied using an external liquid that spreads or pushes the impregnating liquid along the surface  110 . For example, the impregnating liquid  120  (e.g., ethyl oleate) and spreading liquid (e.g., water) may be combined in a container and agitated, sonicated, and/or stirred. The fluid flow within the container may distribute the impregnating liquid  120  around the container, allowing it to impregnate the solid features  112 . 
     In some embodiments, the impregnating liquid may be nontoxic for occasional contact with skin because it the liquids relative inertness. These materials may not be safe to eat however, but they could be suitable in many industrial applications or health and beauty applications. For example these materials  120  can include, silicone oil, a perfluorocarbon liquid, a perfluorinated vacuum oil (such as Krytox 1506 or Fomblin 06/6), a fluorinated coolant (e.g., perfluoro-tripentylamine sold as FC-70, manufactured by 3M), an ionic liquid, a fluorinated ionic liquid that is immiscible with water, a silicone oil comprising polydimethylsiloxane (PDMS), a silicone oil (e.g., fluorinated), fluorosilicone oil, a liquid metal, a synthetic oil, mineral oil, a vegetable oil, halocarbon oil, an electro-rheological fluid, a magneto-rheological fluid, a ferrofluid, a dielectric liquid, a hydrocarbon liquid, a fluorocarbon liquid (e.g., fluorocarbon oils, such as polyhexafluoropropylene oxide, propene, 1,1,2,3,3,3-hexa-fluoro oxidized polymerized or tris(perfluorobut-1-yl)amine), a refrigerant, a vacuum oil, a phase-change material, a semi-liquid, grease, synovial fluid, bodily fluid, or any other aqueous fluid, or any other impregnating liquid described herein. In some embodiments the following nontoxic liquids can be used: oleic acid, linoleic acid, triacetin, ethyl linoleate, glycerol, tributryn, tripropionin, dimethicone, perfluorononyl dimethicone, silicone fluids, amyl phthalate, any other nontoxic liquid and any combination thereof. 
     The ratio of the solid features  112  (e.g., particles) to the impregnating liquid  120  (such ratio referred to, in some embodiments, as “phi,” or “φ”) can be configured to minimize the occurrence of portions of the solid features  112  protruding above the liquid-product interface. For example, in some embodiments, the solid features  112  make up a percentage of a surface area of the surface  110 , with respect to the impregnating liquid, of less than about 15%, or less than about 5%. In some embodiments, the percentage of a surface area of the surface  110  comprising the solid features  112  can be less than about 50%, about 45%, about 40%, about 35%, about 30%, about 25%, about 20%, about 15%, about 10%, about 5%, or less than about 2%. In some embodiments, the percentage of a surface area of the surface  110  comprising the solid features  112  can be in the range of about 5% to about 50%, about 10% to about 30%, or about 15% to about 20%, inclusive of all ranges therebetween. In some embodiments, the ratio of the solid features  112  to the impregnating liquid  120  can be less than about 0.5, about 0.45, about 0.4, about 0.35, about 0.3, about 0.25, about 0.2, about 0.15, about 0.1, about 0.05, or less than about 0.02. In some embodiments, the ratio of the solid features  112  to the impregnating liquid  120  can be in the range of about 0.05 to about 0.5, about 0.1 to about 0.3, or about 0.15 to about 0.2, inclusive of all ranges therebetween. In some embodiments, a low ratio can be achieved using surface textures that are substantially pointed. By contrast, surface textures that are flat may result in higher ratios, with too much solid material being exposed at the surface. In some embodiments, the film dry weight is between about 5×10 −5  g/cm 2  and about 10×10 −5  g/cm 2 , between about 0.1×10 −5  g/cm 2  and about 5×10 −5  g/cm 2 , between about 10×10 −5  g/cm 2  and about 100×10 −5  g/cm 2 , or between about 0.1×10 −5  g/cm 2  and about 100×10 −5  g/cm 2 , and the composition of the liquid-impregnated surface is between 3% and 5% solids, between 5% and 10%, between 10% and 20%, between 20% and 50%, or between 50% and 70%. 
     In some embodiments, the surface  110  may be characterized by its “complexity,” defined as being equal to (r−1)×100% where r is the Wenzel roughness. Depending on the embodiment, the complexity of the surface may be at least 20% (e.g., about 23%), at least 25%, at least 45%, at least 75%, at least 100%, at least 150%, or at least 200%. 
     Interaction Between Various Phases in a Liquid-Impregnated Surface 
     A liquid-impregnated surface that is in contact with a product defines four distinct phases (or 3 distinct phases in a close environment such as a pipe, where there is no vapor phase): an impregnating liquid, a surrounding gas (e.g., air), the product and a textured surface. The interactions between the different phases determine the morphology of the contact line (i.e., the contact line that defines the contact angle of a contact liquid droplet with respect to the liquid-impregnated surface). The contact line morphology, in turn, substantially impacts droplet pinning and mobility of a “contact liquid” on the surface. Some methods have relied on the complete submersion of a textured surface in an impregnating liquid such as oil by applying excess liquid, in order to achieve low hysteresis. Although complete submergence may be achieved temporarily by depositing excess impregnating liquid, eventually this excess will drain away (e.g. under gravity) and the liquid-air interface may thus eventually come into contact the textured surface. Complete, sustained submergence is possible only if the impregnating liquid is able to completely wet the texture, that is, where θ os(a) =0° (where θ os(a)  is the contact angle (this could be an advancing, receding, or static contact angle) of the impregnating liquid (subscript ‘o’) on the textured surface (subscript ‘s’) in the presence of air (subscript ‘a’). The situation is further complicated once a water droplet (or other external phase) is placed on the liquid-impregnated surface, in which case the surface will remain submerged in the impregnating liquid only if θ os(w) =0° as well, where the subscript ‘w’ refers to water. Whether or not θ os(a) =0° and θ os(w) =0° for a given liquid and textured substrate material is an important factor that impacts the choice of an impregnating liquid, for example, the impregnating liquid  120 , that can/should be used for a particular textured surface. Other factors include, for example, properties of the contact liquid that affect how those materials (e.g., of water and/or product) are shed (whether they roll or slip), and what their shedding velocities are. Moreover, questions related to the longevity of the impregnated liquid film and its propensity for depletion, e.g., due to evaporation and entrainment with the droplets (e.g., of water and/or product) being shed, can have substantial bearing on the configuration of a liquid-impregnated surface, for example, the liquid-impregnated surface  100 . 
     Referring now to  FIG. 3 , a textured surface  210  includes square microposts etched in silicon using standard photolithography processes. A photomask with square windows was used, and the pattern was transferred to photoresist using UV light exposure. Next, reactive ion etching with inductively-coupled plasma was used to etch the exposed areas to form microposts  212 , such that microposts  212  are separated by interstitial region  214 . Each micropost  212  had a square geometry with width “a” of about 10 μm, height h of about 10 μm, and varying edge-to-edge spacing b of about 5, 10, 25, or 50 μm. As shown in  FIG. 4 , a second level of roughness was produced on microposts  212  by creating nanograss  216 . To create the nanograss, micropost  212  surfaces were cleaned in Piranha solution (a mixture of sulfuric acid and hydrogen peroxide) etched in alternating flow of sulfur hexafluoride (SF 6 ) and oxygen (O 2 ) gases for 10 minutes, with an inductively-coupled plasma. The samples were again cleaned in a Piranha solution and treated with a low-energy silane (octadecyltrichlorosilane (OTS)) by solution deposition. 
     Referring now to  FIG. 5 , the textured surface  210  was impregnated with the impregnating liquid  220 , in this case “BMIm” (1-butyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide) (other examples of impregnating liquid may include silicone oil and DI water), by slowly dipping the textured surface (i.e., “dip-coating”) into a reservoir of the lubricant. The textured surface  210  was then withdrawn at speed S, at a slow enough rate that capillary number Ca=μ o S/γ oa &lt;10 −5 , to ensure that no excess fluid remained on the micropost  212  tops, where μ o  is the dynamic viscosity and γ oa  is the surface tension of the impregnating liquid  220 . When the advancing angle θ adv,os(a)  is less than θ c  (see Table 1 below), the impregnating liquid  220  film will not spontaneously spread into the textured surface  210 , as can be seen for BMIm in  FIG. 5 .  FIG. 6  shows a higher-magnification view of the region of the textured surface indicated by the arrow A in  FIG. 5 . Visible in  FIG. 6  are a portion of the nanotextured top surface  616  of a micropost, and a portion of the impregnating fluid  620 . By withdrawing the textured surface  210  from a reservoir of BMIm, the impregnating film remains stable, since θ rec,os(a) &lt;θ c  for the microposts  212  with b=5 μm and 10 μm. 
     Table 1 (below) shows various configurations of features formed on the textured surface  210 , the configurations characterized by “post spacing” (“b”), “ratio of total surface area to the projected area of the solid” (“r”), emerged area fraction (“φ” or “phi”), and critical contact angle θ c  defined by θ c =cos −1 ((1−φ)/(r−φ)); h, a=10 μm. Note that if the textured surface  210  is not coated with OTS, θ os(w) &gt;θ c  for impregnating liquids  220  as well as all b. Thus, water droplets were expected to displace the hydrophobic liquid  220  and get impaled by the microposts  212  leading to significant pinning, and such behavior was confirmed, as the droplets did not roll-off of these textured surfaces. 
     
