Confined directional drying of a colloidal dispersion: kinetic modeling

We derive a model to describe the dynamics of confined directional drying of a colloidal dispersion. In such experiments, a dispersion of rigid colloids is confined in a capillary tube or a Hele-Shaw cell. Solvent evaporation from the open end accumulates the particles at the tip up to the formation of a porous packing that invades the cell at a rate . Our model based on a classical description of fluid mechanics and capillary phenomena, predicts different regimes for the growth of the consolidated packing, l versus t. At early times, the evaporation rate is constant and the growth is linear, l ∝ t. At longer times, the evaporation rate decreases and the consolidated packing grows as . This slowdown is either related to the recession of the drying interface within the packing thus adding a resistance to evaporation (capillary-limited regime), or to the Kelvin effect which decreases the partial pressure of water at the drying interface (flow-limited regime). We illustrate these results with numerical relations describing hard spheres, showing that these regimes are a priori experimentally observable. Beyond this description of the confined directional drying of colloidal dispersions, our results also highlight the importance of relative humidity control in such experiments.