Abstract:
In a method of moving droplets, local heat is applied to a surface portion of a droplet for an amount of time sufficient to create a Marangoni flow in the droplet. Droplets are suspended in an emulsion in a carrier liquid on a substrate. A laser beam is used to move one of the droplets. the droplet consists of a first substance and a carrier liquid consists of a second substance that is not mixable with the first substance. The droplet is placed in the carrier liquid, and the mixture is emulsified. The emulsified mixture is placed on a substrate. Then the local heat is applied to the surface of the droplet. The first substance may include oil and the second substance may include water.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     The present application is a National Phase Application of PCT Application No. PCT/US2012/040662, filed Jun. 4, 2012, which claims the benefit of U.S. Provisional Patent Application No. 61/493,102 filed Jun. 3, 2011,the content of which is hereby incorporated by reference in its entirety. 
    
    
     TECHNICAL FIELD 
     The present invention relates to optical techniques for droplet manipulation. 
     BACKGROUND 
     Optical techniques for droplet manipulation are attractive because they provide a contactless dynamic manipulation of droplets. and do not require specific substrate structures. Current approaches include, for example, so-called optical tweezers. Optical tweezers are not ideally suited for droplet manipulation because they exert a relatively low force on a droplet. The force that an optical tweezer can exert on a droplet ranges in an order of magnitude of picoNewtons (pN). For droplets of sizes of several hundreds of micrometers, such forces are insufficient to move the droplet at any significant velocity. Further, the forces have been found to be typically repulsive. Optoelectronic tweezers (OET) have been adapted to manipulated droplets with a force in a range of nanoNewtons (nN). Optoelectronic tweezers typically require on-chip electrodes providing an in-plane AC electric field. 
     SUMMARY 
     According to one aspect of the invention, a method of moving droplets includes the steps of providing a droplet; and applying local heat to a surface portion of the droplet for an amount of time sufficient to create a Marangoni flow in the droplet that causes the droplet to move toward the local heat. Marangoni flow is caused by a gradient of surface tension or interfacial tension that can cause forces exceeding several microNewtons. 
     According to a further aspect of the invention, the droplet consists of a first substance and a carrier liquid consists of a second substance that is not mixable with the first substance. The droplet is placed in the carrier liquid and placed on a substrate. Then the local heat is applied. In the context of the following description, a droplet is defined as consisting of a fluid, which may be a liquid or a gas. 
     According to another aspect, the second substance may be a polar liquid and the first substance may be a substantially nonpolar fluid. For example, the first substance may include oil and the second substance may include water. 
     According to one aspect of the invention, the droplet is placed in the carrier liquid by creating an emulsion of the first substance in the second substance. 
     In one example, the substrate is transparent. Then is it possible to apply the localized heat via a light beam originating under the substrate and propagating through the substrate. The light beam includes at least one wavelength for which both the substrate and the carrier liquid are transparent. 
     For a vertical movement of the droplet, the droplet may initially be suspended in the carrier liquid. Then the local heat is applied until the droplet contacts the substrate. Even after the droplet contacts the substrate, the application of local heat can be continued so that the droplet is trapped laterally. 
     For a horizontal movement of the droplet the light beam may be directed at a surface portion of the droplet in an off-center location, inside the perimeter of the projection of the droplet on a horizontal plane, in a direction substantially perpendicular to the top surface of the substrate. 
     According to one aspect of the invention, the local heat is applied by a laser generating a laser beam with a wavelength in the visible spectrum that is converted to heat upon contact with the droplet surface. The laser may, for example, be a diode laser. But the wavelength is not limited to the visible spectrum. It is preferable, however, that the carrier liquid is substatially transparent to the laser wavelength and that the droplet surface absorbs the laser wavelength at least in part for generating the local heat. 
     The wavelength penetrating the substrate and the carrier liquid may be in a range between about 400 nm and about 500 nm. 
     Preferably, the laser beam is focused with a focal spot size of less than about 130 μm. In particular, the focal spot size is smaller than about 70 μm. The focal spot size may even be smaller than about 30 μm. 