       
         
           
               
               
               
               
               
             
               
                   
                 TABLE 1 
               
               
                   
                   
               
               
                   
                 Post spacing, b (μm) 
                 r 
                 φ 
                 θ c  (°) 
               
               
                   
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
            
               
                   
                 5 
                 2.8 
                 0.44 
                 76 
               
               
                   
                 7.5 
                 2.3 
                 0.33 
                 70 
               
               
                   
                 10 
                 2.0 
                 0.25 
                 65 
               
               
                   
                 25 
                 1.3 
                 0.08 
                 42 
               
               
                   
                 50 
                 1.1 
                 .093 
                 26 
               
               
                   
                   
               
            
           
         
       
     
     Referring now to  FIGS. 7A-7J , in some embodiments, the impregnating liquid  220 , for example, oil may spread over and “cloak” the contact liquid, for example, a water droplet, as shown in  FIG. 7A . Cloaking can cause the progressive loss of the impregnating liquid  220  through entrainment in the water (or other composition) droplets as they are shed from the surface. The criterion for cloaking is given by the spreading coefficient, S ow(a) ≡γ wa −γ wo −γ oa , where γ is the interfacial tension between the two phases designated by subscripts w, o, and a. Thus, the expression “S ow(a) &gt;0” implies that the impregnating liquid  220  will cloak the water droplet ( FIG. 7A ), whereas S ow(a) &lt;0 implies otherwise ( FIG. 7B ). Based on these criterion, two different impregnating liquids  220 , were selected: (1) silicone oil, for which S ow(a) ≈6 mN/m, and (2) an ionic liquid (1-butyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide-BMIm) for which S ow(a) ≈−5 mN/m. Ionic liquids have extremely low vapor pressures (˜10 −12  mmHg), and therefore they mitigate concern for the loss of impregnating liquid through evaporation. Goniometric measurements of the advancing and receding contact angles of these liquids in the presence of air and water, as well as their interfacial tensions, were performed and are presented in Table 2 and Table 3 (below). 
     
       
         
           
               
               
               
               
               
               
             
               
                 TABLE 2 
               
               
                   
               
               
                 Liquid 
                 Substrate 
                 θ adv, os(a)  (°) 
                 θ rec, os(a)  (°) 
                 θ adv, os(w)  (°) 
                 θ rec, os(w)  (°) 
               
               
                   
               
             
            
               
                 Silicone oil 
                 OTS-treated silicon 
                 0 
                 0 
                  20 ± 5 
                 0 
               
               
                 BMIm 
                 OTS treated silicon 
                 67.8 ± 0.3 
                 60.8 ± 1.0 
                  61.3 ± 3.6 
                  12.5 ± 4.5 
               
               
                 DI water 
                 OTS-treated silicon 
                 112.5 ± 0.6  
                 95.8 ± 0.5 
                 NA 
                 NA 
               
               
                 Silicone oil 
                 Silicon 
                 0 
                 0 
                 153.8 ± 1.0 
                     122 ± 0.8 
               
               
                 BMIm 
                 Silicon 
                 23.5 ± 1.8 
                  9.8 ± 0.9 
                 143.4 ± 1.8 
                 133.1 ± 0.9 
               
               
                 DI water 
                 Silicon 
                     20 ± 5° 
                 0 
                 NA 
                 NA 
               
               
                   
               
            
           
         
       
     
     Table 3 shows surface and interfacial tension measurements and resulting spreading coefficients S ow(a) =γ wa −γ ow −γ oa  of 9.34, 96.4, and 970 cP for Dow Corning PMX 200 Silicone oils on water in air. Values of γ ow  were provided by Dow Corning. 
     
       
         
           
               
               
               
               
               
               
             
               
                   
                 TABLE 3 
               
               
                   
                   
               
               
                   
                   
                 γ ow   
                 γ oa   
                 γ wa   
                 S ow(a)   
               
               
                   
                 Liquid 
                 (mN/m) 
                 (mN/m) 
                 (mN/m) 
                 (mN/m) 
               
               
                   
                   
               
             
            
               
                   
                 Silicone oil 
                 46.7 
                 20.1 
                 72.2 
                 5.4 
               
               
                   
                 (9.34 cP, 96.4 cP) 
               
               
                   
                 Silicone oil 
                 45.1 
                 21.2 
                 72.2 
                 5.9 
               
               
                   
                 (970 cP) 
               
               
                   
                   
               
            
           
         
       
     
       FIG. 7C  shows an 8 μl water droplet placed on the silicone oil impregnated textured surface  210 . The droplet forms a large apparent contact angle (˜100 degrees), but very close to the solid surface (red arrows in  FIG. 7   c ) its profile changes from convex to concave. When a fluorescent dye was added to the silicone oil and imaged under UV light, it was observed that the point of inflection (i.e., the profile change noted above) corresponded to the height to which an annular ridge of silicone oil was pulled up in order to satisfy a vertical force balance of the interfacial tensions at the inflection point ( FIG. 7E ). Although the oil was expected to have spread over the entire droplet ( FIG. 7C ), the cloaking film was too thin to be captured in these images. The “wetting ridge” was also observed in the case of ionic liquid ( FIG. 7D  and  FIG. 7F ). Such wetting ridges are reminiscent of those observed around droplets on soft substrates. 
     As described herein, the textured surface  210  can be completely submerged in the impregnating liquid  220  if θ os(a) =0°. This condition was found to be true for silicone oil, implying that the tops of the microposts  212  should be covered by a stable thin oil film. This film was observed experimentally using laser confocal fluorescence microscopy (LCFM); the micropost  212  tops appear bright due to the presence of a fluorescent dye that was dissolved in the oil ( FIG. 7G ). Environmental SEM images of the surface ( FIG. 7I ) show the oil-filled texture, and confirm that this film is less than a few microns thick, consistent with prior estimates for completely-wetting films. On the other hand, BMIm has a non-zero contact angle on a smooth OTS-coated silicon surface (θ os(a) =65±5°), indicating that with this impregnating liquid, the post tops should remain dry. Indeed, LCFM images confirmed this (FIG.  7 H)—the post tops appear dark because there is no dye present to fluoresce. Since BMIm is conductive and has an extremely low vapor pressure, it can be imaged in a SEM. As shown in  FIG. 7J , discrete droplets resting on micropost tops are seen, confirming that a thin film was not stable on the post tops in this case. 
     Stable Configuration of Contact Liquid Droplets on Liquid-Impregnated Surfaces 
     As shown in  FIG. 7B , in the case of BMIm there are three distinct 3-phase contact lines at the perimeter of the drop that confine the wetting ridge: the oil-water-air contact line, the oil-solid-air contact line outside the drop, and the oil-solid-water contact line underneath the drop. These contact lines exist because θ os(a) &gt;0, θ os(w) &gt;0, and S ow(a) &lt;0. In contrast, in the case of silicone oil ( FIG. 7A ), none of these contact lines exist because θ os(a) =0, θ os(w) =0, and S ow(a) &gt;0. These configurations are just two of the 12 different configurations in such a four-phase system where impregnation by impregnating liquid  220  is possible. These configurations are discussed below. 
     A thermodynamic framework is outlined that can predict which of the above-noted  12  states will be stable for a given contact liquid droplet, impregnating liquid  220 , and textured surface  210  substrate material. There are three possible configurations to consider for the interface “outside” of the droplet (i.e., not directly adjacent to or beneath the droplet, but rather spaced from the droplet, e.g., horizontally) (i.e., in an air environment), and three possible configurations to consider for the interface “underneath the droplet” (e.g., in a water environment). These configurations are shown in  FIG. 8 , along with the total interface energy of each configuration. The configurations possible outside the droplet are A1 (not impregnated, i.e. dry), A2 (impregnated with emergent features), and A3 (impregnated with submerged features—i.e. encapsulated). On the other hand, underneath the droplet, the possible configurations are W1 (impaled), W2 (impregnated with emergent features), and W3 (impregnated with submerged features—i.e. encapsulated). The stable configuration will be the one that has the lowest total interface energy. 
     First, the configurations outside of the droplet are focused on. A textured surface, for example, textured surface  210 , is slowly withdrawn from a reservoir of oil. The resulting surface could be in any of states A1, A2, and A3 depending on which has the lowest energy. For example, state A2 would be stable if it has the lowest total interface energy, i.e. E A2 &lt;E A1 , E A3 . From  FIG. 8 , this results in: 
         E   A2   &lt;E   A1   (γ sa −γ os )/γ oa &gt;(1−φ)/( r −φ)  (1)
 
