TY - JOUR

T1 - Diffusion of curvature on a sheared semi-infinite film

AU - Satomi, Ryo

AU - Grassia, Paul

AU - Cox, S.

AU - Mishuris, G.

AU - Lue, Leo

N1 - Satomi, R., Grassia, P., Cox, S., Mishuris, G., Lue, L. (2013). Diffusion of curvature on a sheared semi-infinite film. Proceedings of the Royal Society A: Mathematical, Physical & Engineering Sciences, 469 (2159)

PY - 2013/9/11

Y1 - 2013/9/11

N2 - The viscous frothmodel is used to study the evolution of a long and initially straight soap film which is sheared by moving its endpoint at a constant velocity in a direction perpendicular to the initial film orientation. Film elements are thereby set into motion as a result of the shear, and the film curves. The simple scenario described here enables an analysis of the transport of curvature along the film, which is important in foam rheology, in particular for energyrelaxing 'topological transformations'. Curvature is shown to be transported diffusively along films, with an effective diffusivity scaling as the ratio of film tension to the viscous froth drag coefficient. Computed (finite-length) film shapes at different times are found to approximate well to the semiinfinite film and are observed to collapse with distances rescaled by the square root of time. The tangent to the film at the endpoint reorients so as to make a very small angle with the line along which the film endpoint is dragged, and this angle decays roughly exponentially in time. The computed results are described in terms of a simple asymptotic solution corresponding to an infinite film that initially contains a right-angled corner.

AB - The viscous frothmodel is used to study the evolution of a long and initially straight soap film which is sheared by moving its endpoint at a constant velocity in a direction perpendicular to the initial film orientation. Film elements are thereby set into motion as a result of the shear, and the film curves. The simple scenario described here enables an analysis of the transport of curvature along the film, which is important in foam rheology, in particular for energyrelaxing 'topological transformations'. Curvature is shown to be transported diffusively along films, with an effective diffusivity scaling as the ratio of film tension to the viscous froth drag coefficient. Computed (finite-length) film shapes at different times are found to approximate well to the semiinfinite film and are observed to collapse with distances rescaled by the square root of time. The tangent to the film at the endpoint reorients so as to make a very small angle with the line along which the film endpoint is dragged, and this angle decays roughly exponentially in time. The computed results are described in terms of a simple asymptotic solution corresponding to an infinite film that initially contains a right-angled corner.

KW - viscous froth model

KW - cruvature-driven motion

KW - diffusion of cruvature

KW - foam rheology

KW - surface evolver

KW - asymptotic analysis

UR - http://www.scopus.com/inward/record.url?scp=84888160003&partnerID=8YFLogxK

UR - http://hdl.handle.net/2160/13572

U2 - 10.1098/rspa.2013.0359

DO - 10.1098/rspa.2013.0359

M3 - Article

AN - SCOPUS:84888160003

SN - 1364-5021

VL - 469

JO - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

JF - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

IS - 2159

ER -