FIG. 2.

Effect of the solute-induced water vapor-pressure reduction on the drying process in the limit of an infinitely large internal water diffusion constant $D_w^l\to \infty$. The solute concentration dependence of evaporation cooling is neglected (i.e., the results are obtained using ${\psi }_c={\psi }_c^{{\Phi }_0\to 0}$), the liquid solution is assumed ideal ($\gamma =1$), and data are shown for initial radius $R_0=50\hspace{0.17em}\mu \mathrm{m}$ and relative humidity $RH=0.5$. Panel (a) shows the variation of the droplet radius $R$ with time $t$ for two different initial solute volume fractions of ${\Phi }_0=0.001$ (main figure) and ${\Phi }_0=0.01$ (inset). The solid red line indicates the results obtained from the numerical solution of Eq. (3). The solid blue and the broken green lines indicate the results obtained from Eq. (6), which is an approximate solution of Eq. (3), with and without considering the logarithmic term that reflects the solute-induced water vapor-pressure reduction. Panel (b) shows the evaporation time ${\overline{\tau }}_{ev,s}$ as a function of the initial solute volume fraction ${\Phi }_0$. The solid red line indicates the results calculated from the numerical solution of Eqs. (3) and (9). The solid blue line shows the results from Eq. (10), which is an approximate solution of Eqs. (3) and (9). Green and gray broken lines indicate the non-logarithmic and the logarithmic contributions to the evaporation time, which are obtained from Eqs. (7) and (11), respectively.