         E   A2   &lt;E   A3   γ sa −γ os −γ oa &lt;0  (2)
 
     where φ is the fraction of the projected area of the surface that is occupied by the solid and r is the ratio of total surface area to the projected area of the solid. In the case of square posts with width a, edge-to-edge spacing b, and height h, φ=a 2 /(a+b) 2  and r=1+4ah/(a+b) 2 . Applying Young&#39;s equation, cos(θ os(a) )=(γ sa −γ os )/γ oa , Eq. (1) reduces to the hemi-wicking criterion for the propagation of a oil through a textured surface: cos(θ os(a) )&gt;(1−φ)/(r−φ)=cos(θ c ). This requirement can be conveniently expressed as θ os(a) &lt;θ c . In Eq. (2), γ sa −γ os −γ oa , is simply the spreading coefficient S os(a)  of oil on the textured surface in the presence of air. This can be reorganized as (γ sa −γ os )/γ oa &lt;1, and applying Young&#39;s equation again, Eq. (2) can be written as θ os(a) &gt;0. Expressing Eq. (1) in terms of the spreading coefficient S os(a) , yields: −γ oa (r−1)/(r−φ)&lt;S os(a) . The above simplifications then lead to the following equivalent criteria for the surface to be in state A2: 
         E   A2   &lt;E   A1   ,E   A3   θ c &gt;θ os(a) &gt;0 −γ oa ( r− 1)/( r −φ)&lt; S   os(a) &lt;0  (3)
 
     Similarly, state A3 would be stable if E A3 &lt;E A2 , E A1 . From  FIG. 8 , this gives: 
         E   A3   &lt;E   A2   θ os(a) =0 γ sa −γ os −γ oa   ≡S   os(a) ≧0  (4)
 
         E   A3   &lt;E   A1   θ os(a) &lt;cos −1 (1 /r )   S   os(a) &gt;−γ oa (1−1 /r )  (5)
 
     Note that Eq. (5) is automatically satisfied by Eq. (4), thus the criterion for state A3 to be stable (i.e. encapsulation) is given by Eq. (4). Following a similar procedure, the condition for state A1 to be stable can be derived as: 
         E   A1   &lt;E   A2   ,E   A3   θ os(a) &gt;θ c     S   os(a) &lt;−γ oa ( r− 1)/( r −φ)  (6)
 
     Note that the rightmost expression of Eq. (4) can be rewritten as (γ sa −γ os )/γ oa ≧1. Young&#39;s equation would suggest that if θ os(a) =0, then (γ sa −γ os )/γ oa =1 (i.e. S os(a) =0). However, θ os(a) =0 is also true for the case that (γ sa −γ os )/γ oa &gt;1 (i.e. S os(a) &gt;0). Young&#39;s equation predicts the contact angle based on balancing the surface tension forces on a contact line, such that the equality only exists for a contact line at static equilibrium. For a spreading film (S os(a) &gt;0) a static contact line doesn&#39;t exist, hence precluding the applicability of Young&#39;s equation. 
     Referring now to the configurations possible underneath the droplet, upon contact with water, the interface beneath the droplet will attain one of the three different states—W1, W2, or W3 (FIG.  8 )—depending on which has the lowest energy. Applying the same method to determine the stable configurations of the interface beneath the droplet as described herein, and using the total interface energies provided in  FIG. 8 , the stability requirements take a form similar to Eqs (3), (4), and (6), with γ oa , γ sa , θ os(a) , S os(a) , replaced with γ ow , γ sw , θ os(w) , S os(w)  respectively. θ c  is not affected by the surrounding environment as it is only a function of the texture parameters, φ and r. Thus, the texture will remain impregnated with oil beneath the droplet with emergent post tops (i.e. state W2) when: 
         E   W2   &lt;E   W1   ,E   W3   θ c &gt;θ os(w) &gt;0  −γ ow ( r− 1)/( r −φ)&lt; S   os(w) &lt;0  (7)
 
     State W3 will be stable (i.e. the oil will encapsulate the texture) when: 
         E   W3   &lt;E   W1   ,E   W2   θ os(w) =0 γ sw −γ os −γ ow   ≡S   os(w) ≧0.  (8)
 
     and the droplet will displace the oil and be impaled by the textures (state W1) when: 
         E   W1   &lt;E   W2   ,E   W3   θ os(w) &gt;θ c     S   os(w) &lt;−γ ow ( r− 1)/( r −φ)  (9)
 
     Combining the above criteria along with the criterion for cloaking of the water droplet by the oil film described herein, the various possible states can be organized in a regime map, as shown in  FIG. 9 . The cloaking criterion is represented by the upper two schematic drawings. For each of these cases, six different configurations are possible depending on how the oil interacts with the surface texture in the presence of air (vertical axes in  FIG. 9 ) and water (horizontal axes in  FIG. 9 ). The vertical and horizontal axes are the normalized spreading coefficients S os(a) /γ oa  and S os(w) /γ ow  respectively. Considering first the vertical axis of  FIG. 9 , when S os(a) /γ oa &lt;−(r−1)/(r−φ) (i.e., when Eq. (6) holds), oil does not impregnate the texture. As S os(a) /γ oa  increases above this critical value, impregnation becomes feasible but the post tops are still left emerged. Once S os(a) /γ oa &gt;0, the post tops are also submerged in the oil leading to complete encapsulation of the texture. Similarly, on the x-axis of  FIG. 9 , moving from left to right, as S os(w) /γ ow  increases, the droplet transitions from an impaled state to an impregnated state to a fully-encapsulated state. 
       FIG. 9  shows that there can be up to three different contact lines, two of which can get pinned on the texture. The degree of pinning determines the roll-off angle α*, the angle of inclination at which a droplet placed on the textured solid begins to move. Droplets that completely displace the oil (states A3-W1, A2-W1 in  FIG. 8 ) are not expected to roll off the surface. These states are achieved when θ os(w) &gt;θ c  as is the case for both BMI-Im and silicone oil impregnated surfaces when the silicon substrates are not treated with OTS (see Table 1). As expected, droplets did not roll off of these surfaces. Droplets in states with emergent post tops (A3-W2, A2-W2, A2-W3) are expected to have reduced mobility that is strongly texture dependent, whereas those in states with encapsulated posts outside and beneath the droplet (the A3-W3 states in  FIG. 8 ) are expected to exhibit no pinning and consequently infinitesimally small roll-off angles. 
       FIG. 10A  shows measurements of roll-off angles for 5 μL water droplets on silicone oil impregnated and BMIm impregnated textures, with varying post spacing b. For comparison, the same textures without an impregnating liquid (no impregnating liquid, which is the conventional super impregnating case) were also evaluated. The silicone oil encapsulated surfaces have extremely low roll-off angles regardless of the post spacing b and oil viscosity, showing that contact line pinning was negligible, as predicted for a liquid droplet in an A3-W3 state with no contact lines on the textured substrate. On the other hand, BMIm impregnated textures showed much higher roll-off angles, which increased as the spacing decreased—a trend that is similar to Cassie droplets on super impregnating surfaces. This observation shows that pinning was significant in this case, and occurs on the emergent post tops. (as shown in  FIG. 10B ). Pinning on BMIm impregnated textures was significantly reduced by adding a second smaller length scale texture (i.e. nanograss) to the posts, so that BMIm impregnated the texture even on the post tops, thereby substantially reducing φ ( FIG. 10C ). The roll-off angle decreased from over 30 degrees (for BMIm impregnated posts without nanotexture) to only about 2 degrees (for BMIm impregnated posts with nanotexture). Note that the reduction in the emergent area fraction φ is not due to the absolute size of the texture features, since the oil-water and oil-air interfaces intersect surface features at contact angles θ os(w)  and θ os(a) , and φ depends on these contact angles and feature geometry. 
     The effect of texture on the roll-off angle can be modeled by balancing gravitational forces with pinning forces. A force balance of a water droplet on a smooth solid surface at incipient motion gives ρ w Ωg sin α*≈2R b γ wa  (cos θ rec,ws(a) −cos θ adv,ws(a) ), where ρ w  is the density of the liquid droplet of volume Ω, g is the gravitational acceleration, R b  is the droplet base radius, and θ adv,ws(a)  and θ rec,ws(a)  are the advancing and receding contact angles of droplet in air on the smooth solid surface. Pinning results from contact angle hysteresis of up to two contact lines: an oil-air-solid contact line with a pinning force per unit length given by γ oa  (cos θ rec,os(a) −cos θ adv,os(a) ), and an oil-water-solid contact line with a pinning force per unit length given by γ ow  (cos θ rec,os(w) −cos θ adv,os(w) ). The length of the contact line over which pinning occurs is expected to scale as R b  φ 1/2  where φ 1/2  is the fraction of the droplet perimeter (˜R b ) making contact with the emergent features of the textured substrate. Thus, a force balance tangential to the surface gives: 
       ρ w   Ωg  sin α*˜R b φ 1/2 [γ ow (cos θ rec,os(w) −cos θ adv,os(w) )+γ oa (cos θ rec,os(a) −cos θ adv,os(a) )]  (10)
 
