Tortuosity of Aligned Channels in Alumina Membranes Produced by Vacuum-Induced Surface Directional Freezing

Vacuum-induced surface freezing of colloidal alumina was used to produce membranes that have elongated, aligned channels and, hence, are tortuous in the direction perpendicular to ice crystal growth. The effective tortuosity of the membranes was measured by steady-state diffusion of a solute, methylene blue. The resulting diffusion profiles show an initial step-increase in amount of dye reaching the acceptor that is caused by capillarity drawing the donor solution through any non-wetted channels in the membrane. This is followed by a linear steady-state phase whose flux is proportional to dye concentration in the donor and inversely proportional to the colloid's volume fraction of dispersed phase. From the steady-state flux, the effective tortuosity, τ* = (α/τ)-1, was calculated. This is the reciprocal quotient of the reduced available area for diffusion within the membrane, α = A*/A, where A* is the available area and A is the cross-sectional area of the membrane, and the increased mean diffusional path length, i.e., tortuosity = L * / L , where L* is the mean path length and L is the membrane thickness. The values of τ* lie in the range of 2-38 and increase as the volume fraction of dispersed phase is larger. This latter effect indicates that τ* > 1 results, to a larger extent, from the reduced available diffusion area, α, than from the lengthened pathway, τ, in these aligned porous membranes.