Impact of shear and dilational membrane viscosities on capsule shape and dynamics under shear flow: a theoretical study
Abstract
In artificial (micro)capsules or cells such as red blood cells for example, the two-dimensional (2D) rheology of the membrane (or the shell) is viscoelastic and not only elastic. The deformation and inclination of such a capsule are theoretically studied under shear and extensional flows. The membrane mechanics is described by the Kelvin-Voigt model: the 2D dissipation with the Boussinesq-Scriven law associated to specific dilational and shear Boussinesq numbers Bqd and Bqd respectively while the elastic constitutive law is either Hookean, strain-softening (neoHookean) or strain-hardening (Skalak). The dynamics depends on the elastic capillary number Ca, the Poisson ratio (or C in Skalak law), the viscosity ratio λ, the nonlinearities included in the constitutive law and both boussinesq numbers. Three dynamics are identified in the limit of weak deformations: a tank-treading motion in the limit of small elastic capillary number with a characteristic time depending on λ, Bqs and Bqd, an oscillation without any elasticity and a damped oscillation leading to a tank-treading motion in the limit of large Boussinesq numbers. In all cases, both shear and dilational 2D dissipations contribute differently leading to non-trivial results. In the case of a Skalak law with C=1, Bq=Bqs=Bqd and Bq>>λ, the deformations in the limits Ca<<1, Bq=O(1) and Ca=O(1), Bq>>1 determined in the seminal work of \cite{barthes1985role} are recovered.
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BibTeX
@misc{regazzi2026impact,
title = {{Impact of shear and dilational membrane viscosities on capsule shape and dynamics under shear flow: a theoretical study}},
author = {Paul Regazzi and Marc Leonetti},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.16739},
eprint = {2610.16739},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.16739},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Impact of shear and dilational membrane viscosities on capsule shape and dynamics under shear flow: a theoretical study
AU - Paul Regazzi
AU - Marc Leonetti
PY - 2026
DA - 2026/10/12
PB - arXiv
DO - 10.48550/arxiv.2610.16739
UR - https://arxiv.org/abs/2610.16739
AB - In artificial (micro)capsules or cells such as red blood cells for example, the two-dimensional (2D) rheology of the membrane (or the shell) is viscoelastic and not only elastic. The deformation and inclination of such a capsule are theoretically studied under shear and extensional flows. The membrane mechanics is described by the Kelvin-Voigt model: the 2D dissipation with the Boussinesq-Scriven law associated to specific dilational and shear Boussinesq numbers Bq_d and Bq_d respectively while the elastic constitutive law is either Hookean, strain-softening (neoHookean) or strain-hardening (Skalak). The dynamics depends on the elastic capillary number Ca, the Poisson ratio (or C in Skalak law), the viscosity ratio λ, the nonlinearities included in the constitutive law and both boussinesq numbers. Three dynamics are identified in the limit of weak deformations: a tank-treading motion in the limit of small elastic capillary number with a characteristic time depending on λ, Bq_s and Bq_d, an oscillation without any elasticity and a damped oscillation leading to a tank-treading motion in the limit of large Boussinesq numbers. In all cases, both shear and dilational 2D dissipations contribute differently leading to non-trivial results. In the case of a Skalak law with C=1, Bq=Bq_s=Bq_d and Bq>>λ, the deformations in the limits Ca<<1, Bq=O(1) and Ca=O(1), Bq>>1 determined in the seminal work of \cite{barthes1985role} are recovered.
ER -