     Dividing Eq. (10) by R b γ wa  we obtain a non-dimensional expression: 
         Bo  sin α* f (θ)˜φ 1/2 [γ ow (cos θ rec,os(w) −cos θ adv,os(w) )+γ oa (cos θ rec,os(a) −cos θ adv,os(a) )]/γ wa   (11)
 
     where f(θ)=Ω 1/3 /R b =[(π/3)(2+cos θ)(1−cos θ) 2 /sin 3 θ)] 1/3  by assuming the droplet to be a spherical cap making an apparent contact angle θ with the surface. Bo=Ω 2/3 ρ w g/γ wa  is the Bond number, which compares the relative magnitude of gravitational forces to surface tension forces. Values for θ rec,os(w) , θ adv,os(w) , θ rec,os(a) , θ adv,os(a) , γ ow , γ oa , and γ wa  are provided in Tables 2 and 3.  FIG. 10D  shows that the measured data is in reasonable agreement with the scaling of Eq. (11). The data for the silicone oil encapsulated surface and for the BMIm impregnated, nanograss-covered posts, lie close to the origin as both φ and α* are very small in these cases. 
     Dynamics of Droplet Shedding 
     Once gravitational forces on a droplet overcome the pinning forces, the velocity attained by the droplet determines how quickly it can be shed, which reflects the non-wetting performance of the surface. For a droplet of volume Ω, this velocity would be expected to depend on both the contact line pinning and viscosity of the lubricant. The steady-state shedding velocity V of water droplets was measured using a high-speed camera while systematically varying lubricant dynamic viscosity μ o , post spacing b, textured surface tilt angle α, and droplet volume, Ω. These measurements are shown in  FIG. 11A , where V is plotted as a function of a for different μ o , b, and Ω. As shown in  FIG. 11A , the velocity V increases with α and Ω because both increase the gravitational force acting on the droplet. As also shown in  FIG. 11A , V decreases with μ o  and φ because both increase the resistance to droplet motion. 
     To explain these trends, it is first determined whether the droplet is rolling or sliding. Consider the oil-water interface beneath the droplet as shown in  FIG. 11B . The shear stress at this interface, on the water side, scales as τ w ˜μ w (V−V i )/h cm , and on the oil side the shear stress scales as τ o ˜μ o V i /t, where V i  is the velocity of the oil-water interface, h cm  is the height of the centre of mass of the droplet above the solid surface, and t is the thickness of the oil film. Since τ w  must be equal to τt o  at the oil-water interface, μ w (V−V i )/h cm ˜μ o V i /t. Rearranging this gives: 
     
       
         
           
             
               
                 
                   
                     
                       V 
                       i 
                     
                     / 
                     V 
                   
                   ∼ 
                   
                     
                       ( 
                       
                         1 
                         + 
                         
                           
                             
                               μ 
                               o 
                             
                             
                               μ 
                               w 
                             
                           
                            
                           
                             
                               h 
                               cm 
                             
                             t 
                           
                         
                       
                       ) 
                     
                     
                       - 
                       1 
                     
                   
                 
               
               
                 
                   ( 
                   12 
                   ) 
                 
               
             
           
         
       
     
     Since (μ o /μ w )(h cm /t)&gt;&gt;1 as described herein, V i /V&lt;&lt;1, i.e. the oil-water interface moves at a negligibly small velocity relative to that of the droplet&#39;s centre of mass. This suggests that the droplets being shed on the textured surface, for example, textured surface  210 , are rolling. This was further confirmed by adding ground coffee particles to the water droplet and tracking their motion relative to the droplet with a high-speed camera as the droplet moved across the surface. Particle trajectories, shown in  FIG. 11C , clearly show that the droplets roll across the liquid-impregnated surface as they are shed (μ o =96.4 cP). 
     To determine the magnitude of V, the rate of change of gravitational potential energy is balanced as the droplet rolls down the incline with the total rate of energy dissipation due to contact line pinning and viscous effects. The resulting energy balance gives: 
     
       
         
           
             
               
                 
                   
                     V 
                      
                     
                       ( 
                       
                         
                           F 
                           g 
                         
                         - 
                         
                           F 
                           p 
                         
                       
                       ) 
                     
                   
                   ∼ 
                   
                     
                       
                         μ 
                         w 
                       
                        
                       
                         
                           ∫ 
                           
                             Ω 
                             drop 
                           
                         
                          
                         
                           
                             
                               ( 
                               
                                 ∇ 
                                 
                                     
                                 
                                  
                                 
                                   u 
                                   _ 
                                 
                               
                               ) 
                             
                             drop 
                             2 
                           
                            
                           
                               
                           
                            
                           
                              
                             Ω 
                           
                         
                       
                     
                     + 
                     
                       
                         μ 
                         o 
                       
                        
                       
                         
                           ∫ 
                           
                             Ω 
                             film 
                           
                         
                          
                         
                           
                             
                               ( 
                               
                                 ∇ 
                                 
                                     
                                 
                                  
                                 
                                   u 
                                   _ 
                                 
                               
                               ) 
                             
                             film 
                             2 
                           
                            
                           
                               
                           
                            
                           
                              
                             Ω 
                           
                         
                       
                     
                     + 
                     
                       
                         μ 
                         o 
                       
                        
                       
                         
                           ∫ 
                           
                             Ω 
                             ridge 
                           
                         
                          
                         
                           
                             
                               ( 
                               
                                 ∇ 
                                 
                                     
                                 
                                  
                                 
                                   u 
                                   _ 
                                 
                               
                               ) 
                             
                             ridge 
                             2 
                           
                            
                           
                               
                           
                            
                           
                              
                             Ω 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   13 
                   ) 
                 
               
             
           
         
       
     
     where F g  and F p  represent the net gravitational and pinning forces acting on the droplet, the Ω terms are the volume over which viscous dissipation occurs, and the ∇ū terms are the corresponding velocity gradients. The form of Eq. (13) is similar to that for viscous droplets rolling on completely non-wetting surfaces though additional terms are present due to the presence of the impregnated oil. The three terms on the right side of Eq. (13) represent the rate of viscous dissipation within the droplet (I), in the oil film beneath the droplet (II), and in the wetting ridge near the three-phase contact line (III). 
     The rate of viscous dissipation within the droplet (I) is primarily confined to the volume beneath its center of mass and can be approximated as I˜μ w (V/h cm ) 2 R b   2 h cm , where R b  is the base radius of the droplet. Applying geometrical relations for a spherical cap, R b /h cm =g(θ)=4/3(sin θ)(2+cos θ)/(1+cos θ) 2  results in: 
         I˜μ   w   V   2   R   b   g (θ)
 
     The rate of viscous dissipation within the film (II) can be approximated as II˜μ o (V i /t) 2 R b   2 t. Since (μ w /μ o )(t/h cm )&lt;&lt;1, from Eq. (12) ∇ū film ˜V i /t˜(μ w /μ o )(V/h cm ). Using h cm =R b /g(θ), the rate of viscous dissipation within the film (II) can be rewritten, such that: 
     
       
         
           
             II 
             ∼ 
             
               
                 
                   μ 
                   w 
                   2 
                 
                 
                   μ 
                   o 
                 
               
                
               
                 
                   
                     V 
                     2 
                   
                    
                   
                     [ 
                     
                       g 
                        
                       
                         ( 
                         θ 
                         ) 
                       
                     
                     ] 
                   
                 
                 2 
               
                
               t 
             
           
         
       
     
     Finally, the rate of viscous dissipation in the wetting ridge (III) can be approximated as III˜μ o (V/h ridge ) 2 R b h ridge   2  since fluid velocities within the wetting ridge must scale as the velocity of the centre of mass and vanish at the solid surface, giving velocity gradients that scale as ∇ū ridge ˜V/h ridge , where h ridge  is the height of the wetting ridge. Thus, 
         III˜μ   o   V   2   R   b . 
     Noting that F g =ρ w Ωg sin α and F p =ρ w Ωg sin α* and dividing both sides of Eq. (13) by R b Vγ wa  yields 
     
