A note on a traveling wave on an extensible capsule membrane –with bending rigidity– in poiseuille flow
M.A.H. Reyesª , F. Méndez–Lavielleª, and E. Geffroyb
ª Facultad de Ingeniería, Universidad Nacional Autónoma de México, e–mail: mreyes@maxwell.iimatercu.unam.mx
b Instituto de Investigaciones en Materiales, Universidad Nacional Autónoma de México.
Recibido el 29 de enero de 2010 ]]> Aceptado el 3 de marzo de 2010
Abstract
We consider the effects of the bending rigidity of a capsule membrane convected by Poiseuille flow. We show numerically how the transition from a "discoidal shape" to "V shape or cordial form" capsules is mediated by travelling waves responsible for the required change in curvature. We show numerically that the wave velocity is an increasing function of both the rigidity of the membrane and the pressure gradient. A qualitative explanation of the observation is given in terms of a Burger's type equation for the curvature.
Keywords: Capsules; waves; Poiseuille flow.
Resumen
Consideramos los efectos de la rigidez de doblez de una capsula convectada por el flujo de Poiseville. Demostramos numéricamente cómo la transición de una "forma discoide" a una tipo "V o cordial" de las cápsulas son mediante ondas viajeras responsables del cambio requerido en curvatura. Demostramos numéricamente que la velocidad de onda es una función de aumento de la rigidez de la membrana y del gradiente de presión. Una explicación cualitativa del la observación se da en términos de una ecuación tipo Burger para la curvatura.
Descriptores: Cápsula; ondas; flujo de Poiseuille.
]]> PACS: 46.40.–f; 83.50.–v
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Acknowledgments
We thank PROFIP–DGAPA of UNAM for their continued support and encouragement, as well as CONACyT for funding of this research work.
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