Creeping flow over a composite sphere: Solid core with porous shell

Masliyah, Jacob H.; Neale, Graham H.; Małysa, K.; Ven, Theodorus G. M. van de

doi:10.1016/0009-2509(87)85054-6

Cited by 127 publications

(94 citation statements)

References 21 publications

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“…Achieving a similar level of control over the streamlines of the fluid flow outside the structure would imply canceling the viscous drag exerted on the structure. In this Letter, we demonstrate the possibility of fluid flow cloaking using porous media whose properties are more general than those considered in earlier studies [27,28].To allow a simple analytical treatment, we consider a solid spherical object of radius a impermeable to the fluid, surrounded by a concentric permeable porous shell of exterior radius b, immersed in a fluid occupying an unbounded region (which we refer to as free space), and subject to a stationary, uniform flow with asymptotic velocity u 0 in the z direction [ Fig. 1(a)].…”

mentioning

confidence: 65%

“…Here, we generalize the known solutions [27,28] of the forward problem to allow the inclusion of inhomogeneous, although still radially symmetric, uniaxially anisotropic permeability (6), and use them to solve the inverse problem (problem B).…”

Section: Prl 107 074501 (2011) P H Y S I C a L R E V I E W L E T T Ementioning

confidence: 99%

“…(3) that satisfies the condition of plug flow (7) at r ! 1 can be written as [28] u r ¼ u 0 cos 1 À A r 3 À B r ;…”

Section: Prl 107 074501 (2011) P H Y S I C a L R E V I E W L E T T Ementioning

confidence: 99%

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Fluid Flow Control with Transformation Media

2011

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We introduce a new concept for the manipulation of fluid flow around three-dimensional bodies. Inspired by transformation optics, the concept is based on a mathematical idea of coordinate transformations and physically implemented with anisotropic porous media permeable to the flow of fluids. In two situations-for an impermeable object placed either in a free-flowing fluid or in a fluid-filled porous medium-we show that the object can be coated with an inhomogeneous, anisotropic permeable medium, such as to preserve the flow that would have existed in the absence of the object. The proposed fluid flow cloak eliminates downstream wake and compensates viscous drag, hinting at the possibility of novel propulsion techniques. As a subset of the separation of variables method, conformal transformations thus offer a unique and powerful approach to the forward problems of incompressible flow, as well as electro-and magnetostatics.The utility of more general coordinate transformations in the inverse electromagnetic [3][4][5] and acoustic [6][7][8][9] problems has been demonstrated recently, most impressively by showing the possibility of electromagnetic invisibility, dubbed cloaking [3,4,[10][11][12]. The key idea that enabled progress in those areas was the combination of coordinate transformations with coordinate-dependent, and often extremely exotic [5,[13][14][15], material properties. Transformation optics [3][4][5]11,16] and transformation acoustics [6-8] offer solutions to some inverse scattering problems [17] by reducing them to an elementary one-for example, scattering off a point object in free space.There is no reason why this conceptual approach cannot be used in other areas of physics [18], and, in fact, it has already been applied to conductive heat transfer [19], linear elastodynamics [5,8,[20][21][22][23][24], surface wave [25], and quantum-mechanical matter wave [26] dynamics. The fundamental requirement for the applicability of this concept is the presence of a medium with sufficiently flexible properties, which enables manipulation of the coefficients in the equations describing the dynamical process. Here, we propose porous media as a substrate for transformation fluid dynamics and investigate the feasibility of controlling certain features of incompressible fluid flow.The electromagnetic cloak of invisibility, which inspired this approach, manipulates the field lines of electric and magnetic fields, and the streamlines of momentum flux, in such a manner that these lines are virtually indistinguishable from those in the absence of any object [3]. Because the streamlines are unperturbed in the free space outside the cloak, electromagnetic radiation avoids scattering off the structure and therefore exerts no electromagnetic pressure on it. Achieving a similar level of control over the streamlines of the fluid flow outside the structure would imply canceling the viscous drag exerted on the structure. In this Letter, we demonstrate the possibility of fluid flow cloaking using porous media whose properties...