       
         
           
             
               
                 
                   
                     
                       Bo 
                        
                       
                         ( 
                         
                           
                             sin 
                              
                             
                                 
                             
                              
                             α 
                           
                           - 
                           
                             sin 
                              
                             
                                 
                             
                              
                             
                               α 
                               * 
                             
                           
                         
                         ) 
                       
                     
                      
                     
                       f 
                        
                       
                         ( 
                         θ 
                         ) 
                       
                     
                   
                   ∼ 
                   
                     Ca 
                      
                     
                       { 
                       
                         
                           g 
                            
                           
                             ( 
                             θ 
                             ) 
                           
                         
                         + 
                         
                           
                             
                               [ 
                               
                                 g 
                                  
                                 
                                   ( 
                                   θ 
                                   ) 
                                 
                               
                               ] 
                             
                             2 
                           
                            
                           
                             
                               μ 
                               w 
                             
                             
                               μ 
                               o 
                             
                           
                            
                           
                             t 
                             
                               R 
                               b 
                             
                           
                         
                         + 
                         
                           
                             μ 
                             o 
                           
                           
                             μ 
                             w 
                           
                         
                       
                       } 
                     
                   
                 
               
               
                 
                   ( 
                   14 
                   ) 
                 
               
             
           
         
       
     
     Where Ca=μ w V/γ wa , is the capillary number, Bo=, Ω 2/3 ρ w g/γ wa  is the Bond number, and f(θ)=Ω 1/3 /R b  (described before herein). Since (μ w /μ o )(t/R b )&lt;&lt;1, and μ o /μ w &gt;&gt;g(θ) in our experiments, Eq. (14) can be simplified to: 
     
       
         
           
             
               
                 
                   
                     
                       Bo 
                        
                       
                         ( 
                         
                           
                             sin 
                              
                             
                                 
                             
                              
                             α 
                           
                           - 
                           
                             sin 
                              
                             
                                 
                             
                              
                             
                               α 
                               * 
                             
                           
                         
                         ) 
                       
                     
                      
                     
                       f 
                        
                       
                         ( 
                         θ 
                         ) 
                       
                     
                   
                   ∼ 
                   
                     Ca 
                      
                     
                       
                         μ 
                         o 
                       
                       
                         μ 
                         w 
                       
                     
                   
                 
               
               
                 
                   ( 
                   15 
                   ) 
                 
               
             
           
         
       
     
     The datasets shown in  FIG. 11A  were organized according to Eq. (15) and were found to collapse onto a single curve ( FIG. 1  ID), demonstrating that the above scaling model captures the essential physics of the phenomenon: the gravitational potential energy of the rolling droplet is primarily consumed in viscous dissipation in the wetting ridge around the base of the rolling droplet. Similar conclusions apply to solid spheres rolling on thin films of viscous oil. Furthermore, Eq. (14) and Eq. (15) apply for cloaked and uncloaked droplets, because inertial and gravitational forces in the cloaking films are very small. Consequently, the velocity is uniform across the film and viscous dissipation is negligible. 
     In some embodiments, the φ can be less than about 0.30, about 0.25, about 0.20, about 0.15, about 0.10, about 0.05, about 0.01, or less than about 0.005. In some embodiments, φ can be greater than about 0.001, about 0.005, about 0.01, about 0.05, about 0.10, about 0.15, or greater than about 0.20. In some embodiments, φ can be in the range of about 0 to about 0.25. In some embodiments, φ can be in the range of about 0 to about 0.01. In some embodiments, φ can be in the range of about 0.001 to about 0.25. In some embodiments, φ can be in the range of about 0.001 to about 0.10. 
     In some embodiments, a liquid-impregnated surface, for example the liquid-impregnated surface  100 ,  200 , or any of the liquid-impregnated surfaces described herein can be configured such that cloaking by the impregnating liquid can either be eliminated or induced. Without being bound to any particular theory, impregnating liquids that have S ow(a)  less than 0 will not cloak, resulting in no loss of impregnating liquids, whereas impregnating liquids that have S ow(a)  greater than 0 will cloak a product P in contact with the liquid-impregnated surface (e.g., food products, drugs, health and beauty products, water, bacterial colonies, etc.) and this may be exploited to prevent corrosion, fouling, etc. In some embodiments, cloaking can be used for preventing vapor-liquid transformation (e.g., water vapor, metallic vapor, etc.). In some embodiments, cloaking can be used for inhibiting liquid-solid formation (e.g., ice, metal, etc.). In some embodiments, cloaking can be used to make reservoirs for carrying the materials, such that independent cloaked materials can be controlled and directed by external means (like electric or magnetic fields). 
     In some embodiments, cloaking can be desirable and can be used as a means for preventing environmental contamination, like a time capsule preserving the contents of the cloaked material. Cloaking can result in encasing of the material thereby cutting its access from the environment. This can be used for transporting materials (e.g., bioassays) across a length in a way that the material is not contaminated by the environment. 
     In some embodiments, the amount of cloaking can be controlled by various lubricant properties such as viscosity, surface tension of the impregnating liquid. Additionally or alternatively, the de-wetting of the cloaked material can also be controlled to release the material, for example a system in which a product is disposed on the liquid-impregnated surface at one end, and upon reaching the other end is exposed to an environment that causes the product to uncloak. 
     In some embodiments, the impregnating liquid can be selected to have a S ow(a)  less than 0. 
     In some embodiments, liquid-impregnated surfaces described herein can have advantageous droplet roll-off properties that minimize the accumulation of the contacting liquid on the surfaces. Without being bound to any particular theory, a roll-off angle “α” of the liquid-impregnated surface in some embodiments can be less than about 50°, less than about 40°, less than about 30°, less than about 25°, or less than about 20°. 
     Typically, flow through a pipe or channel having a liquid-impregnated surface on its interior can be described by the following equation: 
         Q /(Δ p/L )˜( R   4 /μ 1 )(1 +C ( h/r )(μ 1 /μ 2 )  (16)
 
     where Q is the volumetric flow rate, R is pipe radius, h is the height of the texture, μ 2  is the viscosity of lubricant and μ 1  is the viscosity of the fluid flowing through the pipe. C is a constant that relates to the obstruction of the flow of the impregnating liquid due to the texture. C=1 in the limit of infinitely sparse textures (no texture), and C approaches 0 for very tightly spaced textures. Δp/L is the pressure drop per L. Note that C*h*(μ 1 /μ 2 ) defines a slip length, b. Without being bound to any particular theory, it is believed that (h/R)(μ 1 /μ 2 ) should be greater than 1 for the texture to have a significant effect on flow, and this sets the height of the texture in relation to the viscosity ratio. 
       Power˜(Δ p/L )* Q (here “˜” means “scales as”)
 
     So equation (16) becomes: 
     
       
         
           
             
               
                 
                   
                     
                       Q 
                       2 
                     
                     Power 
                   
                   ∼ 
                   
                     
                       ( 
                       
                         
                           R 
                           4 
                         
                         
                           μ 
                           1 
                         
                       
                       ) 
                     
                      
                     
                       [ 
                       
                         1 
                         + 
                         
                           
                             C 
                              
                             
                               ( 
                               
                                 t 
                                 R 
                               
                               ) 
                             
                           
                            
                           
                             ( 
                             
                               
                                 μ 
                                 1 
                               
                               
                                 μ 
                                 2 
                               
                             
                             ) 
                           
                         
                       
                       ] 
                     
                   
                 
               
               
                 
                   ( 
                   17 
                   ) 
                 
               
             
           
         
       
     
     Then the ratio of the flow rate of a liquid without the coating to one with the coating, at the same pumping power, is: 
     
       
         
           
             
               
                 
                   
                     
                       Q 
                       coated 
                     
                     
                       Q 
                       uncoated 
                     
                   
                   ∼ 
                   
                     
                       [ 
                       
                         1 
                         + 
                         
                           
                             C 
                              
                             
                               ( 
                               
                                 h 
                                 R 
                               
                               ) 
                             
                           
                            
                           
                             ( 
                             
                               
                                 μ 
                                 1 
                               
                               
                                 μ 
                                 2 
                               
                             
                             ) 
                           
                         
                       
                       ] 
                     
                     
                       1 
                       2 
                     
                   
                 
               
               
                 
                   ( 
                   18 
                   ) 
                 
               
             
           
         
       
     
     Or the reduction in power require to achieve the same flow rate is: 
     
       
         
           
             
