Buoyancy-driven dispersion in confined drying of liquid binary mixtures

Abstract

We investigate the impact of buoyancy on the solute mass transport in an evaporating liquid mixture (nonvolatile solute + solvent) confined in a slit perpendicular to the gravity. Solvent evaporation at one end of the slit induces a solute concentration gradient which in turn drives free convection due to the difference between the densities of the solutes and the solvent. From the complete model coupling mass transport and hydrodynamics, we first use a standard Taylor-like approach to derive a one dimensional non-linear advection-dispersion equation describing the solute concentration process for a dilute mixture. We then perform a complete analysis of the expected regimes using both scaling analysis and asymptotic solutions of this equation. The validity of this approach is confirmed using a thorough comparison with the numerical resolution of both the complete model and the 1D advection-dispersion equation. Our results show that buoyancy-driven free convection always impacts solute mass transport at long time scales, dispersing solutes in a steadily increasing length scale along the slit. Beyond this confined drying configuration, our work also provides an easy way for evaluating the relevance of buoyancy on mass transport in any other microfluidic configuration involving concentration gradients.

Drying-induced back flow of colloidal suspensions confined in thin unidirectional drying cells

“…Particles were condensed due to drying but they were treated as suspended and transported by ow in the analysis because the drying suspension was very dilute. 21 Conversely, some particles clearly packed and xed at the drying front in our study. Packing of particles decreases the number of suspended particles in a drying cell and this would cause such different result.…”

“…We note that they also analyzed a width of diffusive layer in which there was a concentration gradient of solute. 21 This diffusive layer would correspond to the back-ow region in this study. However, the diffusive layer was predicted to grow as drying proceeded and a width of the layer was proportional to t 2/5 , in which t is drying time.…”

“…In this section, we consider a mathematical model to understand important factors that dominantly determine a width of the back-ow region w. Before starting mathematical modeling, we refer a very recent study on buoyancy-driven circulation ow on solutal mass transport by Salmon and Doumenc. 21 They studied drying of dilute binary solution of a volatile solvent and involatile solute analytically. They summarized four different regimes for solutal mass transport, two diffusive regimes and two dispersive regimes.…”

“…When PeRa » a 0.5 , solutal mass transport is in the dispersive regimes, in which a is a characteristic constant equal to 362 880. 21 According to the denition in ref. 21, Pe ¼ V evap H/D and Ra ¼ r 0 4 sus_0 gH 3 / (mD), in which V evap is an evaporation rate, H is a gap height of a drying cell, D is a diffusion constant for suspended particles, r 0 is a density difference between silica particles and water, g is the gravitational acceleration and m is a viscosity of water, respectively.…”

“…Because of the thin geometry, it has been assumed that suspension ow is almost ideal. However, recent studies have revealed that vertical ows are induced spontaneously, even in a thin liquid layer owing to drying-induced increase in the solute concentration [18][19][20][21] and in the concentration of suspended particles. 22 These examples suggest that ow is complex, even in a drying thin liquid layer between parallel plates.…”