Cavitation in Drying Droplets of Soft Matter Solutions

When a droplet of a soft matter solution is dried, cavities are often formed in the droplet, giving a hollow sphere in the end. A theoretical model is given for this phenomenon. It is shown that the formation of a gel-like layer (skin layer), which has a finite shear modulus, is essential for the phenomenon to take place. The condition for cavity formation (how it depends on the shear modulus and thickness of the skin layer), and the variation of the droplet volume and cavity volume after the cavity formation are examined.

Figure 1

Behaviors of a droplet of a soft matter solution in drying. See the text for explanation.

Figure 2

(a) Free energy of the system plotted as a function of reduced cavity volume $v_c=(r_c/r_0{)}^3$ for various weight losses $\mathrm{\Delta }W$. (b) Reduced cavity volume $v_c=V_c/V_0$ plotted as a function of reduced weight loss $\mathrm{\Delta }W/W_0$.

Figure 3

Reduced apparent volume of the droplet, $v_d=V_d/V_0=(r_d/r_0{)}^3$, and that of the cavity, $v_c=V_c/V_0=(r_c/r_0{)}^3$, plotted against the reduced weight loss of the droplet $\mathrm{\Delta }W/W_0$. The curves are obtained with the use of Eq. (10) for ${\ell }_e/h_0=0.1$, $\mathrm{\Delta }p/p_e=0$, $n_0{v}_m=10^{-2}$, and $\chi =-0.1$.

Figure 4

(a) Critical cavity volume $v_c^{*}$ plotted as a function of ${\ell }_e/h_0$ for various values of $\mathrm{\Delta }p/p_e$. Results of the linear theory are shown by the dashed lines. (b) Critical weight loss $\mathrm{\Delta }{W}^{*}$ plotted as a function of ${\ell }_e/h_0$. (c) Critical cavity volume $v_c^{*}$ plotted as a function of $\mathrm{\Delta }p/p_e$. (d) Critical weight loss $\mathrm{\Delta }{W}^{*}$ plotted as a function of $\mathrm{\Delta }p/p_e$. Parameters used in the nonlinear calculations are $\chi =-0.1$ and $n_0{v}_m=10^{-2}$.