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

Tank-treading dynamics of red blood cells in shear flow: On the membrane viscosity rheology

In this article, extensive three-dimensional simulations are conducted for tank-treading (TT) red blood cells (RBCs) in shear flow with different cell viscous properties and flow conditions. Apart from recent numerical studies on TT RBCs, this research considers the uncertainty in cytoplasm viscosity, covers a more complete range of shear flow situations of available experiments, and examines the TT behaviors in more details. Key TT characteristics, including the rotation frequency, deformation index, and inclination angle, are compared with available experimental results of similar shear flow conditions. Fairly good simulation-experiment agreements for these parameters can be obtained by adjusting the membrane viscosity values; however, different rheological relationships between the membrane viscosity and the flow shear rate are noted for these comparisons: shear thinning from the TT frequency, Newtonian from the inclination angle, and shear thickening from the cell deformation. Previous studies claimed a shear-thinning membrane viscosity model based on the TT frequency results; however, such a conclusion seems premature from our results and more carefully designed and better controlled investigations are required for the RBC membrane rheology. In addition, our simulation results reveal complicate RBC TT features and such information could be helpful for a better understanding of in vivo and in vitro RBC dynamics.

Similar but Distinct Roles of Membrane and Interior Fluid Viscosities in Capsule Dynamics in Shear Flows

PURPOSE

The dynamics of biological capsules and red blood cells in shear flows has been studied extensively with experimental, analytical, and numerical methods. In particular, the effects of various parameters, including the shear rate or shear stress, membrane elasticity, capsule shape, and interior fluid viscosity, have been investigated carefully. The role of the membrane viscosity for capsule deformation dynamics has not been examined adequately. In previous studies, the so-called energy dissipation ratio has been used to account for the membrane viscosity effect by increasing the interior viscosity; however, the applicability and accuracy of this treatment have not been evaluated carefully.

METHODS

In this study, using the recently developed finite-difference scheme for immersed boundary simulations of viscoelastic membranes, we conduct comprehensive numerical simulations of the deformation processes of an originally spherical capsule in shear flows with various combinations of membrane and interior fluid viscosities.

RESULTS

Our results show that the membrane and interior fluid viscosity have similar however different effects on the capsule deformation dynamics. While the capsule deformation decreases with both membrane and interior fluid viscosities, a typical decrease-then-increase variation is observed for the inclination angle as the membrane viscosity increases, instead of the monotonic decrease in the inclination angle with the interior fluid viscosity increase. Also, although both large membrane and interior fluid viscosity values can introduce oscillations in the capsule deformation and inclination, larger aptitudes and slow decay processes are noticed at larger membrane viscosities. The variations of other dynamic parameters of the capsule, including the circumference, average membrane velocity, and rotation frequency, are also analyzed, and an intuitive mechanism is proposed to relate the membrane velocity and rotation frequency to the capsule deformation and inclination angle. The simple mechanism is then applied to explain the spoon-like variation patterns for membrane velocity and rotation frequency observed in our results. Furthermore, we examine the validity of the energy dissipation ratio approach based on the mathematical functional dependence.

CONCLUSIONS

Our results and analysis show that the dissipation ratio is a system and process dependent variable and it cannot be treated as a constant even for the same capsule. This research is valuable for a better understanding of the complex capsule dynamics in flows and also suggests that the membrane viscosity needs to be considered explicitly for accurate and reliable results in future studies.

Biomolecular phase separation through the lens of sodium-23 NMR

Phase separation is a fundamental physicochemical process underlying the spatial arrangement and coordination of cellular events. Detailed characterization of biomolecular phase separation requires experimental access to the internal environment of dilute and especially condensed phases at high resolution. In this study, we take advantage from the ubiquitous presence of sodium ions in biomolecular samples and present the potentials of ²³Na NMR as a proxy to report the internal fluidity of biomolecular condensed phases. After establishing the temperature and viscosity dependence of ²³Na NMR relaxation rates and translational diffusion coefficient, we demonstrate that ²³Na NMR probes of rotational and translational mobility of sodium ions are capable of capturing the increasing levels of confinement in agarose gels in dependence of agarose concentration. The ²³Na NMR approach is then applied to a gel‐forming phenylalanine‐glycine (FG)‐containing peptide, part of the nuclear pore complex involved in controlling the traffic between cytoplasm and cell nucleus. It is shown that the ²³Na NMR together with the ¹⁷O NMR provide a detailed picture of the sodium ion and water mobility within the interior of the FG peptide hydrogel. As another example, we study phase separation in water‐triethylamine (TEA) mixture and provide evidence for the presence of multiple microscopic environments within the TEA‐rich phase. Our results highlight the potentials of ²³Na NMR in combination with ¹⁷O NMR in studying biological phase separation, in particular with regards to the molecular properties of biomolecular condensates and their regulation through various physico‐ and biochemical factors.

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

The membrane or interfacial viscosity is an important property in many multiphase and biofluidic situations, such as the red blood cell dynamics and emulsion stability. The immersed boundary method (IBM), which incorporates the dynamic flow-membrane interaction via force distribution and velocity interpolation, has been extensively employed in simulations of such systems. Unfortunately, direct implementation of membrane viscosity in IBM suffers severe numerical instability, which causes an IBM calculation to break down before generating any useful results. Few attempts have been recently reported; however, several concerns exist in these attempts, such as the inconsistency to the classical definition of membrane viscosity, the inability to model the shear and dilatational viscosities separately, the unjustified mathematical formulations, and the complicated algorithms and computation. To overcome these concerns, in this paper, we propose a finite difference approach for implementing membrane viscosity in immersed boundary simulations. The viscous stress is obtained via finite difference approximations to the differential strain-stress relationship, with the help of a subsampling scheme to reduce the numerical noise in the calculated strain rates. This simple method has also avoided the complicated matrix calculations in previous attempts, and hence, a better computational efficiency is expected. Detailed mathematical description of the method and key steps for its implementation in immersed boundary programs are provided. Validation and illustration calculations are performed, and our results are compared with analytical solutions and previous publications with satisfactory agreement. The influences of membrane mesh resolution and simulation time step are also examined; and the results show no indication that our finite difference method has downgraded the general IBM accuracy. Based on these simulations and analysis, we believe that our method would be a better choice for future IBM simulations of capsule dynamics with viscoelastic membranes.