Simple Model of Skin Formation Caused by Solvent Evaporation in Polymer Solutions

A simple model is proposed for the skin formation in the evaporation process of a polymer solution at a free surface. In this model the skin is regarded as a gel phase formed near the free surface, and the dynamics is described by a diffusion equation for the polymer concentration with moving boundaries. The equation is solved both analytically and numerically. It is shown that the skin phase appears when the evaporation rate is high or when the initial polymer concentration is high. An analytical expression is given for the criterion for the skin phase to be formed.

Figure 1

Schematic pictures of profiles of $\varphi$ in the three regimes: (a) In regime I, ${\varphi }_0<{\varphi }_h<{\varphi }_g$, a polymer rich region with a characteristic length $b$ is formed near the free surface. (b) In regime II, ${\varphi }_g\le {\varphi }_h$, a skin layer ($h_g<z<h$) is formed. (c) In regime III, the whole system forms a skin.

Figure 2

Space-time plot of $\varphi (z,t)$ obtained by the numerical simulation of Eqs. (1, 4, 5, 6) for $\mathrm{Pe}=10$.

Figure 3

Plots of $h(t)$ (open circles) and $h_g(t)$ (solid circles) as functions of $t$ using the data obtained by the numerical simulation for $\mathrm{Pe}=10$. The inset shows the comparison with the analytical expressions Eq. (15) for $h(t)$ (solid line) and Eq. (19) for $h_g(t)$ (dashed line).

Figure 4

Space-time plot of $\varphi (z,t)$ obtained by the numerical simulation of Eqs. (1, 4, 5, 6) or $\mathrm{Pe}=1$.

Figure 5

Diagram of skin formation based on Eq. (21). For the parameters above the solid line, well-structured skin layers are formed.