Fluid permeation through a membrane with infinitesimal permeability under Reynolds lubrication

This article has been published in a revised form in Journal of Mechanics [https://doi.org/10.1017/jmech.2020.38]. This version is published under a Creative Commons CC-BY-NC-ND. No commercial re-distribution or re-use allowed. Derivative works cannot be distributed. © 2020 The Society of Theoretical and Applied Mechanics

Numerical Simulation of Selected Two-Dimensional and Three-Dimensional Fluid-Structure Interaction Problems Using OpenFOAM Technology

Fluid-structure interaction (FSI) problems are increasing in various engineering fields. In this thesis, different cases of FSI in two- and three-dimensions (2D and 3D) are simulated using OpenFOAM and foam-extend. These packages have been used to create a coupling between fluid and solid. The vortex-induced vibration (VIV) phenomenon of flow past a circular cylinder is studied using PIMPLE algorithm for pressure-velocity coupling. This VIV study is restricted to incompressible flow simulation at a Reynolds number (Re) of 100. The changes of drag and lift coefficient values depend on the study case and the spring-mass-damper system for the flow past a free oscillatory cylinder. The free vibrating cylinder examined in one-degree-of-freedom (1DOF) and two-degrees-of-freedom (2DOF) systems with linear damping and spring properties. Both will affect the behaviour of the cylinder within the flow with some noticeable differences. The response time of the cylinder and the drag coefficient are the most affected by the spring and damper. Besides the vortex-induced vibration test cases, the two-dimensional and three-dimensional fluid-structure interaction benchmarking is also studied. A partitioned solution method for strongly coupled solver with independent fluid and solid meshes for transient simulation has been applied. The fluid domain dynamics is governed by the incompressible Navier-Stokes equations; however, the structural field is described by the nonlinear elastodynamic equations. Fluid and solid domains are discretised by finite volume method (FVM) in space and time. A strong coupling scheme for partitioned analysis of the thin-walled shell structure exposed to wind-induced vibration (WIV) is presented. The achievement of the 3D membrane roof coupling scheme is studied by applying the 2D model. Additionally, numerical models for the slender shell structures coupling and the 3D flows indicate possible applications of the presented work. The computational fluid dynamics (CFD) simulation results revealed that even the flow is considered as a laminar, turbulence modelling or more refined meshes should be used to capture the generation and release of vortices. A partitioned solution procedure for FSI problems in the building aeroelasticity area is also studied. An illustrative real-world model on the coupled behaviour of membrane structure under wind flow influence is given. A four-point tent subjected to wind motion is a typical application of this work applying with various physical factors that are a necessity for the thin membrane structure. The fluid domain is described by the incompressible Navier-Stokes equations at a Reynolds number of Re = 3,750. However, the motion of the solid field is modeled by total Lagrangian strategy for nonlinear elastic deformation. The FSI simulation, particularly 3D problems require in very long calculation time. Some limitations of the FSI solver in foam-extend package called fsiFoam is discussed. All solvers that used in this thesis are considered to be applied to a wide use of the implementation of FSI models, despite some problems in parallelisation, particularly in the latest FSI solver version. The analysis results are presented to demonstrate accuracy, convergence, and stability

Coupled/combined compact IRBF schemes for fluid flow and FSI problems

The thesis is concerned with the development of compact approximation methods based on Integrated Radial Basis Functions (IRBFs) and their applications in fluid flows and FSI problems. The contributions include (i) new compact IRBF stencils where first- and second-order derivatives are included; (ii) a preconditioning technique where a preconditioner to enhance the stability of the flat IRBF solutions; and, (iii) the incorporation of the proposed stencils into the immersed boundary methods. Numerical experiments show the present schemes generally produce more accurate solutions and better convergence rates than existing methods (e.g. FDM, high-order compact FDM and compact IRBF methods)

On the damped oscillations of an elastic quasi-circular membrane in a two-dimensional incompressible fluid

We propose a procedure - partly analytical and partly numerical - to find the frequency and the damping rate of the small-amplitude oscillations of a massless elastic capsule immersed in a two-dimensional viscous incompressible fluid. The unsteady Stokes equations for the stream function are decomposed onto normal modes for the angular and temporal variables, leading to a fourth-order linear ordinary differential equation in the radial variable. The forcing terms are dictated by the properties of the membrane, and result into jump conditions at the interface between the internal and external media. The equation can be solved numerically, and an excellent agreement is found with a fully-computational approach we developed in parallel. Comparisons are also shown with the results available in the scientific literature for drops, and a model based on the concept of embarked fluid is presented, which allows for a good representation of the results and a consistent interpretation of the underlying physics.Comment: in press on JF

Modelling the Fluid Mechanics of Cilia and Flagella in Reproduction and Development

