Wednesday, 27 June 2007 - 9:40 AM
Clayton 119
359

A Generalized Hertzian Model for the Cracking of Thin Latex Films Saturated With Fluid

William B. Russel and Ning Wu. Princeton University, Princeton, NJ

The concentration of a thin film of a stable colloidal dispersion increases as water evaporates until the particles eventually reach a random or ordered close packing. Further water evaporation generates a negative capillary pressure that puts the film in tension. If the process temperature is below the glass transition temperature of the elastic particles, the latex film beyond a critical thickness will eventually crack. We develop a generalized model to understand this question of cracking. We first construct a constitutive equation relating the stress to the strain with the assumption of Hertzian contact between colloidal particles. Then, employing a thin film approximation, we are able to reduce the three-dimensional problem into two dimensions and calculate the relaxation of stress fields upon opening of a crack. Based on the well-known Griffith's energy criterion (by equating the recovery of elastic energy to surface energy), the theory predicts critical capillary pressures necessary for opening of a single infinite crack, a finite isolated crack, parallel cracks, and intersecting cracks, respectively. The accompanying crack spacings are also predicted and they decrease with increasing capillary pressures. Coupling the critical capillary pressure for cracking with the maximum capillary pressure sustainable with the air-water interface at the surface of the film then yields a critical film thickness below which cracking will not occur. Finally, the comparison between our theoretical predictions and experimental results will be discussed briefly.