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Abstract: We propose a novel, demonstrably effective, utmost versatile and computationally highly efficient pseudo-rigid body approach for tracking the barycenter and shape dynamics of soft, i.e. nonlinearly deformable micro-particles dilutely suspended in viscous flow. Pseudo-rigid bodies are characterized by affine deformation and thus represent a first-order extension to the kinematics of rigid bodies. Soft particles in viscous flow are ubiquitous in nature and sciences, prominent examples, among others, are cells, vesicles or bacteria. Typically, soft particles deform severely due to the mechanical loads exerted by the fluid flow. Since the shape dynamics of a soft particle - a terminology that shall here also include its orientation dynamics - also affects its barycenter dynamics, the resulting particle trajectory as a consequence is markedly altered as compared to a rigid particle. Here, we consider soft micro-particles of initially spherical shape that affinely deform into an ellipsoidal shape. These kinematic conditions are commensurate with i) the affine deformation assumption inherent to a pseudo-rigid body and ii) the celebrated Jeffery-Roscoe model for the traction exerted on an ellipsoidal particle due to creeping flow conditions around the particle. Without loss of generality, we here focus on non-linear hyperelastic particles for the sake of demonstration. Our novel numerical approach proves to accurately capture the particular deformation pattern of soft particles in viscous flow, such as for example tank-treading, thereby being completely general regarding the flow conditions at the macro-scale and, as an option, the constitutive behavior of the particle. Moreover, our computational method is highly efficient and allows straightforward integration into established Lagrangian tracking algorithms as employed for the point-particle approach to track rigid particles in dilute viscous flow.
Keywords: soft particles, pseudo-rigid bodies, Barycenter and shape dynamics, Lagrangian particle tracking
Published in DKUM: 19.09.2024; Views: 0; Downloads: 10
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Abstract: A numerical study of particle motion in a cubic lid driven cavity is presented. As a computational tool, a boundary element based flow solver with a Lagrangian particle tracking algorithm is derived. Flow simulations were performed using an in-house boundary element based 3D viscous flow solver. The Lagrangian particle tracking algorithm is capable of simulation of dilute suspensions of particles in viscous flows taking into account gravity, buoyancy, drag, pressure gradient and added mass. The derived algorithm is used to simulate particle behaviour in a cellular flow field and in a lid driven cavity flow. Simulations of particle movement in a cellular flow field were used to validate the algorithm. The main goal of the paper was to numerically simulate the flow behaviour of spheres of different densities and different diameters, as experimentally observed in work of Tsorng et al.The study of slightly buoyant and non-buoyant particles in a lid driven cavity was aimed at discovering cases when particles leave the primary vortex and enter into secondary vortices, a phenomenon described in the work of Tsorng et al. A parametric study of this phenomenon was preformed. The presented computational results show excellent agreement with experiments, confirming the accuracy of the developed computational method.
Keywords: dispersed two phase flow, Lagrangian particle tracking, cellular flow, lid driven cavity, boundary element method
Published in DKUM: 04.08.2017; Views: 1279; Downloads: 404
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