Strongly coupled peridynamic and lattice Boltzmann models using immersed boundary method for flow-induced structural deformation and fracture

To simulate the dynamics of structural deformation and fracture caused by fluid-structure interactions accurately and efficiently, a strong coupling between the peridynamic model and the lattice Boltzmann method using the immersed boundary method is developed here. In this novel method, the peridynamic model predicts structural deformation and fracture, the cascaded lattice Boltzmann method serves as the flow solver, and the immersed boundary method is to enforce a no-slip boundary condition on the fluid-solid interface. The strong coupling is achieved by adding velocity corrections for the fluid and solid phases simultaneously at each time step, which are calculated by solving a linear system of equations derived from an implicit velocity correction immersed boundary scheme. Therefore, this new scheme based on the immersed boundary method eliminates the need to iteratively solve the dynamics of the fluid and solid phases at each time step. The proposed method is rigorously validated considering the plate with a pre-existing crack under velocity boundary conditions, the sedimentation of an elastic disk, the cross-flow over a flexible beam, and the flow-induced deformation of an elastic beam attached to a rigid cylinder. More importantly, the structural deformation, crack formation, and fracture due to interaction with the fluid flow are captured innovatively

Multiscale Modeling of Biological Flow using Lattice Boltzmann Method

In this dissertation, we have developed a fluid-structure interaction code specifically designed to simulate soft microparticle deformation in biological flow. We have used this tool for two different applications. First, we study red blood cell deformation under shear flow to evaluate stress distribution on membrane and subsequently pore formation on RBC membrane. Second, we utilized this code to show a proof of concept for an idea where we can separate soft particles based on their biophysical properties. In the following, these applications are discussed in more details.Under high shear rates, pores form on RBC membrane through which hemoglobin leaks out and increases free hemoglobin content of plasma leading to hemolysis. We hypothesize that local flow dynamics such as flow rate and shear stress determines blood cell damage. In this dissertation, a novel model is presented to study red blood cell (RBC) hemolysis at cellular level. The goal of the proposed work is to establish multiscale computational techniques to predict the blood cell dynamics and damage in complex flow conditions, i.e., blood-wetting biomedical devices. The cell membrane damage model will be coupled with local fluid flow to study cell deformation and rupture and a generalized cellular level blood cell damage model will be developed based on these simulations. By coupling Lattice Boltzmann and spring connected network models through immersed boundary method, we estimate hemolysis of a single red blood cell under various shear rates. First, we use adaptive meshing to find local strain distribution and critical sites on RBC membrane, then we apply underlying molecular dynamic simulations to evaluate damage. Our approach is comprised of three sub-models: defining criteria of pore formation, calculating pore size, and measuring Hb diffusive flux out of pores. Our damage model uses information of different scales to predict cellular level hemolysis. Results are compared with experimental studies and other models in literature. The developed cellular damage model can be used as a predictive tool for hydrodynamic and hematologic design optimization of blood-wetting medical devices.Isolating cells of interest from a heterogeneous mixture has been of critical importance in biological studies and clinical applications. In this dissertation, we have proposed to use ciliary system in microfluidic devices to isolate target subpopulation of soft particles based on their biophysical properties. In this model, the bottom of microchannel is covered with an equally spaced cilia array which can be magnetically actuated. A series of simulations are performed to study cilia-particle interaction and isolation dynamic. It is shown that these elastic hair-like filaments can influence particle’s trajectories differently depending on their biophysical properties. This modeling study also uses immersed boundary (IB) method coupled with lattice Boltzmann method. Soft particles are simulated by connected network of nonlinear springs. Moreover, cilia is modeled by point-particle scheme. It is demonstrated that active ciliary system is able to continuously and non-destructively sort cells based on their size, shape and stiffness. Ultimately, a design map for fabrication of a programmable microfluidic device capable of isolating various subpopulation of cells is developed. This biocompatible, label-free design can separate cells/soft microparticles with high throughput which can greatly complement existing separation technologies

Stochastic Eulerian Lagrangian Methods for Fluid-Structure Interactions with Thermal Fluctuations

