Drops that buckle

T he collapse of structures under the effect of their weight or other mechanical stress is of interest in many domains of mechanical and civil engineering [1], Recently such phe­ nomena have also been approached theoretically in the physics of instabilities dealing with shell and plate geometries [2]. When a structure, subjected to compression, displays large displace­ ments transverse to the load, it is said to buckle [3]. A simple demonstration can be obtained by pressing the opposite edges of a flat sheet towards each other. This instability can be found in various systems, particularly when the volume enclosed with­ in a thin and elastic envelope is made to decrease: collapse of concrete domes, vessels, etc. In general, for small volume varia­ tions the shape of the envelope remains the same (the flat sheet is kept plane). However for variations larger than a threshold value, deformations leading to variations of curvature can take place (the flat sheet bends). In this case, the inner volume can become very small with the outer surface displaying large wrinkles. It has been recently shown that the buckling process is not only relevant to macroscopic systems that can be described through classical mechanics approaches. It is also important in a large variety of systems displaying a broad range of characteristic length scales: for example, amphiphilic or biological polymerized membranes or the buckling-driven delamination of metallic films, or morphology of certain leaves of plants, to name some. The present work deals with the drying of sessile drops (drops deposited upon a solid surface) of a polymer solution which is controlled by the diffusion of solvent vapour in air. The drying process first leads to the formation of a superficial rigid skin to be discussed below. In such systems, the buckling process results from complex spatial and temporal evolutions leading thus to var­ ious unexpected final shapes of the drops. For instance, the diagram in Figure 1 displays the top views of the drop shapes observed at the final stage of the drying process under different conditions (different initial contact angles of the drop onto the substrate and different relative humidity of the surroundings of the sessile drop). The experiments were carried out using solutions of Dextran, a water-soluble polysaccharide, at high concentration ωp = 0.40g/g. At room temperature, the pure dry polymer is glassy and mechanically hard (its glass transition temperature is 220 ± 10°C). For a solution, the glass transition temperature ranges between that of the pure solvent and that of the pure polymer; it increases continuously with the polymer concentration. At a given inter­ mediate temperature, there will be a concentration ωpg such that the solution is fluid when ωp< ωpg and glassy when wp > ωpg. Also, during the drying process due to solvent removal, the polymer concentration increases with time and the solution, which is ini­ tially fluid, becomes glassy. The geometry considered here is that of a drop which is deposited onto a glass slide; the wetting prop­ erties of the substrates can be modified in order to vary the initial contact angle, θo. The setup is placed inside a glove box inside which the relative humidity, RH, is controlled. Following solvent