On the effects of membrane viscosity on transient red blood cell dynamics

Abstract

<p>Computational Fluid Dynamics is currently used to design and improve the hydraulic properties of biomedical devices, wherein the large scale blood circulation needs to be simulated by accounting for the mechanical response of RBCs at the mesoscale.</p>

Lattice Boltzmann simulations on the tumbling to tank-treading transition: effects of membrane viscosity

“…After having computed the viscous stress tensor τ1pxτν, the force acting on the ith node can be computed as boldFi=τ1pxτνF1pxF−Tnormal∇1px∇NiAm, where F1pxscriptF is the gradient deformation tensor which is contracted with the viscous tensor τ1pxτν, normal∇1px∇Ni is the gradient of the shape functions and Am is the surface area of the mth face of the triangular mesh [1,23]. More details are given in [15,18].…”

“…The interpolation is performed by means of discrete Delta functions (in particular, we use a four-point stencil). For more details on the model adopted, we refer to our previous work [15].…”

“…This paper aims at taking some steps further to fill this gap. In our previous work [15], the effect of membrane viscosity during the relaxation after the cessation of a mechanical load was investigated; here, the quantitative effect of the membrane viscosity on the TB-TT transition is explored, adopting the same numerical model as in [15]. More specifically, the Skalak model [16] and the Helfrich formulation [17] are implemented to describe the elastic behaviour, while the standard linear solid model is employed to account for the membrane viscosity [18]; the fluid is resolved in the framework of the lattice Boltzmann method (LBM) [1].…”

Rayleigh–Plateau instability of anisotropic interfaces. Part 1. An analytical and numerical study of fluid interfaces

“…Phase diagrams of the dominant wavelength and the corresponding growth rate are shown in figures 8(a) and 8(b), respectively. Typical values for the interface viscosity of vesicles and red blood cells reported in the literature vary from 10 −10 Pa s m to 10 −7 Pa s m (Dimova et al 2006;den Otter & Shkulipa 2007;Guglietta et al 2020). In combination with typical fluid viscosities ( § 2.4) and sizes of the order of R 0 = 1 μm for vesicles and R 0 = 4 μm for red blood cells this leads to typical viscosity ratios 2η S /(ηR 0 ) = 0.1-40.…”

“…We now investigate how anisotropic interfacial tension influences the instability wavelength and growth rate in the Stokes regime if the interface in addition possesses interface viscosity (Boussinesq 1913;Scriven 1960;Whitaker 1976;Hajiloo, Ramamohan & Slattery 1987;Powers 2010;Yazdani & Bagchi 2013;Narsimhan et al 2015;Martínez-Calvo & Sevilla 2018;Guglietta et al 2020). The dispersion relation in presence of interface viscosity and tension anisotropy is derived in appendix B.3 and reads Guglietta et al 2020). In combination with typical fluid viscosities ( § 2.4) and sizes of the order of R 0 = 1 μm for vesicles and R 0 = 4 μm for red blood cells this leads to typical viscosity ratios 2η S /(ηR 0 ) = 0.1-40.…”