Cilia and flagella are actively bending slender organelles, performing functions such as motility, feeding and embryonic symmetry breaking. We review the mechanics of viscous-dominated microscale flow, including time-reversal symmetry, drag anisotropy of slender bodies, and wall effects. We focus on the fundamental force singularity, higher order multipoles, and the method of images, providing physical insight and forming a basis for computational approaches. Two biological problems are then considered in more detail: (1) left-right symmetry breaking flow in the node, a microscopic structure in developing vertebrate embryos, and (2) motility of microswimmers through non-Newtonian fluids. Our model of the embryonic node reveals how particle transport associated with morphogenesis is modulated by the gradual emergence of cilium posterior tilt. Our model of swimming makes use of force distributions within a body-conforming finite element framework, allowing the solution of nonlinear inertialess Carreau flow. We find that a three-sphere model swimmer and a model sperm are similarly affected by shear-thinning; in both cases swimming due to a prescribed beat is enhanced by shear-thinning, with optimal Deborah number around 0.8. The sperm exhibits an almost perfect linear relationship between velocity and the logarithm of the ratio of zero to infinite shear viscosity, with shear-thickening hindering cell progress.Comment: 20 pages, 24 figure

A parallel interaction potential approach coupled with the immersed boundary method for fully resolved simulations of deformable interfaces and membranes

In this paper we show and discuss the use of a versatile interaction potential approach coupled with an immersed boundary method to simulate a variety of flows involving deformable bodies. In particular, we focus on two kinds of problems, namely (i) deformation of liquid-liquid interfaces and (ii) flow in the left ventricle of the heart with either a mechanical or a natural valve. Both examples have in common the two-way interaction of the flow with a deformable interface or a membrane. The interaction potential approach (de Tullio & Pascazio, Jou. Comp. Phys., 2016; Tanaka, Wada and Nakamura, Computational Biomechanics, 2016) with minor modifications can be used to capture the deformation dynamics in both classes of problems. We show that the approach can be used to replicate the deformation dynamics of liquid-liquid interfaces through the use of ad-hoc elastic constants. The results from our simulations agree very well with previous studies on the deformation of drops in standard flow configurations such as deforming drop in a shear flow or a cross flow. We show that the same potential approach can also be used to study the flow in the left ventricle of the heart. The flow imposed into the ventricle interacts dynamically with the mitral valve (mechanical or natural) and the ventricle which are simulated using the same model. Results from these simulations are compared with ad- hoc in-house experimental measurements. Finally, a parallelisation scheme is presented, as parallelisation is unavoidable when studying large scale problems involving several thousands of simultaneously deforming bodies on hundreds of distributed memory computing processors

The Flat Phase of Crystalline Membranes

We present the results of a high-statistics Monte Carlo simulation of a phantom crystalline (fixed-connectivity) membrane with free boundary. We verify the existence of a flat phase by examining lattices of size up to $128^2$. The Hamiltonian of the model is the sum of a simple spring pair potential, with no hard-core repulsion, and bending energy. The only free parameter is the the bending rigidity $\kappa$. In-plane elastic constants are not explicitly introduced. We obtain the remarkable result that this simple model dynamically generates the elastic constants required to stabilise the flat phase. We present measurements of the size (Flory) exponent $\nu$ and the roughness exponent $\zeta$. We also determine the critical exponents $\eta$ and $\eta_u$ describing the scale dependence of the bending rigidity ($\kappa(q) \sim q^{-\eta}$) and the induced elastic constants ($\lambda(q) \sim \mu(q) \sim q^{\eta_u}$). At bending rigidity $\kappa = 1.1$, we find $\nu = 0.95(5)$ (Hausdorff dimension $d_H = 2/\nu = 2.1(1)$), $\zeta = 0.64(2)$ and $\eta_u = 0.50(1)$. These results are consistent with the scaling relation $\zeta = (2+\eta_u)/4$. The additional scaling relation $\eta = 2(1-\zeta)$ implies $\eta = 0.72(4)$. A direct measurement of $\eta$ from the power-law decay of the normal-normal correlation function yields $\eta \approx 0.6$ on the $128^2$ lattice.Comment: Latex, 31 Pages with 14 figures. Improved introduction, appendix A and discussion of numerical methods. Some references added. Revised version to appear in J. Phys.

A modelling approach towards Epidermal homoeostasis control

In order to grasp the features arising from cellular discreteness and individuality, in large parts of cell tissue modelling agent-based models are favoured. The subclass of off-lattice models allows for a physical motivation of the intercellular interaction rules. We apply an improved version of a previously introduced off-lattice agent-based model to the steady-state flow equilibrium of skin. The dynamics of cells is determined by conservative and drag forces,supplemented with delta-correlated random forces. Cellular adjacency is detected by a weighted Delaunay triangulation. The cell cycle time of keratinocytes is controlled by a diffusible substance provided by the dermis. Its concentration is calculated from a diffusion equation with time-dependent boundary conditions and varying diffusion coefficients. The dynamics of a nutrient is also taken into account by a reaction-diffusion equation. It turns out that the analysed control mechanism suffices to explain several characteristics of epidermal homoeostasis formation. In addition, we examine the question of how {\em in silico} melanoma with decreased basal adhesion manage to persist within the steady-state flow-equilibrium of the skin.Interestingly, even for melanocyte cell cycle times being substantially shorter than for keratinocytes, tiny stochastic effects can lead to completely different outcomes. The results demonstrate that the understanding of initial states of tumour growth can profit significantly from the application of off-lattice agent-based models in computer simulations.Comment: 23 pages, 7 figures, 1 table; version that is to appear in Journal of Theoretical Biolog