Confined directional drying of a colloidal dispersion: kinetic modeling

Abstract

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...

Directional drying of a colloidal dispersion: quantitative description with water potential measurements using water clusters in a poly(dimethylsiloxane) microfluidic chip

“…This relation can be derived strictly from convection-diffusion models 40 (see also ref. 24 discussing its validity for a non constant evaporation rate), and includes the variation of height h → h d at the compaction front. This relation is consistent with the linear relationship observed between the compaction front x c and the position of the meniscus x m , see Fig.…”

“…In this capillary-limited regime, i.e., c cap 4 c ext , the quantitative prediction of the evaporation rate remains an open question. All theoretical works [24][25][26] consider a one-dimensional description of directional drying. These models suggest that desaturation takes place from the tip of the solid at x = 0, and over a very small length due to the strong resistance to mass transfer by vapour diffusion through the porous dry layer.…”

“…22,23 Despite all these studies, the evaporation kinetics, J vs. t, and the growth of the porous solid, x c vs. t, remain open questions to this day. 24 In the case of nanoparticles with typical radii a r 20 nm, experiments have shown that the solid layer first grows linearly, x c B t, and then follows a square root growth x c B t 0.5 indicating a decrease of the evaporation-induced flow rate J. 6,11,14,25 Most theoretical works suggest that this slowdown is actually due to the minute recession of the evaporation interface within the porous solid, adding a high resistance to evaporation linked to the diffusion of water vapour in the dry porous layer, the so-called capillary-limited regime.…”

“…6,11,14,25 Most theoretical works suggest that this slowdown is actually due to the minute recession of the evaporation interface within the porous solid, adding a high resistance to evaporation linked to the diffusion of water vapour in the dry porous layer, the so-called capillary-limited regime. 7,[24][25][26] For very small colloids (a o 10 nm), the water pore pressure at the evaporation interface can decrease down to values that affect the partial pressure of water in the gas phase, the so-called Kelvin effect. 27 In this flow-limited regime, there is no resistance to evaporation in the gas phase, and the slowdown is explained by the increasing resistance due to the flow through the growing porous solid.…”

“…27 In this flow-limited regime, there is no resistance to evaporation in the gas phase, and the slowdown is explained by the increasing resistance due to the flow through the growing porous solid. 24 To date, no work has been done to differentiate experimentally between these two regimes (except ref. 28, but for drying-induced permeation in nanoporous media), nor has quantitative modelling been carried out, due to the lack of data describing the porous solid, in particular its hydraulic permeability κ (m 2 ).…”