Kinematic and dynamic forcing strategies for predicting the transport of inertial capsules via a combined lattice Boltzmann – Immersed Boundary method

Abstract

Modeling the transport of deformable capsules under different flow regimens is crucial in a variety of fields, including oil rheology, blood flow and the dispersion of pollutants.The aim of this study is twofold. Firstly, a combined Lattice Boltzmann -Immersed Boundary (LBM -IB) approach is developed for predicting the transport of inertial deformable capsules. A Moving Least Squares (MLS) scheme has been implemented to correlate the pressure, velocity and force fields of the fluid domain with the capsule dynamics. This computational strategy has been named LBM -Dynamic IB. Secondly, this strategy is directly compared with a more conventional approach, named LBM -Kinematic IB, where capsules move with the same velocity of the surrounding fluid.Multiple test cases have been considered for assessing the accuracy and efficiency of the Dynamic over Kinematic IB scheme, including the stretching of circular capsules in shear flow, the transport in a plane Poiseuille flow of circular and biconcave capsules, with and without inertia. By monitoring the capsule geometry over time, the two schemes have been documented to be in excellent agreement, especially for low Capillary numbers (Ca ≤ 10 -2 ), in the case of non-inertial capsules. Despite a moderate increase in computational burden, the presented LBM -Dynamic IB scheme is the sole capable of predicting the dynamics of both non-inertial and inertial deformable capsules.The proposed approach can be efficiently employed for studying the transport of blood cells, cancer cells and nano/micro capsules within a capillary flow. 3 INTRODUCTIONThe coupling between fluid and structure dynamics is of great relevance in different disciplines. Biophysicists are investing increasingly more efforts into modeling the flow of complex fluids, such as whole blood, to better understand the mechanisms underlying the development of diseases and their possible cure. [1][2][3][4] In a wide range of engineering problems, there is a growing demand to investigate the rheology of active fluids, oils, polymeric suspension, or colloidal mixtures moving into tortuous channels, with either fixed or variable geometries. This is specifically the case of enhanced oil recovery, trickle bed reactors, and microfluidics devices. [5][6][7][8][9][10][11][12] Regardless of the application, it is easy to recognize that immersed structures may be dragged away downstream by large distances, far from their original locations, or significantly deformed due to an incoming flux. On this premise, it is crucial to have access to computational tools capable of efficiently handle the variation in time of immersed geometries without any loss of accuracy. [13][14][15][16] One of the most suitable computational technique to deal with the motion and deformation of particles into fluids is the Immersed Boundary (IB) method, which was originally developed by Peskin in 1972 to simulate cardiac mechanics [17]. This technique prescribes the evolution of the fluid on an Eulerian Cartesian grid, which is not conforming to the geomet...

Capsules Rheology in Carreau–Yasuda Fluids

“…In the proposed scheme, the total force acting on the fluid is composed of a body force, f ib [19,20] accounting for the presence of immersed bodies and a shear-dependent force, f nw , accounting for the non-Newtonian effects on the apparent viscosity of the fluid [28]. Finally, Dirichlet boundary conditions are imposed on external boundaries and treated with the known-velocity bounce back procedure by Zou and He [46].…”

“…The immersed body is a worm-like chain of nv vertices linked with nl linear elements, whose centroids are usually called Lagrangian markers. The IB procedure, extensively proposed and validated by Coclite and colleagues [19,20], is adopted here and a moving-least squares reconstruction is employed to exchange all MRT-LB distribution functions between the Eulerian lattice and the Lagrangian chain. Finally, the body force term in Equation (5), f ib , is evaluated through the formulation by Favier et al [47].…”

“…In this work, a dynamic-Immersed-Boundary (IB) method is combined with a Multi-Relaxationtime Lattice Boltzmann (MRT-LB) scheme for describing the evolution of capsules transported in incompressible flows [19]. This method was extensively studied and validated by Coclite and collaborators [20][21][22][23][24][25].…”

“…Such forcing term accounts for spreading onto the lattice the total force exerted by the fluid: the body force due to the presence of an immersed body and the force induced by the adopted shear-dependent viscosity model. On one hand, no-slip boundary conditions on an immersed structures are imposed by a body-force accounting for the hydrodynamics force generated by the presence of the immersed body [19]. Immersed structures are transported as a collection of massive Lagrangian points connected by linear elements and their motion is obtained by solving the Euler-Newton equations for the center of mass and the revolution angle [27].…”

Simulations of self-propelled anguilliform swimming using the immersed boundary method in OpenFOAM

“…Following this strategy, a variety of refinements and modifications of the IBM have been developed during the past few decades (Diao et al, 2018;Dillon & Li, 2009;Hopkins, Vanderlei, & Fauci, 2012;Mittal & Iaccarino, 2005;Peskin, 2003;Tutkun & Edis, 2017). With proper methods being used to program the IBM solvers, several FSI problems have been solved (Ardekani & Brandt, 2019;Coclite, Ranaldo, de Tullio, Decuzzi, & Pascazio, 2019). However, these methods are quite advanced and sophisticated to develop, and the in-house codes are not widely accessible to others.…”