Dynamics of biconcave vesicles in a confined shear flow

Static interface profiles for contact lines on an elastic membrane with the Willmore energy

We consider a fluid interface in contact with an elastic membrane and study the static profiles of the interface and the membrane. Equilibrium conditions are derived by minimizing the total energy of the system with volume constraints. The total energy consists of surface energies and the Willmore energy; the latter penalizes the bending of the membrane. It is found that, while the membrane is locally flat at the contact line with the contact angle satisfying the Young-Dupré equation, the gradient of the mean curvature of the membrane exhibits a jump across the contact line. This jump balances the surface tension of the fluid interface in the normal direction of the membrane. Asymptotic solutions are obtained for two-dimensional systems in the limits as the reduced bending modulus ν tends to +∞ and 0, respectively. In the stiff limit as ν→+∞, the leading-order solution is given by that of a droplet sitting on a rigid substrate with the contact angle satisfying the Young-Dupré equation; in contrast, in the soft limit as ν→0, a transition layer appears near the contact line and the interfaces have constant curvatures in the outer region with apparent contact angles obeying Neumann's law. These solutions are validated by numerical experiments.

Temperature dependency of whole blood viscosity and red cell properties in desert ungulates: Studies on scimitar-horned oryx and dromedary camel

Background

The dromedary camel and the oryx antelope are exposed to excessive heat and solar radiation in their desert habitat. Desertification of areas with by now little rainfall may occur eventually. Well-adapted large animal species show us what is needed to survive in scorching regions.

Methods

Four scimitar-horned oryx antelopes (Oryx dammah), 10 camels (Camelus dromedarius), nine South African Merino sheep, and 17 Nguni cows were tested for RBC aggregation, RBC elongation, and plasma viscosity. The temperature dependency of blood viscosity was tested in 10 camels and compared to human reference values.

Results

Unlike sheep, Nguni cow, and dromedary camel, oryx RBCs aggregate in native plasma (M0:5.2 (3.3/6.7); M1:18.1 (16.7/27.9); Myrenne MA1). Elongation indices of oryx RBCs were intermediate to low (EImax: 22.6 (19.2/25.3); SS1/2 3.67 (2.52/4.95); Rheodyn SSD). Camel RBCs did not display the typical SS/EI curve by rotational ektacytometry. In-vitro blood viscosity (Physica MCR302) was lower in camels than in human blood at equal hematocrit. A decrease of temperature had only little effect on camel blood. At 10 s−1, blood viscosity in camel increased from 2.18mPa*s (2.01/2.37) at 42◦C to 4.39mPa*s (4.22/4.51) at 12◦C. In human blood, viscosity ranged from 8.21mPa*s (6.95/8.25) at 37◦C to 15.52mPa*s (14.25/16.03) at 12◦C. At 1000 s−1, blood viscosity in camel ranged from 2.00mPa*s (1.95/2.04) at 42◦C to 3.98mPa*s (3.88/4.08) at 12◦C. In human blood, viscosity ranged from 5.35mPa*s (4.96/5.87) at 37◦C to 11.24mPa*s (10.06/11.17) at 12◦C.

Conclusions

Desert ungulates may need RBC membranes, which are fortified to withstand changes in osmolality during dehydration-rehydration cycles. This reduces RBC deformability. Dromedary camel blood does not undergo stark changes in viscosity with changes in temperature. Therefore, blood fluidity could be rather maintained during the day and night cycle. This should reduce the need of the vascularity to rhythmically adapt to changing shear forces when camels experience heterothermy.

