An experimental test of the scaling prediction for the spatial distribution of water during the drying of colloidal films

Abstract

A Peclet number, Pe, for the drying of colloidal films can be used as a predictor of the uniformity of water concentration in the direction normal to the film. Uniform drying is predicted to occur when Pe < 1, whereas with $\textit{Pe}>1$, a layer of packed particles is expected to develop above a more dilute layer. Routh and Zimmerman have more recently proposed that the particle concentration gradient between the packed and dilute layers, $d \phi _{p} / d \textit{z}$, will scale as $\textit{Pe}^{1/2}$. Here, this scaling relation is tested experimentally with magnetic resonance profiling data obtained from waterborne colloidal films dried under conditions to yield a range of Pe. It is found that $d\phi_{p}/d\textit{z}$ increases with Pe but scales as $\textit{Pe}^{0.8}$. This disagreement with the prediction can be attributed to an underestimate of Pe when there are greater non-uniformities of drying, because of an unquantified slowing down of the evaporation rate.