(159e) Dynamics of Cracking in Drying Saturated Colloidal Film

A successful prediction of the response of poroelastic material to external forces depends critically on the use of appropriate constitutive relation for the material. The most commonly used stress-strain relation that captures the behavior of poroelastic materials saturated with a liquid is that proposed by M A Biot [Biot, J. Appl. Phys. , 1941, 12, 155-164]. It is a linear theory akin to the generalised Hooke's law containing material constants such as the effective bulk and shear modulus of the porous material. However, the effective elastic coefficients are not known a priori and need to be determined either via separate experiments or by fitting predictions with measurements. The main cause for this drawback is that Biot's theory does not account for the microstructural details of the system. This limitation in Biot's model can be overcome by utilising the constitutive relation proposed by Russel and coworkers [Russel et al. , Langmuir, 2008, 1721-1730] for the case of colloidal packings. We show that in the linear limit, the constitutive relation proposed by Russel and coworkers is equivalent to that of Biot. The elastic coefficients obtained from such a linearisation are related to the micro-structural details of the packing such as the particle modulus, the packing concentration and the nature of packing, thereby enabling a more effective utilisation of Biot's model for problems in the linear limit. The derivation ignores surface forces between the particles, which makes the results applicable to particles whose sizes are beyond the colloidal range. We solve the problem of crack propagation in a saturated colloidal packing using the Russel’s model. While a number of studies have focused on deriving the critical conditions for cracking, few have investigated the dynamics of cracking. In this work, we investigate the dynamics of cracking by developing an analytical theory for a propagating crack in a colloidal film saturated with liquid. The theory includes the effects of particle size and modulus, and packing characteristics to yield the asymptotic solution of stress, displacement, pressure fields and crack-tip velocity. The stress and the pressure field show inverse of square root singularity near the crack tip, same as observed for brittle solids. The speed of the crack is predicted to be lower by an order of magnitude compared to that obtained for a homogeneous, non-porous brittle film. The predictions are then compared with observations from recent experiments.