| The flow of liquid through foam, known as foam drainage, is an essential issue in many technological applications. In the last half century, attempts to develop an understanding of drainage in foams through both theory and experiment resulted in a simple model of foam drainage. Recent experimental efforts, however, contradicted this simple model and a new model was proposed. There is currently an active effort underway to develop a fundamental understanding of drainage in foams. The goal of this dissertation is to develop bubble-scale numerical simulations to assist in basic understandings of foam drainage. In particular, the dependence of the foam permeability on boundary conditions and system parameters is addressed in detail.; Numerical simulations of flow through a channel with a Plateau border cross-section with no-slip boundary conditions are compared with simulations of flow through a similar channel that instead has surface tension gradients. Although these two flows scale similarly with system length scales, the resulting permeabilities vary widely.; A three-dimensional boundary integral algorithm on curved surfaces that is accurate to quadratic order is developed. This algorithm is used to simulate three-dimensional flow through foam. Flows with no-slip and with free surface boundary conditions are calculated and analyzed. |