               
                 
                   
                     
                       P 
                       coated 
                     
                     
                       P 
                       uncoated 
                     
                   
                   ∼ 
                   
                     
                       [ 
                       
                         1 
                         + 
                         
                           
                             C 
                              
                             
                               ( 
                               
                                 h 
                                 R 
                               
                               ) 
                             
                           
                            
                           
                             ( 
                             
                               
                                 μ 
                                 1 
                               
                               
                                 μ 
                                 2 
                               
                             
                             ) 
                           
                         
                       
                       ] 
                     
                     
                       - 
                       1 
                     
                   
                 
               
               
                 
                   ( 
                   19 
                   ) 
                 
               
             
           
         
       
     
     If h&lt;&lt;R, then the flow of the product also drags the material within the film at a flow rate Q f  given by: 
         Q   f   /Q=h/R[ 2 b/R +( b/R )]/[½+2 b/R +( b/R ) 2 ]  (20)
 
       If  b/R&lt;&lt; 1 then: 
         Q   f   /Q˜ 4 hb/R   2 (valid for  h&lt;R  and  b/R )  (21)
 
     Although modeled for pipe flow, the general principals discussed above also apply to open systems, for example, product containers, where R is replaced with the characteristic depth of the flowing material. The average velocity of the flow ˜Q/A, where A is the cross-sectional area of the flowing fluid. 
     For example, mayonnaise, which is a Bingham plastic, has a viscosity that approaches infinity at low shear rates (it is non-Newtonian), and therefore behaves like a solid as long as shear stress within it remains below a critical value. By way of comparison, for honey, which is Newtonian, the flow is much slower. For both systems, h and R are of the same order of magnitude, and μ 2  is the same. However, since 
       μ honey &lt;&lt;μ mayonnaise ,then( h/R )(μ honey /μ 2 )&lt;&lt;( h/R )(μ mayonnaise /μ 2 )
 
