(621b) Three-Dimensional Micro-Scale Model for Convective Drying

The sol-gel route can produce highly porous solid aggregates with large surface area, which are usually dried under supercritical conditions. Convective drying is not yet suited to produce such dry gels. In the small pores, the liquid-gas interface causes high capillary stress, which results in mechanical damage of the commonly very fragile solid. However, a better understanding of micro-scale phenomena inducing shrinkage, breakage or cracks during convective drying is expected to lead to an extended range of applications for this inexpensive and safe process.

We propose a 3D micro-scale model for convective drying, which resolves the three phases (solid, liquid, and gas). The solid phase is described as an aggregate of rigid primary particles, which are accelerated by capillary and contact forces. The diameter of the primary particles also determines the characteristic length scale of the problem, which is ~10^-8 m. At this length scale, gravitational forces are negligible compared to surface tension forces and a continuum description is used for the fluid phases. A quasi-steady state approach is used, where the solid and liquid phases are allowed to relax to equilibrium (small time scale) in each evaporation step (large time scale).

The full space containing all three phases is discretized with a stationary grid of cubic cells, where phase distributions are described in terms of cell volume fractions. A finite difference method is used to compute the partial pressure of vapor in the gas phase at quasi-steady state; local evaporation rates at the liquid-gas interface are computed from the solution, and liquid volume fractions in interface cells are reduced accordingly. During relaxation, the liquid redistribution is governed by volume conserving mean curvature flow, with an additional contact angle condition at three-phase contact lines. The volume-of-fluid method is used to track the liquid-gas interface. The implicit description of the interface allows for sudden topological changes such as splitting and merging of liquid clusters over time. The capillary pressure in each liquid cluster is computed from the equilibrium curvature. Capillary forces on each primary particle of the solid phase are computed by integrating the capillary pressure over the wet area and the surface tension along the three-phase contact line. These forces are then passed as external loads to a discrete element method, which computes the stress in inter-particular contacts, and may predict micro cracks as well as compute the motion of the solid phase.

Numerical results of the liquid distribution over time are compared to experimental data from X-ray microtomography measurements performed on highly porous glass bead assemblies. In a one-way coupling approach, cracks and damage in the solid phase over time is also shown. Future work will include the full two-way coupling, which allows for particle motion and can thus describe shrinkage. Furthermore, rate-dependent effects in liquid distribution and non-uniform shrinkage will be addressed with macroscopic gradients in the liquid pressure.

The simulation tool presented here is set out to examine the influence of aggregate structure and parameters such as bond strength, surface tension and equilibrium contact angle, as well as of different drying conditions, on the expected shrinkage and damage in the gel during convective drying.