Off-center motion of a trapped elastic capsule in a microfluidic channel with a narrow constriction

Owing to their significance in capsule-related engineering and biomedical applications, a number of studies have considered the dynamics of elastic capsules flowing in constricted microchannels. However, these studies have focused on capsules moving along the channel centerline. In the present study, we numerically investigate the transient motion of an elastic capsule in a microfluidic channel with a rectangular constriction, which is initially trapped at the constriction inlet while off the channel centerline (i.e., on the channel bottom-wall). Under the push of the surrounding flow, the capsule can squeeze into the constriction, but only if the capsule deformability or the constriction size is sufficiently large. We find that the critical capillary number leading to the penetration of the capsule into the constriction is larger for off-centerline capsules compared to centered capsules. The centered capsule is stationary at the steady state when it remains stuck at the constriction; in contrast, the off-centerline capsule is not stationary but exhibits a tank-treading motion, i.e., its overall shape maintains a nonspherical shape with a protrusion into the constriction while its membrane exhibits a continuous rotation. Further, we examine the dependence of the capsule motion type, capsule deformation degree and membrane tension distribution on the capillary number (measuring the effects of flow strength and membrane mechanics) and constriction geometries (including the constriction height and width). Finally, we discuss the mechanism governing the capsule motion by analyzing the hydrodynamic forces acting on the capsule. The shear force acting on the capsule top owing to the fluid flow in the gap between the capsule top and the channel top-wall is the main source inducing the membrane tank-treading rotation.

Theory and algorithms to compute Helfrich bending forces: a review

Cell membranes are vital to shield a cell's interior from the environment. At the same time they determine to a large extent the cell's mechanical resistance to external forces. In recent years there has been considerable interest in the accurate computational modeling of such membranes, driven mainly by the amazing variety of shapes that red blood cells and model systems such as vesicles can assume in external flows. Given that the typical height of a membrane is only a few nanometers while the surface of the cell extends over many micrometers, physical modeling approaches mostly consider the interface as a two-dimensional elastic continuum. Here we review recent modeling efforts focusing on one of the computationally most intricate components, namely the membrane's bending resistance. We start with a short background on the most widely used bending model due to Helfrich. While the Helfrich bending energy by itself is an extremely simple model equation, the computation of the resulting forces is far from trivial. At the heart of these difficulties lies the fact that the forces involve second order derivatives of the local surface curvature which by itself is the second derivative of the membrane geometry. We systematically derive and compare the different routes to obtain bending forces from the Helfrich energy, namely the variational approach and the thin-shell theory. While both routes lead to mathematically identical expressions, so-called linear bending models are shown to reproduce only the leading order term while higher orders differ. The main part of the review contains a description of various computational strategies which we classify into three categories: the force, the strong and the weak formulation. We finally give some examples for the application of these strategies in actual simulations.

State diagram for adhesion dynamics of deformable capsules under shear flow

Due to the significance of understanding the underlying mechanisms of cell adhesion in biological processes and cell capture in biomedical applications, we numerically investigate the adhesion dynamics of deformable capsules under shear flow by using a three-dimensional computational fluid dynamic model. This model is based on the coupling of the front tracking-finite element method for elastic mechanics of the capsule membrane and the adhesion kinetics simulation for adhesive interactions between capsules and functionalized surfaces. Using this model, three distinct adhesion dynamic states are predicted, such as detachment, rolling and firm-adhesion. Specifically, the effects of capsule deformability quantified by the capillary number on the transitions of these three dynamic states are investigated by developing an adhesion dynamic state diagram for the first time. At low capillary numbers (e.g. Ca < 0.0075), whole-capsule deformation confers the capsule a flattened bottom in contact with the functionalized surface, which hence promotes the rolling-to-firm-adhesion transition. It is consistent with the observations from previous studies that cell deformation promotes the adhesion of cells lying in the rolling regime. However, it is surprising to find that, at relatively high capillary numbers (e.g. 0.0075 < Ca < 0.0175), the effect of capsule deformability on its adhesion dynamics is far more complex than just promoting adhesion. High deformability of capsules makes their bottom take a concave shape with no adhesion bond formation in the middle. The appearance of this specific capsule shape inhibits the transitions of both rolling-to-firm-adhesion and detachment-to-rolling, and it means that capsule deformation no longer promotes the capsule adhesion. Besides, it is interesting to note that, when the capillary number exceeds a critical value (e.g. Ca = 0.0175), the rolling state no longer appears, since capsules exhibit large deviation from the spherical shape.