Red blood cells are known to change shape in response to local flow conditions. Deformability affects red blood cell physiological function and the hydrodynamic properties of blood. The immersed boundary method is used to simulate three-dimensional membrane-fluid flow interactions for cells with the same internal and external fluid viscosities. The method has been validated for small deformations of an initially spherical capsule in simple shear flow for both neoHookean and the Evans-Skalak membrane models. Initially oblate spheroidal capsules are simulated and it is shown that the red blood cell membrane exhibits asymptotic behavior as the ratio of the dilation modulus to the extensional modulus is increased and a good approximation of local area conservation is obtained. Tank treading behavior is observed and its period calculated.

Leukocyte recruitment to sites of inflammation is initiated by their tethering and rolling on the activated endothelium under flow. Even though the fast kinetics and high tensile strength of selectin-ligand bonds are primarily responsible for leukocyte rolling, experimental evidence suggests that cellular properties such as cell deformability and microvillus elasticity actively modulate leukocyte rolling behavior. Previous theoretical models either assumed cells as rigid spheres or were limited to two-dimensional representations of deformable cells with deterministic receptor-ligand kinetics, thereby failing to accurately predict leukocyte rolling. We therefore developed a three-dimensional computational model based on the immersed boundary method to predict receptor-mediated rolling of deformable cells in shear flow coupled to a Monte Carlo method simulating the stochastic receptor-ligand interactions. Our model predicts for the first time that the rolling of more compliant cells is relatively smoother and slower compared to cells with stiffer membranes, due to increased cell-substrate contact area. At the molecular level, we show that the average number of bonds per cell as well as per single microvillus decreases with increasing membrane stiffness. Moreover, the average bond lifetime decreases with increasing shear rate and with increasing membrane stiffness, due to higher hydrodynamic force experienced by the cell. Taken together, our model captures the effect of cellular properties on the coupling between hydrodynamic and receptor-ligand bond forces, and successfully explains the stable leukocyte rolling at a wide range of shear rates over that of rigid microspheres.

Drop breakup in a linear extensional flow is simulated numerically using a nonlinear model for the surface tension that accounts for maximum packing at the interface. Surface convection sweeps surfactant to the drop poles, where it accumulates and drives the surface tension to near zero. The drop assumes a transient shape with highly pointed tips. From these tips, thin liquid threads are pulled. Subsequently, small, surfactant-rich droplets are emitted from the termini of these threads. The scale of the shed drops depends on the initial surfactant coverage. Dilute initial coverage leads to tip streaming, while high initial coverage leads to the tip dropping breakup mode.

A drop in an axisymmetric extensional ow is studied using boundary integral methods to understand the effects of a monolayer-forming surfactant on a strongly deforming interface. Surfactants occupy area, so there is an upper bound to the surface concentration that can be adsorbed in a monolayer, Γ∞. The surface tension is a highly nonlinear function of the surface concentration Γ because of this upper bound. As a result, the mechanical response of the system varies strongly with Γ for realistic material parameters. In this work, an insoluble surfactant is considered in the limit where the drop and external fluid viscosities are equal.For Γ<Γ∞, surface convection sweeps surfactant toward the drop poles. When surface diffusion is negligible, once the stable drop shapes are attained, the interface can be divided into stagnant caps near the drop poles, where Γ is non-zero, and tangentially mobile regions near the drop equator, where the surface concentration is zero. This result is general for any axisymmetric fluid particle. For Γ near Γ∞, the stresses resisting accumulation are large in order to prevent the local concentration from reaching the upper bound. As a result, the surface is highly stressed tangentially while Γ departs only slightly from a uniform distribution. For this case, Γ is never zero, so the tangential surface velocity is zero for the steady drop shape.This observation that Γ dilutes nearly uniformly for high surface concentrations is used to derive a simplified form for the surface mass balance that applies in the limit of high surface concentration. The balance requires that the tangential flux should balance the local dilatation in order that the surface concentration profile will remain spatially uniform. Throughout the drop evolution, this equation yields results in agreement with the full solution for moderate deformations, and underscores the dominant mechanism at high deformation. The simplified balance reduces to the stagnant interface condition at steady state.Drop deformations vary non-monotonically with concentration; for Γ<Γ∞, the reduction of the surface tension near the poles leads to higher deformations than the clean interface case. For Γ near Γ∞, however, Γ dilutes nearly uniformly, resulting in higher mean surface tensions and smaller deformations. The drop contribution to the volume averaged stress tensor is also calculated and shown to vary non-monotonically with surface concentration.