Temperature-driven motion of a wetting layer.

The wetting layer formed by a phase-separated binary liquid mixture in contact with a glass substrate is observed to have a large nonequilibrium response in thickness to small temperature perturbations. An independent theoretical and physical picture is developed, which also provides a direct means of measuring the forces responsible for wetting and their effect on the dynamics of diffusion-limited interfacial motion. As an example, the curvature and anharmonicity of the minimum in the effective interface potential are found. Disciplines Physical Sciences and Mathematics | Physics Comments At the time of publication, author Douglas J. Durian was affiliated with Cornell University. Currently, he is a faculty member at the Physics Department at the University of Pennsylvania. This journal article is available at ScholarlyCommons: https://repository.upenn.edu/physics_papers/637 PHYSICAL REVIEW A VOLUME 40, NUMBER 9 NOVEMBER 1, 1989 Temperature-driven motion of a wetting layer Douglas J. Durian* and Carl Franck Laboratory ofAtomic and Solid State Physics and Materials Science Center, Cornell University, Ithaca, New York 14853-2501 (Received 16 March 1989) The wetting layer formed by a phase-separated binary liquid mixture in contact with a glass substrate is observed to have a large nonequilibrium response in thickness to small temperature perturbations. An independent theoretical and physical picture is developed, which also provides a direct means of measuring the forces responsible for wetting and their effect on the dynamics of diffusionlimited interfacial motion. As an example, the curvature and anharmonicity of the minimum in the effective interface potential are found. Consider a phase-separated binary liquid mixture in contact with the horizontal solid substrate constituting the bottom of its container. With suitable choice of liquids and substrate, a thick wetting layer of the upper phase can intrude between the lower phase and the substrate. The physics of wetting phenomena, such as this, is very rich and has attracted much attention in the past several years. ' Questions motivating recent theoretical work include what determines the thickness of a wetting layer, ' and how does a wetting layer attain its equilibrium thickness. ' For the geometry under consideration, the answer to the former depends on the balance between the substrate-liquid interaction, which favors a thick layer, and gravity, which favors a thin layer. A construct known as the effective interface potential V(l) includes both effects. It is the free energy per unit area for the configuration with wetting layer of thickness I; its minimum determines the equilibrium thickness. The issues raised in the latter question are familiar from diverse examples of interfacial dynamics. Neither question has yet received a definitive, or even adequate, experimental attention. In this paper, we describe a striking method of perturbing the wetting layer, of interest in its own right, and develop a theoretical model to exploit it for experimental investigation of the above questions. We studied a phase-separated critical-composition mixture of carbon disulfide plus nitromethane in contact with a borosilicate glass substrate using a reflectivity technique described earlier. Since wetting behavior can be very sensitive to experimental detail, the following points are noteworthy. Our sample ce11 design follows Ref. 7, but with the thermistor can truncated above the mixture. Standard cleaning procedures were used for both stainless-steel and glass parts. The sample cell was assembled in air, vacuum baked, and filled with liquids in an Ar atmosphere, sealed with a stainless-steel gasket, then installed in a thermostat having rms thermal fluctuations of less than 0.3 mK, and no drift, over 2 h. The dimensions were such that each bulk phase had vertical height L =0.6 cm, and the thermal relaxation time was less than 4 min. The critical temperature below which our liquid mixture phase separated was T, =63.6 C and had an initial drift of +15 mK/day. After one month, the drift settled to +5 mK/day and the liquids were slightly yellow. Reflectivity of an s-polarized He-Ne laser beam (0.5 mW, 1 mm diam. incident 74. 1' from normal) was converted to wetting layer thickness by assuming that the layer is a homogeneous dielectric film between two bulk media, all with known indices of refraction. The wetting layers were uniform as seen by eye and by measuring different portions of the surface. Because of the T, drift and the unknown role of temperature gradients, we cannot be certain that the observed steadystate wetting-layer thickness represents true thermodynamic equilibrium. Reference 7 showed that a thick wetting layer of the upper, nitromethane-rich, phase will intrude between the glass substrate and the heavier, carbon disulfide —rich, phase. To prepare a homogeneous layer, we raised the temperature to the desired point, stirred gently for several hours, stopped stirring, then waited more than 8 h until a steady-state thickness was established. This apparent equilibrium thickness was independent of temperature to within experimental resolution, +0.5%, over the range studied here: 15.3+0.2 K below T, . Even so, a temperature increase (decrease) generally results in a tern porary decrease (increase) in wetting-layer thickness; this has been known but not understood for some time. ' ' Figure 1 shows how very sensitive the wetting layer is to temperature conditions: Tiny perturbations, as small as 2.5 mK at 15 K away from T„produce a response in wetting-layer thickness of several percent. Other data, not shown, indicate that the response to temperature jumps of opposite direction is symmetric for jumps smaller than about 1 mK; the perturbations of Fig. 1 can be called large in this sense. At the very least, we warn experimentalists wishing to measure equilibrium-wetting phenomena: Precise temperature control is crucial. The following theoretical model can predict such sensitivity to small temperature perturbations. Lipowsky and Huse (LH) studied the motion of a wetting layer when the system is otherwise equilibrated; here we consider the behavior of a wetting layer when the bulk liquids are also out of equilibrium. Suppose that the liquid mixture is 40 522