     thus mayonnaise flows much more quickly out of the bottle than honey. In some embodiments, μ 1 /μ 2  can be greater than about 1, about 0.5, or about 0.1. 
     In some embodiments, the impregnating liquid includes an additive to prevent or reduce evaporation of the impregnating liquid, for example a surfactant. The surfactants can include, but are not limited to, docosenoic acid, trans-13-docosenoic acid, cis-13-docosenoic acid, nonylphenoxy tri(ethyleneoxy)ethanol, methyl 12-hydroxyoctadecanate, 1-Tetracosanol, fluorochemical “L-1006”, and any combination thereof. Examples of surfactants described herein and other surfactants which can be included in the impregnating liquid can be found in White, I., “Effect of Surfactants on the Evaporation of Water Close to 100 C,”  Industrial  &amp;  Engineering Chemistry Fundamentals  15.1 (1976): 53-59, the content of which is incorporated herein by reference in its entirety. In some embodiments, the additives can include C 16 H 33 COOH, C 17 H 33 COOH, C 18 H 33 COOH, C 19 H 33 COOH, C 14 H 29 OH, C 16 H 33 OH, C 18 H 37 OH, C 20 H 41 OH, C 22 H 45 OH:, C 17 H 35 COOCH, C 15 H 31 COOC 2 H 5 , C 16 H 33 OC 2 H 4 OH, C 18 H 37 OC 2 H 4 OH, C 20 H 41 OC 2 H 4 OH, C 22 H 45 OC 2 H 4 OH. Sodium docosyl sulfate, poly(vinyl stearate), Poly (octadecyl acrylate), Poly(octadecyl methacrylate) and any combination thereof. Further examples of additives can be found in Barnes, G. T., “The potential for monolayers to reduce the evaporation of water from large water storages,”  Agricultural Water Management  95.4 (2008): 339-353, the content of which is hereby by incorporated herein by reference in its entirety. 
     Non-Toxic Liquid-Impregnated Surfaces 
     In some embodiments, any of the liquid-impregnated surfaces described herein can include non-toxic materials, for example impregnating liquid and/or solid (e.g., solid particles used to form solid features such as, for example, wax), that are non-toxic to humans and/or animals. Non-toxic liquid-impregnated surfaces can therefore be safely disposed on surfaces, for example the interior surface(s) of containers that are configured to house products formulated for human use or consumption. Such products can include, for example food products, drugs (e.g., FDA approved drugs), or health and beauty products. 
     In some embodiments, the solid features (e.g., solid particles) and/or the impregnating liquid can be removed or depleted from the surface due to friction and abrasion due to product sliding over the liquid-impregnated surface. The impregnating liquid may be particularly prone to being depleted from the surface by entrainment within the product or dissolution into the product. The concentration of the depleted impregnating liquid entrained in the product can be in the range of about 5 ppm to about 500 ppm, which is not negligible. Therefore, there is a need for liquid impregnating surfaces that include impregnating liquid and/or solids (e.g., solid particles that form the solid features) that are non-toxic and safe for human use or consumption. In some embodiments, any solvents used in the processing of any components of the liquid-impregnated surface, for example the solid surface, may remain in the liquid-impregnated surface in some concentration, and thus the solvents can also be chosen to be non-toxic. Examples of solvents that are nontoxic in residual quantities include ethyl acetate, ethanol (e.g., 200 proof, 140 proof), water, or any other non-toxic solvent. In other embodiments, the solvent may comprise ethyl acetate and/or heptane. 
     The non-toxicity requirements can vary depending upon the intended use of the product in contact with the liquid-impregnated surface. For example, liquid-impregnated surfaces configured to be used with food products or products classified as drugs would be required to have a much higher level of non-toxicity when compared with products meant to contact only the oral mucosa (e.g., toothpaste, mouth wash, etc.), or applied topically such as, for example, health and beauty products (e.g., hair gel, shampoo, lotion, cosmetics, etc.). 
     In some embodiments, the non-toxic liquid-impregnated surface can be disposed on a substrate, for the example, the interior wall of a container configured to house a food product or an ingredient of a food product for consumption by a human or an animal. In some embodiments, the substrate can be any surface, for example a surface of a food processing equipment that makes contact with food or food ingredients. The food product or food ingredient can include, for example, a sticky, highly viscous, and/or non-Newtonian food product. Such food products can include, for example, candy, chocolate syrup, mash, yeast mash, beer mash, taffy, food oil, fish oil, marshmallow, dough, batter, baked goods, chewing gum, bubble gum, butter, peanut butter, jelly, jam, dough, gum, cheese, cream, cream cheese, mustard, yogurt, sour cream, curry, sauce, ajvar, currywurst sauce, salsa lizano, chutney, pebre, fish sauce, tzatziki, sriracha sauce, vegemite, chimichurri, HP sauce/brown sauce, harissa, kochujang, hoisin sauce, kim chi, cholula hot sauce, tartar sauce, tahini, hummus, shichimi, ketchup, mustard, pasta sauce, Alfredo sauce, spaghetti sauce, icing, dessert toppings, or whipped cream, liquid egg, ice cream, animal food, any other food product or combination thereof. In such embodiments, the components of the non-toxic liquid-impregnated surfaces can include materials that are non-toxic when consumed orally by a human or an animal. For example, the liquid-impregnated surface can include materials that are a U.S. Food and Drug Administration (FDA) approved direct or indirect food additive, an FDA approved food contact substance, satisfy FDA regulatory requirements to be used as a food additive or food contact substance, and/or is an FDA GRAS material. Examples of such materials can be found within the FDA Code of Federal Regulations Title 21, located at “http://www.accessdata.fda.gov/scripts/cdrh/cfdocs/cfcfr/cfrsearch.cfm,” the entire contents of which are hereby incorporated by reference herein. In some embodiments, the components of the non-toxic liquid-impregnated surface, for example the impregnating liquid, can exist as a component of the food product disposed within the container. In some embodiments, the components of the non-toxic liquid-impregnated surface can include a dietary supplement or ingredient of a dietary supplement. The components of the non-toxic liquid-impregnated surface can also include an FDA approved food additive or color additive. In some embodiments, the non-toxic liquid impregnating surface can include materials that exist naturally in, or are derived from plants and animals. In some embodiments, the non-toxic liquid-impregnated surface for use with food products includes solids or impregnating liquid that are flavorless or have a high flavor threshold of below 500 ppm, are odorless or have high odor threshold, and/or are substantially transparent. In addition, or alternatively, the non-toxic liquid-impregnated surface for use with food products includes solids or impregnating liquid that are tasteless and/or immiscible with an adjacent phase. 
     In some embodiments, the non-toxic liquid-impregnated surface can be disposed on a substrate, for the example, the interior side wall of a container configured to house a drug or products classified as a drug, for example, an FDA approved drug for consumption by a human or an animal. The drug can be in the form of a liquid, a cream, an ointment, a lotion, an eye drop, an oral drug, an intravenous drug, an intramuscular drug, a suspension, a colloid, or any other form and can include any drug included within the FDA&#39;s database of approved drugs. In such embodiments, the materials included in the non-toxic liquid-impregnated surface can include an FDA approved drug ingredient, for example any ingredient included in the FDA&#39;s database of approved drugs, “http://www.accessdata.fda.gov/scripts/cder/drugsatfda/index.cfm.” the entire contents of which are hereby incorporated herein by reference. In some embodiments, the non-toxic liquid-impregnated surface can include materials that satisfy FDA requirements to be used in drugs or are listed within the FDA&#39;s National Drug Discovery Code Directory, “http://www.accessdata.fda.gov/scripts/cder/ndc/default.cfm”, the entire contents of which are hereby incorporated herein by reference. In some embodiments, the materials can include inactive drug ingredient of an approved drug product as listed within FDA&#39;s database, “http://www.accessdata.fda.gov.scripts/cder/ndc/default.cfm”, the entire contents of which are hereby incorporated herein by reference. In some embodiments, the materials can include any materials that satisfy the requirement of materials that can be used in liquid-impregnated surfaces configured to be used with food products, and/or include a dietary supplement or ingredient of a dietary supplement. 
     In some embodiments, the non-toxic liquid-impregnated surface can be disposed on a substrate, for the example, the interior side wall of a container configured to house a health and beauty product which is also classified as a drug. Examples of such product can include, but are not limited to toothpaste, sun screens, anti-perspirants, anti-dandruff shampoos, anti-dandruff conditioners, or anti-bacterial cleansers. In such embodiments, the health and beauty product, for example, toothpaste can include an impregnating liquid and/or a solid which is FDA approved and satisfies FDA drug requirements as are listed within the FDA&#39;s National Drug Discovery Code Directory and can also include FDA approved health and beauty ingredient, that satisfy FDA requirements to be used in health and beauty products, satisfies FDA regulatory laws included in the Federal Food, Drug and Cosmetic Act (FD&amp;C Act), or the Fair Packaging and Labeling Act (FPLA). 
     In some embodiments, the non-toxic liquid-impregnated surface can be disposed on a substrate, for the example, the interior side wall of a container configured to house a health and beauty product, which does not include a compound classified by FDA as a drug compound or an active ingredient of a drug. Such products can include product configured to contact the oral mucosa, for example non-fluoride toothpaste, some mouth washes, mouth creams, denture fixing compounds, or any other oral hygiene product. In some embodiments, the health and beauty product can include a products configured for topical application, for example cosmetics, lotions, shampoo, conditioner, moisturizers, face washes, hair-gels, medical fluids (e.g., anti-bacterial ointments or creams), any other health or beauty product, and or combination thereof. In such embodiments, the non-toxic liquid impregnated coating can include, for example, a material that is an FDA approved health and beauty ingredient, or that satisfies FDA requirements to be used in health and beauty products, FDA regulatory laws included in the Federal Food, Drug and Cosmetic Act (FD&amp;C Act), and/or the Fair Packaging and Labeling Act (FPLA). In some embodiments, the solids and or impregnating liquid included in the non-toxic liquid-impregnated surface can include a flavor or a fragrance. 
     In some embodiments, the materials included in any of the non-toxic liquid-impregnated surfaces described herein (e.g., liquid-impregnated surfaces configured to contact food products, drugs, or health and beauty products) can be flavorless or have high flavor thresholds below 500 ppm, and can be odorless or have a high odor threshold. In some embodiments, the materials included in any of the non-toxic liquid impregnating surfaces described herein can be substantially transparent. For example, the solid and the impregnating liquid can be selected so that they have substantially the same or similar indices of refraction. By matching their indices of refraction, they may be optically matched to reduce light scattering and improve light transmission. For example, by utilizing materials that have similar indices of refraction and have a clear, transparent property, a surface having substantially transparent characteristics can be formed. In some embodiments, the materials included in the liquid-impregnated surfaces are organic or are derived from organically grown products. 
     In some embodiments, the liquid surface film includes a liquid having a melting point that is higher than the temperature at which the container bearing said liquid surface film would typically be stored, shipped, transported, etc. In other words, the liquid may be frozen during certain such periods. When the liquid surface film is solidified through freezing, it dissolves much more slowly (e.g., in the presence of an adjacent product), and to a lesser extent, thereby enhancing the lifetime of the liquid surface film during storage. Upon thawing, the liquid surface film regains the performance characteristics that it had prior to freezing (i.e., its “slippery” properties). This ability to freeze the liquid component of the liquid surface film may be desirable, for example, during periods of time when the liquid surface film has been applied to a container but the container does not yet contain a product, or when a product within a container coated with the liquid surface film does not yet need to be dispensed (e.g., during shipment or storage). 
     In some embodiments, the materials included in any of the non-toxic liquid-impregnated surfaces described herein can be recyclable. For example, the solid or impregnating liquid can include materials that wash away during standard container (e.g., glass bottle, plastic bottle, etc.) recycling process. For example, the liquid-impregnated surface can be configured to pass standard recycling tests provided by the Association for Postconsumer Plastic Recyclers (e.g., may be adequately cleaned using the typical wash used in PET bottle recycling). In some embodiments, the liquid-impregnated surface can be configured to dissolve in a caustic wash, for example a solution of Triton X 100 or NaOH at high temperature, an acid wash, a solvent wash, or any other dissolving solution. 
