TY - JOUR
T1 - A theory of the effective yield stress of foam in porous media
T2 - The motion of a soap film traversing a three-dimensional pore
AU - Cox, S. J.
AU - Neethling, S.
AU - Rossen, W. R.
AU - Schleifenbaum, W.
AU - Schmidt-Wellenburg, P.
AU - Cilliers, J. J.
N1 - Funding Information:
S.J.C. wishes to thank K. Brakke for assistance with the Surface Evolver. S.J.C., S.N., W.R.R. and J.J.C. acknowledge support through a grant from the Royal Society and the Royal Irish Academy. WRR acknowledges support of the US Department of Energy, through contract DE-FC26-01BC15318, and a Faculty Research Assignment from The University of Texas at Austin.
Copyright:
Copyright 2017 Elsevier B.V., All rights reserved.
PY - 2004/9/24
Y1 - 2004/9/24
N2 - The effective yield stress of foam in porous media depends on the capillary resistance of the soap films between bubbles, or lamellae, to forward movement. This resistance depends in turn on the shapes lamellae take as they move across pores. Even in idealized, radially symmetric pores, lamellae spontaneously jump to asymmetric shapes in their drive to minimize their surface area. These shapes affect the overall capillary resistance to foam movement. Earlier theoretical study of quasi-static lamella movement in two dimensions (2D) is extended here to three dimensions (3D) using the Surface Evolver computer program. Whereas in 2D, the lamella can take flat, asymmetric shapes in the pore body; in 3D, it can take a sequence of saddle-shapes of increasingly negative mean curvature as the trailing edge of the lamella approaches the middle of the pore. The results based on 2D lamellae are altered in detail but not in essence: the asymmetric jump increases the capillary resistance to foam movement, and for small bubbles in small pores, the minimum pressure gradient required to drive gas flow in foam is substantial.
AB - The effective yield stress of foam in porous media depends on the capillary resistance of the soap films between bubbles, or lamellae, to forward movement. This resistance depends in turn on the shapes lamellae take as they move across pores. Even in idealized, radially symmetric pores, lamellae spontaneously jump to asymmetric shapes in their drive to minimize their surface area. These shapes affect the overall capillary resistance to foam movement. Earlier theoretical study of quasi-static lamella movement in two dimensions (2D) is extended here to three dimensions (3D) using the Surface Evolver computer program. Whereas in 2D, the lamella can take flat, asymmetric shapes in the pore body; in 3D, it can take a sequence of saddle-shapes of increasingly negative mean curvature as the trailing edge of the lamella approaches the middle of the pore. The results based on 2D lamellae are altered in detail but not in essence: the asymmetric jump increases the capillary resistance to foam movement, and for small bubbles in small pores, the minimum pressure gradient required to drive gas flow in foam is substantial.
KW - Foam
KW - Minimal surfaces
KW - Porous media
KW - Surface Evolver
KW - Yield stress
UR - http://www.scopus.com/inward/record.url?scp=4644278204&partnerID=8YFLogxK
U2 - 10.1016/j.colsurfa.2004.07.004
DO - 10.1016/j.colsurfa.2004.07.004
M3 - Article
AN - SCOPUS:4644278204
SN - 0927-7757
VL - 245
SP - 143
EP - 151
JO - Colloids and Surfaces A: Physicochemical and Engineering Aspects
JF - Colloids and Surfaces A: Physicochemical and Engineering Aspects
IS - 1-3
ER -