     Further details and benefits of the present invention become apparent from the following description of various preferred embodiments making reference to the attached drawings. The drawings are included for purely illustrative purposes and not intended to limit the scope of the present invention. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       In the drawings, 
         FIG. 1  illustrates a symmetric Marangoni flow generated by localized optical heating of an oil droplet; 
         FIG. 2  shows an example of isothermal lines induced in an oil drop caused by localized optical heating; 
         FIG. 3  shows a diagram of shear stresses caused in a droplet by a linear temperature gradient compared to a localized temperature gradient; 
         FIG. 4  shows a simulation of vertical droplet trapping by generating a symmetric Marangoni flow as illustrated in  FIG. 1 ; 
         FIG. 5  illustrates a horizontal droplet translation by generating an asymmetrical Marangoni flow; 
         FIG. 6  illustrates three stages of merging two droplets by translating one droplet through an asymmetrical Marangoni flow; 
         FIG. 7  shows a simulation of horizontal droplet translation by generating an asymmetrical Marangoni flow as utilized in  FIGS. 4 and 5 ; and 
         FIG. 8  shows an experimental setup for generating a Marangoni flow in droplets and for recording experimental observations. 
     
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     Referring to  FIG. 1 , an oil droplet  100  is suspended in an aqueous carrier fluid  102  on a glass substrate  104 . A laser beam  106  is focused on an interface  108  located on a bottom surface of the oil droplet  100 . The localized laser beam  106  generates a local rise in temperature at an interface  108  on the bottom surface of the oil droplet  100 . This localized heat causes a toroidal microvortex causing the droplet  100  to move toward the laser beam  106 , as will be explained in connection with the subsequent drawings figures. 
       FIG. 2  illustrates a cross-section of the oil droplet  100  with isothermal lines showing the thermal distribution of the laser energy in the oil droplet  100 . The overall temperature gradient of the droplet  100  encompasses a temperature difference of less than about 10K. But at the location of the laser beam incidence at interface  108 , the temperature gradient is steeper than remote therefrom, as evident from the denser arrangement of the isothermal lines. The local heat on the interface  108  increases the local temperature and consequently reduces the local interfacial tension (IFT), due to the generally prevailing inverse relation between IFT and temperature. 
     The locally reduced IFT generates an interfacial shear stress along the droplet surface, which drives the formation of the toroidal microvortex, of which two fronts  110  and  112  are shown within the droplet  100 . The microvortex fronts  110  and  112  exert a shear force on the surrounding fluid and result in an overall force  114  pulling the droplet  100  toward the axis of the laser beam  106 . Restoring forces are balanced when the droplet is aligned to the axis of the beam as illustrated by the symmetrical arrangement of  FIG. 1 , where all horizontal components of the microvortex fronts  110  and  112  cancel each other out. The overall force  114  keeps the droplet  100  trapped on the axis of the laser beam  106 . The interaction of the laser beam  106  with the interface  108  thus acts as an optofluidic tweezer (OFT). The OFT is based on the Marangoni flow caused by the reduced surface tension or interfacial tension cause by the temperature gradient on the surface of the droplet  100 . 
       FIG. 3  shows a simulation of shear stress and stream function in the droplet  100  with a linear temperature gradient on the left side and with a nearly point-shaped temperature increase as shown in  FIG. 2 . The stream function in the lower half of  FIG. 3  can be derived using a modified Stokes equation, and the total overall force  114  is calculated by integrating the shear stress gradient over the droplet surface. The OFT is driven by the steep temperature gradient, not by the absolute temperature. Therefore, with localized heating of the interface  108 , the droplet  100 , preferably consisting of a fluid with a low thermal conductivity, can be trapped and manipulated with a temperature perturbation in a range of less than about 10K. 
       FIG. 4  illustrates a simulated sequence of an OFT operation, in which the droplet  100  is trapped by and attracted to the laser beam  106 . Initially, according to  FIG. 4   a , the oil droplet  100  is suspended in an aqueous carrier fluid  102 , remote from the substrate  104 . The substrate  104  is transparent to the laser wavelength so that the laser beam  106  progresses from the outside through the substrate  104  into the carrier fluid  102 , until it hits the interface  108  of the droplet  100 . In  FIG. 3 , The droplet  100  is depicted to have a size of about 300 μm, a size that makes the droplet  100  visible to a human eye. 
