No abstract

From macroscopic to microscopic scales it is demonstrated that diffusion through membranes can be modeled using specific boundary conditions across them. The membranes are here considered thin in comparison to the overall size of the system. In a macroscopic scale the membrane is introduced as a transmission boundary condition, which enables an effective modeling of systems that involve multiple scales. In a mesoscopic scale, a numerical lattice-Boltzmann scheme with a partial-bounceback condition at the membrane is proposed and analyzed. It is shown that this mesoscopic approach provides a consistent approximation of the transmission boundary condition. Furthermore, analysis of the mesoscopic scheme gives rise to an expression for the permeability of a thin membrane as a function of a mesoscopic transmission parameter. In a microscopic model, the mean waiting time for a passage of a particle through the membrane is in accordance with this permeability. Numerical results computed with the mesoscopic scheme are then compared successfully with analytical solutions derived in a macroscopic scale, and the membrane model introduced here is used to simulate diffusive transport between the cell nucleus and cytoplasm through the nuclear envelope in a realistic cell model based on fluorescence microscopy data. By comparing the simulated fluorophore transport to the experimental one, we determine the permeability of the nuclear envelope of HeLa cells to enhanced yellow fluorescent protein.

This study addresses the characteristics of the interpolation functions and interface reconstruction routines for the VOF-Volume of Fluid method available in the commercial CFD software ANSYS-FLUENT. This software was used because it has both implicit and explicit VOF approaches along with diverse interpolation functions. Some of these functions were compared from different viewpoints: the quality of the reconstructed interface; the ability to preserve the initial mass inside the system (numerical diffusion); and the computing time. To undertake the qualitative and quantitative comparisons, a test problem that combines the classical dam break and slosh tank benchmark problems was used. No analytical solution available was found for this problem, in which the most interesting feature is a high interaction between the velocity field and volume fraction, thus making it ideal for addressing the issue of interface smearing. ANSYS-FLUENT permits using 5 interpolation functions for transient simulations: PLIC, CICSAM, HRIC (explicit and implicit) and the UPWIND scheme, and four when performing steady state ones: BGM, modified HRIC, COMPRESSIVE and UPWIND schemes. Both transient and steady state solutions were analyzed in this study, using all the above schemes, except the UPWIND one for steady state simulations. It was found that, for thinner grids, PLIC, CISAM and the explicit HRIC schemes had similar performances concerning the quality of the reconstructed interface and mass conservation. On the other hand, PLIC shows the best results for coarser grids, being the only to conserve mass for all tests. The computation time was similar for all transient simulation (within each grid). Concerning the steady state simulations, which are, in fact, distorted transient simulations, the BGM and the COMPRESSIVE schemes produced similar results, but BGM consumed more computational time.