Evaporation of Concentrated Polymer Solutions Is Insensitive to Relative Humidity

A recent theory suggests that the evaporation kinetics of macromolecular solutions is insensitive to the ambient relative humidity (RH) due to the formation of a “polarization layer” of solutes at the air-solution interface. We confirm this insensitivity up to $\mathrm{RH}\approx 80\%$ in the evaporation of polyvinyl alcohol solutions from open-ended capillaries. To explain the observed drop in evaporation rate at higher RH, we need to invoke compressive stresses due to interfacial polymer gelation. Moreover, RH-insensitive evaporation sets in earlier than theory predicts, suggesting a further role for a gelled “skin.” We discuss the relevance of these observations for respiratory virus transmission via aerosols.

Figure 1

(a) Experimental schematic showing one of the five 50 mm capillaries emerging from a 30 mm section of 20 mm diameter perspex tubing glued to a microscope slide. The five capillaries increase evaporation rate, thus allowing faster experiments. (b) Mass loss $m(t)$ of pure water (${\mathrm{H}}_2\mathrm{O}$, open diamonds) and ${\mathrm{H}}_2\mathrm{O}+\mathrm{PVA}$ at $\phi =0.008$ (filled circles) solutions at $\mathrm{RH}=50\%$ and $T=291\mathrm{K}$. Inset: time exponents $\beta$ of a power-law fit to the late-time $m(t)$ for PVA solutions at different RH. (c) PVA $m(t)$ at different RH plotted against time $t$. Inset PVA $m(t)$ versus $t^{1/2}$. Dashed lines are linear fits at long times, after a transient period indicated by the dotted line where $t>300\min$ or $t^{1/2}>15{\min }^{1/2}$. (d) Shaded triangle represents the mass loss rate of pure water, ${\alpha }_0=\dot{m}(t)$, normalized to the value at $\mathrm{RH}=25\%$; Open triangle represents the same quantity for 0.9% ($\mathrm{w}/\mathrm{w}$) NaCl solutions; Shaded circle represents the slope of the linear portions in the inset of part (c) for $\phi =0.008$ PVA solutions, $\mathit{d}m(t)/\mathit{d}{t}^{1/2}=(2\sqrt{D_0}\rho A)\alpha$, normalized to the value at $\mathrm{RH}=25\%$.

Figure 2

Comparison of the measured evaporation prefactor $\alpha$ as a function of RH (Shaded circle, with error bars giving the standard deviation) with theoretical predictions [11] for constant polymer diffusivity and a water activity $a(\phi )$ without elasticity, Eq. (4) (dashed line), and with elasticity, Eq. (6) (full line).

Figure 3

Bright-field image of the polarization layer at the water-air interface at the end ($t\sim {10}^3\min$) of a typical experiment at $\mathrm{RH}=50\%$.

Figure 4

The dependence of evaporation rate on time plotted on log-log scales. Dotted lines represent for early times the dilute evaporation regime, Eq. (1), and for long times the diffusion limited evaporation regime, Eq. (2) (with $f=1$), the transition point is taken as the intercept.