Gustavo C. Buscaglia

Diego S. Rodrigues, Roberto F. Ausas, Fernando Mut et al.

We propose a robust simulation method for phospholipid membranes. It is based on a mixed three-field formulation that accounts for tangential fluidity (Boussinesq-Scriven law), bending elasticity (Canham-Helfrich model) and inextensibility. The unknowns are the velocity, vector curvature and surface pressure fields, all of which are interpolated with linear continuous finite elements. The method is semi-implicit - it requires the solution of a single linear system per time step. Conditional time stability is observed, with a time step restriction that scales as the square of the mesh size. Mesh quality and refinement are maintained by adaptively remeshing. Another ingredient is a numerical force that emulates the action of an optical tweezer, allowing for virtual interaction with the membrane. Extensive relaxation experiments are reported. Comparisons to exact shapes reveal the orders of convergence for position (5/3), vector curvature (3/2), surface pressure (1) and bending energy (2). Tweezing experiments are also presented. Convergence to the exact dynamics of a cylindrical tether is confirmed. Further tests illustrate the robustness of the method (six tweezers acting simultaneously) and the significance of viscous effects on membrane deformation under external forces.

Stevens Paz, Roberto F. Ausas, Juan P. Carbajal et al.

The coupled problem of hydrodynamics and solute transport for the Najafi-Golestanian three-sphere swimmer is studied, with the Reynolds number set to zero and Péclet numbers (Pe) ranging from 0.06 to 60. The adopted method is the numerical simulation of the problem with a finite element code based upon the FEniCS library. For the swimmer executing the optimal locomotion gait, we report the Sherwood number as a function of Pe in homogeneous fluids and confirm that little gain in solute flux is achieved by swimming unless Pe is significantly larger than 10. We also consider the swimmer as an learning agent moving inside a fluid that has a concentration gradient. The outcomes of Q-learning processes show that learning locomotion (with the displacement as reward) is significantly easier than learning chemotaxis (with the increase of solute flux as reward). The chemotaxis problem, even at low Pe, has a varying environment that renders learning more difficult. Further, the learning difficulty increases severely with the Péclet number. The results demonstrate the challenges that natural and artificial swimmers need to overcome to migrate efficiently when exposed to chemical inhomogeneities.

Stevens Paz Sánchez, Gustavo C. Buscaglia

Squirmers are models of a class of microswimmers, such as ciliated organisms and phoretic particles, that self-propel in fluids without significant deformation of their body shape. Available techniques for their simulation are based on the boundary-element method and do not contemplate nonlinearities such as those arising from the fluid's inertia or non-Newtonian rheology. This article describes a methodology to simulate squirmers that overcomes these limitations by using volumetric numerical methods, such as finite elements or finite volumes. It deals with interface conditions at the squirmer's surface that generalize those in the published literature. The actual procedures to be performed on a fluid solver to implement the proposed methodology are provided, including the treatment of metachronal surface waves. Among the several numerical examples, a two-dimensional simulation is shown of the hydrodynamic interaction of two individuals of Opalina ranarum.

Gustavo C. Buscaglia

Surface incompressibility, also called inextensibility, imposes a zero-surface-divergence constraint on the velocity of a closed deformable material surface. The well-posedness of the mechanical problem under such constraint depends on an inf-sup or stability condition for which an elementary proof is provided. The result is also shown to hold in combination with the additional constraint of preserving the enclosed volume, or isochoricity. These continuous results are then applied to prove a modified discrete inf-sup condition that is crucial for the convergence of stabilized finite element methods.