Hydrodynamic interaction of a spherical particle with a planar boundary

Perkins, Greg; Jones, Robert B.

doi:10.1016/0378-4371(92)90056-v

Cited by 56 publications

(56 citation statements)

References 17 publications

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“…(2), it follows that M xθ is positive definite, which is then also true for the matrix C. As the diagonal elements of M xθ are significantly larger than the off-diagonal element [33,38], one easily finds that trC is negative. Therefore, C has two negative eigenvalues, which we denote in the following by λ ± .…”

Section: Definition Of the Dynamic States Of Motion A Experimenmentioning

confidence: 85%

“…In order to obtain accurate results when simulating the motion of the sphere it is essential to properly calculate the mobility matrix M and the shear force F S . In our simulations we use a numerical method described by Jones et al [33,38] which allows to accurately calculate the components of the mobility matrix for a single sphere above a wall for arbitrary sphere wall distances. The values obtained by this method agree very well with the classical results given for some tabulated height values by Goldman et al [39].…”

Section: A Stokesian Dynamicsmentioning

confidence: 99%

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Dynamic states of cells adhering in shear flow: From slipping to rolling

2008

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Motivated by rolling adhesion of white blood cells in the vasculature, we study how cells move in linear shear flow above a wall to which they can adhere via specific receptor-ligand bonds. Our We also investigate the effect of non-molecular parameters. In particular, we find that an increase in viscosity of the medium leads to a characteristic expansion of the region of stable rolling to the expense of the region of firm adhesion, but not to the expense of the regions of free or transient motion. Our results can be used in an inverse approach to determine single bond parameters from flow chamber data on rolling adhesion.

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Section: Definition Of the Dynamic States Of Motion A Experimenmentioning

confidence: 85%

Section: A Stokesian Dynamicsmentioning

confidence: 99%

Dynamic states of cells adhering in shear flow: From slipping to rolling

2008

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“…With the notation we use here it is a N × N matrix (number of particles), whose elements are 3 × 3 matrices (number of spatial dimensions). The diagonal terms μ ii describe the mobility of a single sphere in the vicinity of a wall, for which we use the following expression (20,21) μ ii ¼ 1 6πηa where η is the fluid viscosity and z i the height of the particle i above the surface. Off-diagonal terms describe the velocity of particle i, induced by a force acting on particle j.…”

Section: Materials and Techniquesmentioning

confidence: 99%

Self-assembled artificial cilia

Vilfan

Potočnik²,

Kavčič³

et al. 2010

Proc. Natl. Acad. Sci. U.S.A.

245

252

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Due to their small dimensions, microfluidic devices operate in the low Reynolds number regime. In this case, the hydrodynamics is governed by the viscosity rather than inertia and special elements have to be introduced into the system for mixing and pumping of fluids. Here we report on the realization of an effective pumping device that mimics a ciliated surface and imitates its motion to generate fluid flow. The artificial biomimetic cilia are constructed as long chains of spherical superparamagnetic particles, which selfassemble in an external magnetic field. Magnetic field is also used to actuate the cilia in a simple nonreciprocal manner, resulting in a fluid flow. We prove the concept by measuring the velocity of a cilia-pumped fluid as a function of height above the ciliated surface and investigate the influence of the beating asymmetry on the pumping performance. A numerical simulation was carried out that successfully reproduced the experimentally obtained data.biomimetics | microfluidics | colloids | low Reynold's number | hydrodynamics E fficient pumping and mixing of fluids in microscopic channels is paramount in microfluidic applications (1, 2). Small characteristic dimensions of such devices result in very low Reynolds numbers and one encounters hydrodynamics that is conceptually different from the turbulent macroscopic world. As stated by Purcell's "scallop theorem," nonreciprocal motion is required for generation of fluid flow or directed swimming (3). This is clearly manifested in biological systems, for instance in bending waves of sperm tails or in corkscrew motion of bacterial flagella. Another example are cilia, flexible protrusions on the surface of many eukaryotic cells with a typical length of several micrometers. In humans, ciliated surfaces are found, for example, in the respiratory tract where they sweep mucus, or in the Fallopian tubes where they move an ovum to the uterus. The motion of the fluid above a ciliated surface is generated by periodic beating of cilia. Experimental observations have shown that the beating pattern of an individual cilium is asymmetric and composed of two phases: the effective stroke, during which the outstretched cilium propels the fluid like an oar, followed by the recovery stroke, when the bent cilium returns to the initial position sweeping along the surface in a way that produces as little backward flow as possible (4). Although each cilium can beat independently, cilia densely covering a surface synchronize their cycles and form metachronal waves, thus increasing their fluid pumping efficiency (5). It is believed that the metachronal waves occur as a result of hydrodynamical interactions between the cilia (6, 7).The efficiency of the ciliary pumping mechanism leads to the idea of using the same principle for designing artificial cilia that act as microscale pumps and mixers. An important step towards biomimetic cilia was made by Darnton et al., who created a bacterial carpet by attaching bacteria to a solid surface (8). Due to symmetric rotation and wea...

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“…[22][23][24][25][26][27][28][29][30][31][32][33] We first consider the case of a single spherical particle of radius a held fixed in a parabolic flow given by…”

Section: Particles Near a Wallmentioning

confidence: 99%

A method for determining Stokes flow around particles near a wall or in a thin film bounded by a wall and a gas-liquid interface

Ozarkar

Sangani

2008

Physics of Fluids

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A method for determining Stokes flow around particles near a wall or in a thin film bounded by a wall on one side and a nondeformable gas-liquid interface on the other side is developed. The no-slip boundary conditions at the wall are satisfied by constructing an image system based on Lamb's multipoles. Earlier results for the image systems for the flow due to a point force or a force dipole are extended to image systems for force or source multipoles of arbitrary orders. For the case of a film, the image system consists of an infinite series of multipoles on both sides of the film. Accurate evaluation of the flow due to these images is discussed, including the use of Shanks transforms. The method is applied to several problems including chains of particles, radially expanding particles, drops, and porous particles.

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Hydrodynamic interaction of a spherical particle with a planar boundary

Cited by 56 publications

References 17 publications

Dynamic states of cells adhering in shear flow: From slipping to rolling

Dynamic states of cells adhering in shear flow: From slipping to rolling

Self-assembled artificial cilia

A method for determining Stokes flow around particles near a wall or in a thin film bounded by a wall and a gas-liquid interface

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