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confidence: 65%

Section: Prl 107 074501 (2011) P H Y S I C a L R E V I E W L E T T Ementioning

confidence: 99%

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Fluid Flow Control with Transformation Media

2011

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“…Here for simplicity we make the assumption that we can describe the porous shell through a single constant permeability. A similar problem in this context has been worked out by [MNMG87] where they solved for the flow and the resulting drag coefficient of a sphere with a porous shell that is being pulled in an infinite fluid domain. Here we directly extend their results to a confined flow with a spherical outer boundary.…”

Section: The Effect Of Confinement On the Hydrodynamic Mobility Of MImentioning

confidence: 99%

“…We first investigate the mobility and viscoelastic behavior of a spherical particle surrounded by a fibrous shell and compare our results with analytical results obtained by using the porous medium Brinkman model for the shell [Bri47,MNMG87]. Through this example we clearly demonstrate that HIs play a critical role in setting the dynamics of fibrous networks.…”

Section: Introductionmentioning

confidence: 99%

A fast platform for simulating semi-flexible fiber suspensions applied to cell mechanics

Nazockdast

Rahimian

Zorin

et al. 2017

Journal of Computational Physics

126

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We present a novel platform for the large-scale simulation of fibrous structures immersed in a Stokesian fluid and evolving under confinement or in free-space. One of the main motivations for this work is to study the dynamics of fiber assemblies within biological cells. For this, we also incorporate the key biophysical elements that determine the dynamics of these assemblies, which include the polymerization and depolymerization kinetics of fibers, their interactions with molecular motors and other objects, their flexibility, and hydrodynamic coupling.This work, to our knowledge, is the first technique to include many-body hydrodynamic interactions (HIs), and the resulting fluid flows, in cellular fiber assemblies. We use the non-local slender body theory to compute the fluid-structure interactions of the fibers and a second-kind boundary integral formulation for other rigid bodies and the confining boundary. A kernel-independent implementation of the fast multiple method is utilized for efficient evaluation of HIs. The deformation of the fibers is described by the nonlinear Euler-Bernoulli beam theory and their polymerization is modeled by the reparametrization of the dynamic equations in the appropriate non-Lagrangian frame. We use a pseudo-spectral representation of fiber positions and implicit HIs in the time-stepping to resolve large fiber deformations, and to allow time-steps not constrained by temporal stiffness or fiber-fiber interactions. The entire computational scheme is parallelized, which enables simulating assemblies of thousands of fibers. We use our method to investigate two important questions in the mechanics of cell division: (i) the effect of confinement on the hydrodynamic mobility of microtubule asters; and (ii) the dynamics of the positioning of mitotic spindle in complex cell geometries. Finally to demonstrate the general applicability of the method, we simulate the sedimentation of a cloud of fibers.

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Electrophoretic mobility of a charged spherical colloidal particle covered with an uncharged polymer layer

Ohshima

2002

Electrophoresis

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A general expression is derived for the electrophoretic mobility of a spherical charged colloidal particle covered with an uncharged polymer layer in an electrolyte solution in an applied electric field for the case where the particle zeta potential is low. It is assumed that electrolyte ions as well as water molecules can penetrate the polymer layer. Approximate analytic expressions for the electrophoretic mobility of particles carrying low zeta potentials are derived for the two extreme cases in which the particle radius is very large or very small.

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Creeping flow over a composite sphere: Solid core with porous shell

Cited by 127 publications

References 21 publications

Fluid Flow Control with Transformation Media

Fluid Flow Control with Transformation Media

A fast platform for simulating semi-flexible fiber suspensions applied to cell mechanics

Electrophoretic mobility of a charged spherical colloidal particle covered with an uncharged polymer layer

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