     In some embodiments, the impregnating liquid included in the non-toxic liquid-impregnated surface can include one or more additives. The additive can be configured, for example, to reduce the viscosity, vapor pressure, or solubility of the impregnating liquid. In some embodiments, the additive can be configured to increase the chemical stability of the liquid-impregnated surface. For example, the additive can be an anti-oxidant configured to inhibit oxidation of the liquid-impregnated surface. In some embodiments, the additive can be added to reduce or increase the freezing point of the liquid. In some embodiments, the additive can be configured to reduce the diffusivity of oxygen or CO 2  through the liquid-impregnated surface or enable the liquid-impregnated surface to absorb more ultra violet (UV) light, for example protect the product (e.g., any of the products described herein), disposed within a container on which the non-toxic liquid-impregnated surface is disposed. In some embodiments, the additive can be configured to provide an intentional odor, for example a fragrance (e.g., smell of flowers, fruits, plants, freshness, scents, etc.). In some embodiments, the additive can be configured to provide color to the liquid-impregnated surface and can include, for example a dye, or an FDA approved color additive. In some embodiments, the non-toxic liquid-impregnated surface includes an additive that can be released into the product, for example, a flavor or a preservative. 
     In some embodiments, the materials included in any of the non-toxic liquid-impregnated surfaces described herein can be organic or derived from organically grown products. For example, the impregnating liquids can include organic liquids that are often or sometimes non-toxic. Such non-toxic organic liquids can, for example, include materials that fall within the following classes: lipids, vegetable oils (e.g., olive oil, light olive oil, corn oil, soybean oil, rapeseed oil, linseed oil, grapeseed oil, flaxseed oil, peanut oil, safflower oil, palm oil, coconut oil, or sunflower oil), fats, fatty acids, derivatives of vegetable oils or fatty acids, esters, terpenes, monoglycerides, diglycerides, triglycerides, mixtures of triglycerides such as MCT oil (medium chain triglyceride oil), triacetin, tripropionin, alcohols, and fatty acid alcohols. Examples of vegetable oils, suitable for use as impregnating liquids in the non-toxic liquid impregnated surface of the present disclosure, are described in Gunstone, F., “Vegetable Oils in Food Technology Composition, Properties and Uses: 2 nd  Ed.,” Wiley, John and Sons Inc., Pub. May 2011, the contents of which are hereby incorporated by reference herein in their entirety. 
     In some embodiments, any of the non-toxic liquid-impregnated surfaces described herein can include organic solids, semi-solids, and/or liquids that are non-toxic and that fall within the following classes: lipids, waxes, fats, fibers, cellulose, derivatives of vegetable oils, esters (such as esters of fatty acids), terpenes, monoglycerides, diglycerides, triglycerides, alcohols, triacetin, tripropionin, citric triglycerides, propylene glycol, poly ethylene glycol, fatty acid alcohols, ketones, aldehydes, proteins, sugars, salts, minerals, vitamins, carbonate, ceramic materials, alkanes, alkenes, alkynes, acyl halides, carbonates, carboxylates, carboxylic acids, methoxies, hydroperoxides, peroxides, ethers, hemiacetals, hemiaketals, acetals, ketals, orthoesters, orthocarbonate esters, phospholipids, lecithins, any other organic material or any combination thereof. Some examples of food-safe impregnating liquids are medium chain triglyceride (MCT) oil, ethyl oleate, methyl laurate, propylene glycol, propylene glycol dicaprylate/dicaprate, or vegetable oil, glycerine, and squalene. In some embodiments, any of the non-toxic liquid-impregnated surfaces can include inorganic materials, for example ceramics, metals, metal oxides, silica, glass, plastics, any other inorganic material or combination thereof. In some embodiments, any of the non-toxic liquid-impregnated surfaces described herein can include, for example preservatives, sweeteners, color additives, flavors, spices, flavor enhancers, fat replacers, and components of formulations used to replace fats, nutrients, emulsifiers, surfactants, bulking agents, cleansing agents, depilatories, stabilizers, emulsion stabilizers, thickeners, flavor or fragrance, an ingredient of a flavor or fragrance, binders, texturizers, humectants, pH control agents, acidulants, leavening agents, anti-caking agents, anti-dandruff agents, anti-microbial agents, anti-perspirants, anti-seborrheic agents, astringents, bleaching agents, denaturants, depilatories, emollients, foaming agents, hair conditioning agents, hair fixing agents, hair waving agents, absorbents, anti-corrosive agents, anti-foaming agents, anti-oxidants, anti-plaque agents, anti-static agents, binding agents, buffering agents, chelating agents, cosmetic colorants, deodorants, detangling agents, emulsifying agents, film formers, foam boosting agents, gel forming agents, hair dyeing agents, hair straightening agents, keratolytics, moisturizing agents, oral care agents, pearlescent agents, plasticizers, refatting agents, skin conditioning agents, smooting agents, soothing agents, tonics, and/or UV filters. 
     In some embodiments, the non-toxic liquid-impregnated surface can include non-toxic materials having an average molecular weight in the range of about 100 g/mol to about 600 g/mol. which are included in the Springer Material Landolt-Bornstein database located at, “http://www.springermaterials.com/docs/index.html,” or in the MatNavi database located at “www.mits.nims.go.jp/index_en.html.” In some embodiments, the liquids have boiling points greater than 150° C., for example 250° C. or below about 270° C., such that they are not classified as volatile organic compounds (VOC&#39;s). In some embodiments, a liquid-impregnated surface can include an impregnating liquid whose density is substantially equal to the density of the product. For example, the ratio of impregnating liquid density to product density may be in a range from 0.95:1 to 0.95:1.1. In some embodiments, the density of the impregnating liquid may be about 1 g/cm 3 . 
     In some embodiments the liquid can include materials safe for skin contact or one that is a ingredient in a health and beauty product. Examples include silicone oils, fluorinated hydrocarbons, fluorinated perfluoropolyethers, fluorinated silicones, aryl silicones, phenyl trimethicone, cyclomethicones, aryl cyclomethicones and hydrocarbon liquids including mineral oil, paraffin oil, C13-C14 isoparaffins, C16-C18 isoparaffins, di- and triglycyceride esters, tri alkyl esters of citric acid. 
     In some embodiments the solid material can include materials safe for skin contact or one that is a ingredient in a health and beauty product. Examples include the categories of silicones, alkyl silicone waxes, hydrocarbon waxes, polymethylsilsesquioxane particles, silica particles with hydrophobic treatment (for example a hydrophobic silane), silica particles with polydimethyl siloxane (PDMS) resin outer layer, polymethylsilscsquioxane particles with polydimethylsiloxane resin outer layer, silicone prepolymer mixes with combinations of silica and PDMS particles, UV curable PDMS. 
     In some embodiments it is desirable for the textured solid and the impregnating liquid to have substantially similar chemistry, such that the liquid has a high affinity for the solid and preferentially wet it beneath a product. For example the solid could be PDMS and/or a siliconyl wax, and the liquid could be a silicone oil or dimethicone. These classes of materials are found to be effective combinations for coatings for many consumer products including many hair gels, conditioner, and oil in water lotions. Another effective combination are waxes that are food additives used as a solid that are impregnated with a liquid having substantially similar chemistry. For example, the solid could be a triglyceride based wax and the liquid could be a triglyceride. 
     Creating a Matrix of Solid Features on an Interior Surface of a Bottle: 
     In these experiments, 200-proof pure ethanol (KOPTEC), powdered carnauba wax (McMaster-Carr) and aerosol carnauba wax spray (PPE, #CW-165, which contains trichloroethylene, propane and carnauba wax) were used. The sonicator was from Branson, Model 2510. The advanced hot plate stirrer was from VWR, Model 97042-642. The airbrush was from Badger Air-Brush Co., Model Badger 150. 
     A first surface having a matrix of solid features was prepared by Procedure 1, described as follows. A mixture was made by heating about 40 mL of ethanol to a temperature of about 85° C., slowly adding about 0.4 grams of carnauba wax powder, boiling the mixture for approximately 5 min, and then allowing the mixture to cool while being sonicated for about 5 min. The resulting mixture was sprayed onto a substrate with the airbrush (at an airbrush pressure of about 50 psi), and then allowed to dry at ambient temperature and humidity for about 1 min. SEM images of the resulting surface are shown in  FIGS. 12 and 13  (at 500× and 15,000× magnification, respectively). 
     A second surface was prepared by Procedure 2, described as follows. A mixture was made by adding about 4 grams of powdered carnauba wax to about 40 mL ethanol and vigorously stirring. The resulting mixture was sprayed onto a substrate with the airbrush (at an airbrush pressure of about 50 psi) for about 2 seconds at a distance of about 4 inches from the surface, and then allowed to dry at ambient temperature and humidity for about 1 min. SEM images are shown in  FIGS. 14 and 15  (at 500× and 15,000× magnification, respectively). 
     A third surface was prepared by Procedure 3, described as follows. An aerosol wax was sprayed onto a substrate at a distance of about 10 inches for about 3 seconds. The spray nozzle was moved such that spray residence time was no longer than about 0.5 sec/unit area, and then the substrate was allowed to dry at ambient temperature and humidity for about 1 min. SEM images are shown in  FIGS. 16 and 17  (at 500× and 15,000× magnification, respectively). 
     Impregnating a Wax Coating: 
     A quantity of about 5 to about 10 mL of ethyl oleate (sigma Aldrich) or vegetable oil was swirled around in bottles that initially had an internal surface entirely covered with wax (prepared by Procedure 3 as described above), until the bottles became transparent. Such a coating time was chosen so that a cloudy (not patchy) coating formed over the whole internal surface. The formed coating had a thickness in a range of about 10 microns to about 50 microns. 
     The excess oil was removed by inverting the bottles (i.e., holding them upside down) for about 5 minutes, or drained by adding about 50 mL of water to the bottle and shaking it for 5-10 seconds to entrain most of the excess oil into the water. The water/oil emulsion was then dumped out. In general, after draining, the coating appears clear. When it is over-drained, however, it usually appears cloudy. 
       FIGS. 18 through 23  show time-lapse images of a volume of ketchup on a liquid-impregnated surface, prepared in accordance with an embodiment of the invention. As shown, the spot of ketchup was able to slide along the liquid-impregnated surface due to a slight tilting (e.g., about 5 to about 10 degrees) of the surface. The ketchup moved along the surface as a substantially rigid body, without leaving any ketchup residue along its path. The elapsed time from  FIG. 18  to  FIG. 23  was about 1 second. 
     Freezing a Liquid Impregnated Surface 
     A liquid-impregnated surface which included carnauba wax mixed trichloroethylene as the solid, was impregnated with methyl laurate, which has a freezing point of 5° C. One PET bottle was coated with carnauba wax impregnated with methyl laurate, and another one was coated with carnauba wax impregnated with ethyl oleate, which has a freezing point of −32° C. Both PET bottles were filled with scrambled egg yolk, and showed nearly identical slipperiness at room temperature, based on the sliding speed of about 3 scrambled egg yolks at a 15° angle. Both bottles were then placed in a freezer at −15° C. for 3 days, and upon thawing, the bottle having the liquid-impregnated surface that included methyl laurate showed no detectable change in performance, whereas the liquid-impregnated surface that included ethyl oleate exhibited significantly lower sliding speed. 
     While various embodiments of the system, methods, and apparatuses of the present disclosure have been described above, it should be understood that they have been presented by way of example only, and are not limited to the example set forth herein. Where methods and steps described above indicate certain events occurring in a certain order, those of ordinary skill in the art having the benefit of this disclosure would recognize that the ordering of certain steps may be modified, and such modifications are therefore contemplated by this disclosure. Additionally, certain steps described herein may be performed concurrently, e.g., in a parallel process, when possible, as well as performed sequentially as described above. The embodiments have been particularly shown and described, but it will be understood that various changes in form and details may be made.