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A novel pseudo-rigid body approach to the non-linear dynamics of soft micro-particles in dilute viscous flowJana Wedel,
Matjaž Hriberšek,
Jure Ravnik,
Paul Steinmann, 2024, original scientific article
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: 12
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