     As shown in  FIG. 4   b , the laser beam  106  heats the interface  108  of the droplet  100  and causes the microvortex fronts  110  and  112  previously described in connection with  FIG. 1 . The resulting overall force  114  urges the droplet  100  toward the side of the interface  108 . 
     As shown in  FIG. 4   c , the droplet  100  starts to move toward the laser beam  106 . Eventually, as shown in  FIG. 4   d , the droplet contacts the substrate  104  so that the interface  108  cannot move any further. Accordingly, the overall force  114  causes a flattening of the trapped droplet  100  in the subsequent steps illustrated in  FIGS. 4   e  and  4   f.    
     In addition to axial trapping with respect to the laser beam axis, it is also possible to cause a lateral movement of the droplet  100 . As shown in  FIG. 1 , a laser beam centrally focused on the droplet  100  traps the droplet  100  in its lateral location relative to the laser beam.  FIG. 5  shows a translatory movement caused by a laser beam focused toward an interface  108  that is initially offset from the center of symmetry  116  of the droplet  100  as illustrated in  FIG. 5   a . The local heat applied to the interface  108  causes unequal microvortex fronts so that an addition of all horizontal forces results in an overall horizontal phoretic force directed from the center of symmetry  116  of the droplet  100  toward the laser beam  106 . The droplet is thus urged to occupy the symmetrical position shown in  FIG. 1 . 
       FIG. 5   b  through  5   d  shows that, in response to the local heat at interface  108 , the droplet  100  expands its outer perimeter toward the interface  108  to embrace the interface  108  from all sides. Subsequently, the surface of the drop remote from the interface follows the movement and approaches the interface  108  as shown in  FIG. 5   c . Finally, the droplet  100  returns to a circular shape, and the interface  108  between the laser beam  106  and the droplet  100  is in the center of symmetry  116 .  FIG. 5  represents a recording of an actual oil droplet  100  being moved in the aqueous carrier fluid  102 . 
     Thus, it has been shown that the OFT can trap oil droplets  100  using toroidal Marangoni flows, and manipulate them in a three-dimensional space, toward the laser beam and in two dimensions transverse to the laser beam  106 . The OFT can manipulate single droplets  100  with high resolution and avoids the need for on-chip structures and specialized surfaces. OFT can be performed on plain, transparent surfaces including microscope slides forming the substrate  104 . Thermocapillary forces are in the μN range so that OFT can generate translatory forces on a droplet that are many times stronger than forces generated with optoelectronic tweezers (OET) or optical tweezers. 
       FIGS. 6   a  through  6   c  show an example of merging two droplets  100  and  200  with OFT. In the shown embodiment of  FIG. 6   a , both droplets  100  and  200  have a diameter of about 200 μm. The laser beam  106  points onto the interface  108  on the surface of droplet  100 . As the laser beam  106  is moved toward the droplet  200 , the droplet  100  follows the laser beam  106  because the overall IFT forces urge the droplet toward a symmetrical position with respect to the laser beam  106  as shown in  FIG. 6   b  and described above in connection with  FIG. 5 . Once the droplet  100  moved by the laser beam  106  comes into contact with the droplet  200 , the two droplets  100  and  200  merge into one larger droplet  300  as shown in  FIG. 6   c , thus reducing the surface compared to the two separate droplets  100  and  200  and optimizing the overall IFT forces. 
     An example of a generally horizontal droplet translation is illustrated in  FIGS. 7   a  through  FIG. 7   c . In  FIG. 7   a  in a computer simulation. In  FIG. 7   a , the laser beam  106  points onto the interface  108  of the droplet  100 .  FIG. 7   a  corresponds to  FIG. 1 , where the laser beam  106  causes a symmetrical Marangoni flow. As the laser beam  106  is moved away from the center of the droplet  100  as shown in  FIG. 7   b , the Marangoni flow becomes asymmetrical, where the forces in the direction toward the laser beam  106  become greater than the opposing forces. These forces are indicated by weighted arrows. This phenomenon gives the impression as if the laser beam  106  were pulling the droplet  100  away from its original position. The droplet  100  moves along with the translatory movement of the laser beam  106  as shown in  FIG. 7   c . The movement continues until the laser beam comes to a rest or is turned off. 
