Effects of shear rate and suspending viscosity on deformation and frequency of red blood cells tank-treading in shear flows

Abstract

The tank-treading rotation of red blood cells (RBCs) in shear flows has been studied extensively with experimental, analytical, and numerical methods. Even for this relatively simple system, complicated motion and deformation behaviors have been observed, and some of the underlying mechanisms are still not well understood. In this study, we attempt to advance our knowledge of the relationship among cell motion, deformation, and flow situations with a numerical model. Our simulation results agree well with experimental data, and confirm the experimental finding of the decrease in frequency/shear-rate ratio with shear rate and the increase of frequency with suspending viscosity. Moreover, based on the detailed information from our simulations, we are able to interpret the frequency dependency on shear rate and suspending viscosity using a simple two-fluid shear model. The information obtained in this study thus is useful for understanding experimental observations of RBCs in shear and other flow situations; the good agreement to experimental measurements also shows the potential usefulness of our model for providing reliable results for microscopic blood flows.

A finite difference method with subsampling for immersed boundary simulations of the capsule dynamics with viscoelastic membranes

“…Figure shows the droplet deformation processes for a system with Ca = 0.33, λ = 1, Bq s = 5, and Bq d = 0 with Δ t = 100 δt and τ / T 0 = 1/20. It can be seen there, as observed in previous studies for droplets and capsules,() the droplet gradually deforms into a stable ellipsoidal shape with a constant inclination angle in the shear plane. Once the stable state established, the droplet performs the so‐called tank‐treading rotation with no further apparent change in shape and orientation.…”

“…The initial spherical droplet interface is discretized into 5120 triangular elements. More details on the simulation setup and numerical techniques can be found in Appendix and Oulaid et al As in previous studies,() the following nondimensional numbers are taken as controlling parameters for the system performance: …”

“…The derivation was performed by assuming a hexagonal network configuration around a node, and this will not be true for capsules undergoing significant deformation as shown in previous simulations and experiments. () Again, only one membrane viscosity was established there, and therefore, it is not suitable to model general membranes with independent shear and dilatational viscosities. Moreover, the derived apparent membrane viscosity has a different dimension (unit Pa·s in these studies()) than that from the classical membrane viscosity definition (unit N·s/m) (); and this makes it difficult for direct utilization of measured membrane viscosity in simulations.…”

“…The elastic part of the nodal force can also be calculated directly from the energy function according to the virtual work principle. () Other aspects of membrane mechanics, including the bending modulus, area conservation, and intercellular aggregation, can be considered as well. ()…”

“…To represent the fluidity of the membrane, they flipped the tethers between two possible diagonals of two adjacent triangles based on a Monte Carlo method, and a probability parameter was adjusted to produce different membrane viscous effects. This technique may appear simple and convenient for the node‐link network representation of membrane; however, it is not applicable to the finite element representation typically employed in IBM simulations,() since flipping a link direction between two adjacent triangular elements causes changes in the reference configurations as well as the shape functions for the two elements. The single probability parameter is not adequate either to consider independent shear and dilatational membrane viscosity values.…”