Surface tension gradient drying

But the simple no-flow picture of equation 4 can no longer hold in view of equations 7a and 7b. At the liquid-vapor boundary, the viscous shear force must balance the force imposed by surface tension gradients, rjdu/dz = da/dx (z = h). This boundary condition leads to a linear flow profile toward the drying line,... 

Arguably the most important application of sol-gel technology is the preparation of films to exploit their optical or electronic properties or their chemical or mechanical resistance. Hurd (Sandia National Laboratories) examines the physics of film deposition by dip coating, elucidating the factors that control the thickness and structure of the film. Direct observation of the deposition process reveals the kinetics of the drying process and the existence of flows driven by surface tension gradients when binary solvents are used. Extensive discussion of the preparation of, and applications for, such films are presented in references 4 and 5. 

Marangoni effects can be encountered in both single- and multicomponent liquid systems. In a pure liquid, surface tension gradients result from differences in temperature (or evaporation rate) from one point to another in the system. It is generally found that an increase in temperature lowers ctlv so that where hot spots occur, liquid flows away to cooler regions of the liquid (Fig. 6.13 ). The result of such a phenomenon can be the formation of dimples in a surface that dries or solidifies under uneven temperature conditions. 

The foam-dilatational viscosity, K, arises because of two primary mechanisms (37) (1) viscous flow within the thin films, and (2) interfacial tension gradients acting along the foam bubble surfaces. The effect of interfacial tension gradients is to increase the foam viscosity as they impede flow near the surfaces of the thin foam films by contributing to a larger film stress. As in the wet foam (eq 6), the foam dilatational viscosity for a dry foam, K, is inversely proportional to film thickness as well (eq 9). 

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