     Notably, the timeline of  FIGS. 7   a  through  7   c  indicates that a lateral translation by about twice the droplet diameter can be accomplished in about 100 ms. Such a movement corresponds to several millimeters per second and is visible to the human eye. Experiments have shown that OFT can trap droplets with μN forces and translate them with speeds up to about 10 mm/s. 
       FIG. 8  shows an example of an experimental setup compatible with a standard inverted fluorescence microscope. A diode laser  118  with a power of about 150 mW and a wavelength of about 405 nm is directed horizontally through a filter cube  122  with an Excitation of about 450 nm and an Emission of about 500 nm. A semi-transparent mirror  124  reflects the laser beam  106  at an angle of about 90° upward toward the substrate  104 . A 10X objective  126  focuses the laser beam  106  to a spot size in the order of about 10 μm to about 100 μm depending on the aperture of the diode laser. Images are captured by a mounted CCD camera  120  below the semi-transparent mirror  124  for capturing light emitted by fluorescent particles. 
     The droplets  100  consist of oleic acid is dyed with solvent yellow #14. To obtain droplets of the size of fractions of millimeter, the oleic acid is mixed with about ten parts water. The mixture is then exposed to sonic vibrations to produce droplets of various diameters. 
     In the performed experiments, the focused laser incident on the liquid-liquid interface between the droplets  100  and the carrier liquid  102  creates a localized temperature increase of up to about 10K on the surface of the oil droplet  100 . A corresponding decrease in surface tension occurs with the locally raised temperature. The surface tension singularity drives a toroidal microvortex within the droplet as shown in  FIG. 1  (where two opposite fronts  110  and  112  of the microvortex are shown). OFT is driven by a temperature gradient, not absolute temperature. Therefore, with localized heating and or a low thermal conductivity fluid, one can trap and manipulate drops with temperature perturbation of less than and up to about 10K. 
     Droplets that were smaller than about 30 μm included Span 80 surfactant at a concentration of about 10% by volume. In some experiments, fluorescent particles (Magnaflux) were also added to the oleic acid for visualization. The oil-water emulsion was then placed with a pipette onto the substrate  104  composed of a glass slide  128  with a plastic ring  130  to contain the emulsion. In droplet translation experiments, the mechanical stage of the microscope, at least comprising the mirror  124 , the objective  126 , and the CCD camera  120 , is moved laterally so that the droplet  100  moves relative to the surrounding carrier fluid  102 , in this case water. While the focused laser beam  106  moved and the substrate remained stationary, the droplet  100  followed the laser beam  106 . 
     By recording movements of the fluorescent particles in the oleic acid, the Marangoni flow and the microvortex fronts  110  and  112  in the droplet  100  can be recorded. The droplet  100 , when suspended in the carrier fluid  102  is pulled vertically down towards the substrate by the Marangoni microvortex fronts  110  and  112  as shown in  FIG. 4 . The droplet  100  deforms slightly due to the flow. OFT relies on the tendency to achieve a symmetry of the microvortex fronts as illustrated in  FIGS. 5   a - 5   d ). 
     From a vertical view along the direction of the incident laser beam  106  onto the droplet  100 , the droplet  100  has a perimeter defining a projection of the droplet  100  onto a horizontal plane. If the interface  108  between the laser beam  106  and the droplet surface is near the perimeter of the droplet  110 , the microvortex fronts  110  and  112  are asymmetric so that they pull the center  116  of the droplet projection on the horizontal plane toward the laser. This allows translating droplets  100  in a two-dimensional horizontal space as shown in  FIGS. 5-7 . 
     The high force in the microNewton (μN) range allows OFT to accommodate a range of droplet sizes of about 20-1000 μm. Translational velocities up to about 10 drop diameters per second can be achieved, with a maximum speed exceeding about 10 mm/s, corresponding to holding forces in the μN range. Currently, OFT is well suited to oil droplets because their thermal conductivity is very low compared to water (about 20% of the thermal conductivity of water). Because the applied heat remains localized, it forms sharp temperature gradients and larger shear forces. But generally, this technique is also applicable to aqueous droplets suspended in oil and even to gas or vapor bubbles in a carrier liquid that may be polar or non-polar. 
     While the present invention has been described in terms of preferred embodiments, it will be understood, of course, that the invention is not limited thereto since modifications may be made to those skilled in the art, particularly in light of the foregoing teachings.