We present approaches for the study of fluid-structure interactions subject to thermal fluctuations. A mixed mechanical description is utilized combining Eulerian and Lagrangian reference frames. We establish general conditions for operators coupling these descriptions. Stochastic driving fields for the formalism are derived using principles from statistical mechanics. The stochastic differential equations of the formalism are found to exhibit significant stiffness in some physical regimes. To cope with this issue, we derive reduced stochastic differential equations for several physical regimes. We also present stochastic numerical methods for each regime to approximate the fluid-structure dynamics and to generate efficiently the required stochastic driving fields. To validate the methodology in each regime, we perform analysis of the invariant probability distribution of the stochastic dynamics of the fluid-structure formalism. We compare this analysis with results from statistical mechanics. To further demonstrate the applicability of the methodology, we perform computational studies for spherical particles having translational and rotational degrees of freedom. We compare these studies with results from fluid mechanics. The presented approach provides for fluid-structure systems a set of rather general computational methods for treating consistently structure mechanics, hydrodynamic coupling, and thermal fluctuations.Comment: 24 pages, 3 figure

Spatially Adaptive Stochastic Methods for Fluid-Structure Interactions Subject to Thermal Fluctuations in Domains with Complex Geometries

We develop stochastic mixed finite element methods for spatially adaptive simulations of fluid-structure interactions when subject to thermal fluctuations. To account for thermal fluctuations, we introduce a discrete fluctuation-dissipation balance condition to develop compatible stochastic driving fields for our discretization. We perform analysis that shows our condition is sufficient to ensure results consistent with statistical mechanics. We show the Gibbs-Boltzmann distribution is invariant under the stochastic dynamics of the semi-discretization. To generate efficiently the required stochastic driving fields, we develop a Gibbs sampler based on iterative methods and multigrid to generate fields with $O(N)$ computational complexity. Our stochastic methods provide an alternative to uniform discretizations on periodic domains that rely on Fast Fourier Transforms. To demonstrate in practice our stochastic computational methods, we investigate within channel geometries having internal obstacles and no-slip walls how the mobility/diffusivity of particles depends on location. Our methods extend the applicability of fluctuating hydrodynamic approaches by allowing for spatially adaptive resolution of the mechanics and for domains that have complex geometries relevant in many applications

Active elastohydrodynamics of vesicles in narrow, blind constrictions

Fluid-resistance limited transport of vesicles through narrow constrictions is a recurring theme in many biological and engineering applications. Inspired by the motor-driven movement of soft membrane-bound vesicles into closed neuronal dendritic spines, here we study this problem using a combination of passive three-dimensional simulations and a simplified semi-analytical theory for active transport of vesicles that are forced through such constrictions by molecular motors. We show that the motion of these objects is characterized by two dimensionless quantities related to the geometry and the strength of forcing relative to the vesicle elasticity. We use numerical simulations to characterize the transit time for a vesicle forced by fluid pressure through a constriction in a channel, and find that relative to an open channel, transport into a blind end leads to the formation of an effective lubrication layer that strongly impedes motion. When the fluid pressure forcing is complemented by forces due to molecular motors that are responsible for vesicle trafficking into dendritic spines, we find that the competition between motor forcing and fluid drag results in multistable dynamics reminiscent of the real system. Our study highlights the role of non-local hydrodynamic effects in determining the kinetics of vesicular transport in constricted geometries

The Hydrodynamics of Active Systems

This is a series of four lectures presented at the 2015 Enrico Fermi summer school in Varenna. The aim of the lectures is to give an introduction to the hydrodynamics of active matter concentrating on low Reynolds number examples such as cells and molecular motors. Lecture 1 introduces the hydrodynamics of single active particles, covering the Stokes equation and the Scallop Theorem, and stressing the link between autonomous activity and the dipolar symmetry of the far flow field. In lecture 2 I discuss applications of this mathematics to the behaviour of microswimmers at surfaces and in external flows, and describe our current understanding of how swimmers stir the surrounding fluid. Lecture 3 concentrates on the collective behaviour of active particles, modelled as an active nematic. I write down the equations of motion and motivate the form of the active stress. The resulting hydrodynamic instability leads to a state termed active turbulence characterised by strong jets and vortices in the flow field and the continual creation and annihilation of pairs of topological defects. Lecture 4 compares simulations of active turbulence to experiments on suspensions of microtubules and molecular motors. I introduce lyotropic active nematics and discuss active anchoring at interfaces.Comment: Lecture Notes, 2015 Enrico Fermi Summer School on Soft Matter Self-Assembly, Vienn

