Faxén formulas for particles of arbitrary shape and material composition

Dolata, Benjamin E.; Zia, Roseanna N.

doi:10.1017/jfm.2020.962

Cited by 2 publications

(2 citation statements)

References 40 publications

(71 reference statements)

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“…These two pictures, the dissipative and the inertial-scale ones, are somehow conceptually disconnected, with the only bridging idea being the call into play of so-called Faxén corrections, which account for effects induced by the local curvature of the flow although at scales where the flow field is smooth, typically , hence not yet in the inertial range (Calzavarini et al. 2009) (we note that, while simple for spherical particles, the Faxén corrections are more complex for other particle shapes, see Dolata & Zia 2021).…”

Section: Introductionmentioning

confidence: 99%

“…It is key here to recognize that distinctive flow structures exist at small scales, such as the filament-like vortices where fluid tracers get trapped (Biferale et al 2005;Bentkamp, Lalescu & Wilczek 2019) or from which tiny inertial particles are ejected (Bec et al 2007) and with which spheroidal particles align (Pumir & Wilkinson 2011;Gustavsson, Einarsson & Mehlig 2014;Ni, Ouellette & Voth 2014). These two pictures, the dissipative and the inertial-scale ones, are somehow conceptually disconnected, with the only bridging idea being the call into play of so-called Faxén corrections, which account for effects induced by the local curvature of the flow although at scales where the flow field is smooth, typically 10η, hence not yet in the inertial range (Calzavarini et al 2009) (we note that, while simple for spherical particles, the Faxén corrections are more complex for other particle shapes, see Dolata & Zia 2021).…”

Section: Introductionmentioning

confidence: 99%

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Dynamics of finite-size spheroids in turbulent flow: the roles of flow structures and particle boundary layers

et al. 2022

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We study the translational and rotational dynamics of neutrally buoyant finite-size spheroids in hydrodynamic turbulence by means of fully resolved numerical simulations. We examine axisymmetric shapes, from oblate to prolate, and the particle volume dependences. We show that the accelerations and rotations experienced by non-spherical inertial-scale particles result from volume filtered fluid forces and torques, similar to spherical particles. However, the particle orientations carry signatures of preferential alignments with the surrounding flow structures, which are reflected in distinct axial and lateral fluctuations for accelerations and rotation rates. The randomization of orientations does not occur even for particles with volume-equivalent diameter size in the inertial range, here up to $60$ dissipative units ( $\eta$ ) at Taylor-scale Reynolds number ${Re_{\lambda }=120}$ . Additionally, we demonstrate that the role of fluid boundary layers around the particles cannot be neglected in reaching a quantitative understanding of particle statistical dynamics, as they affect the intensities of the angular velocities and the relative importance of tumbling with respect to spinning rotations. This study brings to the fore the importance of inertial-scale flow structures in homogeneous and isotropic turbulence and their impacts on the transport of neutrally buoyant bodies with sizes in the inertial range.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Dynamics of finite-size spheroids in turbulent flow: the roles of flow structures and particle boundary layers

et al. 2022

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On the Hinch–Kim dualism between singularity and Faxén operators in the hydromechanics of arbitrary bodies in Stokes flows

Procopio,

Giona

2024

Physics of Fluids

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We generalize the multipole expansion and the structure of the Faxén operator in Stokes flows obtained for bodies with no-slip to generic boundary conditions, addressing the assumptions under which this generalization is conceivable. We show that a disturbance field generated by a body immersed in an ambient flow can be expressed, independently on the boundary conditions, as a multipole expansion, the coefficients of which are the moments of the volume forces. We find that the dualism between the operator giving the disturbance field of an nth order ambient flow and the nth order Faxén operator, referred to as the Hinch–Kim dualism, holds only if the boundary conditions satisfy a property that we call Boundary-Condition reciprocity (BC-reciprocity). If this property is fulfilled, the Faxén operators can be expressed in terms of the (m, n)th order geometrical moments of the volume forces (defined in the article). In addition, it is shown that in these cases, the hydromechanics of the fluid-body system is completely determined by the entire set of the Faxén operators. Finally, classical boundary conditions of hydrodynamic applications are investigated in light of this property: boundary conditions for rigid bodies, Newtonian drops at the mechanical equilibrium, porous bodies modeled by the Brinkman equations are BC-reciprocal, while deforming linear elastic bodies, deforming Newtonian drops, non-Newtonian drops, and porous bodies modeled by the Darcy equations do not have this property. For Navier-slip boundary conditions on a rigid body, we find the analytical expression for low order Faxén operators. By using these operators, the closed form expressions for the flow past a sphere with arbitrary slip length immersed in shear and quadratic flows are obtained.

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Faxén formulas for particles of arbitrary shape and material composition

Abstract: Abstract

Cited by 2 publications

References 40 publications

Dynamics of finite-size spheroids in turbulent flow: the roles of flow structures and particle boundary layers

Dynamics of finite-size spheroids in turbulent flow: the roles of flow structures and particle boundary layers

On the Hinch–Kim dualism between singularity and Faxén operators in the hydromechanics of arbitrary bodies in Stokes flows

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