Search Results (4)

The mechanical effects of membrane compositional inhomogeneities are analyzed in a process analogous to neck formation in cellular membranes. We cast on the Canham–Helfrich model of fluid membranes with both the spontaneous curvature and the surface tension being non-homogeneous functions along the cell membrane. The inhomogeneous distribution of necking forces is determined by the equilibrium mechanical equations and the boundary conditions as considered in the axisymmetric setting compatible with the necking process. To establish the role played by mechanical inhomogeneity, we focus on the catenoid, a surface of zero mean curvature. Analytic solutions are shown to exist for the spontaneous curvature and the constrictive forces in terms of the border radii. Our theoretical analysis shows that the inhomogeneous distribution of spontaneous curvature in a mosaic-like neck constrictional forces potentially contributes to the membrane scission under minimized work in living cells. Full article

In this article, we present a finite element method for studying the dynamic behavior of deformable vesicles, which mimic red blood cells, in a non-Newtonian Casson fluid. The fluid membrane, represented by an implicit level-set function, adheres to the Canham–Helfrich model and maintains surface inextensibility constraint through penalty. We propose a two-step time integration scheme that incorporates higher-order accuracy by using an asymmetric composition of discrete flow based on the second-order backward difference formula, followed by a projection onto the real axis. Our framework incorporates variable time steps generated by an appropriate adaptation criterion. We validate our model through numerical simulations against existing experimental and numerical results in the case of purely Newtonian flow. Furthermore, we provide preliminary results demonstrating the influence of the non-Newtonian fluid model on membrane regimes. Full article

A recurring motif in soft matter and biophysics is modeling the mechanics of interacting particles on fluid membranes. One of the main outstanding challenges in these applications is the need to model the strong coupling between the substrate deformation and the particles’ positions as the latter freely move on the former. This work presents a thin-shell finite element formulation based on subdivision surfaces to compute equilibrium configurations of a thin fluid shell with embedded particles. We use a variational Lagrangian framework to couple the mechanics of the particles and the substrate without having to resort to ad hoc constraints to anchor the particles to the surface. Unlike established methods for such systems, the particles are allowed to move between elements of the finite element mesh. This is achieved by parametrizing the particle locations on the reference configuration. Using the Helfrich–Canham energy as a model for fluid shells, we present the finite element method’s implementation and an efficient search algorithm required to locate particles on the reference mesh. Several analyses with varying numbers of particles are finally presented reproducing symmetries observed in the classic Thomson problem and showcasing the coupling between interacting particles and deformable membranes. Full article

Nanopatterned surfaces administer antibacterial activity through contact-induced mechanical stresses and strains, which can be modulated by changing the nanopattern’s radius, spacing and height. However, due to conflicting recommendations throughout the theoretical literature with poor agreement to reported experimental trends, it remains unclear whether these key dimensions—particularly radius and spacing—should be increased or decreased to maximize bactericidal efficiency. It is shown here that a potential failure of biophysical models lies in neglecting any out-of-plane effects of nanopattern contact. To highlight this, stresses induced by a nanopattern were studied via an analytical model based on minimization of strain and adhesion energy. The in-plane (areal) and out-of-plane (contact pressure) stresses at equilibrium were derived, as well as a combined stress (von Mises), which comprises both. Contour plots were produced to illustrate which nanopatterns elicited the highest stresses over all combinations of tip radius between 0 and 100 nm and center spacing between 0 and 200 nm. Considering both the in-plane and out-of-plane stresses drastically transformed the contour plots from those when only in-plane stress was evaluated, clearly favoring small tipped, tightly packed nanopatterns. In addition, the effect of changes to radius and spacing in terms of the combined stress showed the best qualitative agreement with previous reported trends in killing efficiency. Together, the results affirm that the killing efficiency of a nanopattern can be maximized by simultaneous reduction in tip radius and increase in nanopattern packing ratio (i.e., radius/spacing). These findings provide a guide for the design of highly bactericidal nanopatterned surfaces. Full article