A Review on Contact and Collision Methods for Multi-body Hydrodynamic problems in Complex Flows

Modeling and direct numerical simulation of particle-laden flows have a tremendous variety of applications in science and engineering across a vast spectrum of scales from pollution dispersion in the atmosphere, to fluidization in the combustion process, to aerosol deposition in spray medication, along with many others. Due to their strongly nonlinear and multiscale nature, the above complex phenomena still raise a very steep challenge to the most computational methods. In this review, we provide comprehensive coverage of multibody hydrodynamic (MBH) problems focusing on particulate suspensions in complex fluidic systems that have been simulated using hybrid Eulerian-Lagrangian particulate flow models. Among these hybrid models, the Immersed Boundary-Lattice Boltzmann Method (IB-LBM) provides mathematically simple and computationally-efficient algorithms for solid-fluid hydrodynamic interactions in MBH simulations. This paper elaborates on the mathematical framework, applicability, and limitations of various 'simple to complex' representations of close-contact interparticle interactions and collision methods, including short-range inter-particle and particle-wall steric interactions, spring and lubrication forces, normal and oblique collisions, and mesoscale molecular models for deformable particle collisions based on hard-sphere and soft-sphere models in MBH models to simulate settling or flow of nonuniform particles of different geometric shapes and sizes in diverse fluidic systems.Comment: 37 pages, 12 Figure

An IB Method for Non-Newtonian-Fluid Flexible-Structure Interactions in Three-Dimensions

Problems involving fluid flexible-structure interactions (FFSI) are ubiquitous in engineering and sciences. Peskin’s immersed boundary (IB) method is the first framework for modeling and simulation of such problems. This paper addresses a three-dimensional extension of the IB framework for non-Newtonian fluids which include power-law fluid, Oldroyd-B fluid, and FENE-P fluid. The motion of the non-Newtonian fluids are modelled by the lattice Boltzmann equations (D3Q19 model). The differential constitutive equations of Oldroyd-B and FENE-P fluids are solved by the D3Q7 model. Numerical results indicate that the new method is first-order accurate and conditionally stable. To show the capability of the new method, it is tested on three FFSI toy problems: a power-law fluid past a flexible sheet fixed at its midline, a flexible sheet being flapped periodically at its midline in an Oldroyd-B fluid, and a flexible sheet being rotated at one edge in a FENE-P fluid

A Lattice Boltzmann-Immersed Boundary method to simulate the fluid interaction with moving and slender flexible objects

A numerical approach based on the Lattice Boltzmann and Immersed Boundary methods is proposed to tackle the problem of the interaction of moving and/or deformable slender solids with an incompressible fluid flow. The method makes use of a Cartesian uniform lattice that encompasses both the fluid and the solid domains. The deforming/moving elements are tracked through a series of Lagrangian markers that are embedded in the computational domain. Differently from classical projection methods applied to advance in time the incompressible Navier–Stokes equations, the baseline Lattice Boltzmann fluid solver is free from pressure corrector step, which is known to affect the accuracy of the boundary conditions. Also, in contrast to other immersed boundary methods proposed in the literature, the proposed algorithm does not require the introduction of any empirical parameter. In the case of rigid bodies, the position of the markers delimiting the surface of an object is updated by tracking both the position of the centre of mass of the object and its rotation using Newtonʼs laws and the conservation of angular momentum. The dynamics of a flexible slender structure is determined as a function of the forces exerted by the fluid, its flexural rigidity and the tension necessary to enforce the filament inextensibility. For both rigid and deformable bodies, the instantaneous no-slip and impermeability conditions on the solid boundary are imposed via external and localised body forces which are consistently introduced into the Lattice Boltzmann equation. The validation test-cases for rigid bodies include the case of an impulsively started plate and the sedimentation of particles under gravity in a fluid initially at rest. For the case of deformable slender structures we consider the beating of both a single filament and a pair filaments induced by the interaction with an incoming uniformly streaming flow