MSE4: Mathematical modelling of drying colloidal suspensions

Project completed September 30, 2011; Project Report

The drying of soils and colloidal suspensions plays an important role in many agricultural and technological applications. The formation of surface crusts in semi-arid regions can reduce water infiltration and increase erosion, and the development of cracks affects the permeability with important implications for water retention. Cracks in thin colloidal films largely determine the final properties of paints, adhesives and ceramic films for electronics. These commonly observed phenomena nevertheless present many outstanding scientific and technological challenges.  Mathematical models of chemical and porosity changes in drying clays will lead to unique insights into crust formation, while predictions of critical operating parameters for crack initiation will be useful in optimizing a range of industrial processes.

The main aim of this project is to develop a mathematical model of a drying colloidal suspension capable of predicting the chemical and porosity variations in the boundary layer below the air-clay interface, leading to conditions for coagulation and crust formation; critical conditions for the formation of cracks at the drying interface will also be explored. The specific goals are to  

(a) Develop a colloid physics based model of a drying colloidal suspension.
(b) Solve the model using analytical and numerical techniques.
(c) Analyze mathematically the morphological stability of the drying interface.
(d) Utilize upscaling methods to model the mixed-phase region which develops after the formation of cracks.

Our approach to the problem is based on a novel coupling of poroelasticity theory and colloid physics. During the drying of clays and suspensions, the desiccation process causes a portion of the suspension near the air interface to consolidate into a connected porous matrix. Fluid transport in the porous medium is governed by the equations of poroelasticity, while the equations of colloid physics govern processes in the suspension. We have derived new equations describing this process, including unique boundary conditions coupling the two regions, yielding a moving-boundary model of the concentration and stress profiles during drying. A tensile stress can develop in the poroelastic region, and this stress provides the driving force for crack formation. We are currently engaged in solving the mathematical equations describing the stress development, obtaining new analytical and numerical results, in order to predict the extent of the porous region and critical conditions for crack initiation.