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1

Faxén’s law for arbitrary oscillatory Stokes flow past a porous sphere

Prakash J., Raja Sekhar G. P., Kohr M.

Archives of Mechanics

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2012

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Vol. 64, nr 1

41-41

EN

The present article deals with the study of the hydrodynamics of a porous sphere in an oscillatory viscous flow of an incompressible Newtonian fluid. Unsteady Stokes equations are used for the flow outside the porous sphere and Darcy’s equation is used for the flow inside the porous sphere. Corresponding Faxén’s law for drag and torque acting on the surface of the porous sphere is derived. Also the results are compared with few existing special cases. Examples like uniform flow, oscillating Stokeslet, oscillatory shear flow and quadratic shear flow are discussed.

2

The interior Neumann problem for the Stokes resolvent system in a bounded domain in Rn

Kohr M.

Archives of Mechanics

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2007

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Vol. 59, nr 3

283-304

EN

The interior Neumann problem for the Stokes resolvent system is studied from the point of view of the potential theory. The existence and uniqueness results as well as boundary integral representations of the classical solution are given in the case of a bounded domain in Rn, having a compact but not connected boundary of class C1'" (0

3

Boundary integral method for an oscillatory Stokes flow past a solid particle

Kohr M., Pop I.

International Journal of Applied Mechanics and Engineering

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2003

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Vol. 8, no 4

603-620

EN

In this paper, we present a boundary integral method in order to determine the oscillatory Stokes flow due to translational or rotational oscillations of a solid particle in an unbounded viscous incompressible fluid. As an application of this method, we study both cases of small-and high-frequency oscillations. Finally, we give some numerical results in the case of transverse oscillations of a prolate spheroid.

4

A second kind integral equation formulation for the interaction between a solid particle and a compound drop at low Reynolds number

Kohr M.

Applied Mechanics and Engineering

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2000

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Vol. 5, no 3

557-577

EN

In this paper, we determine a boundary integral formulation for the motion and deformation of a compound drop due to its interaction with a solid particle. The problem is reduced to a system of Fredholm integral equations of the second kind. We prove that this system has a unique continous solution when the boundaries of the flow are Lyapunov surfaces and the boundary data are continous.

5

Numerical analysis of the effect of surfactants on a circular liquid lens (II)

Kohr M., Lazar I.

Applied Mechanics and Engineering

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1999

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Vol. 4, no 3

589-608

EN

The spectrum of a two-dimensional flow, due to the presence of a circular liquid obstacle in a liquid layer, is investigated by using a boundary integral equation method.

6

Stokes flow past a cylindrical interface and a rigid obstacle in a tunnel

Kohr M.

Zeszyty Naukowe Politechniki Rzeszowskiej. Matematyka

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1998

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z. 22 [170]

79-99

EN

A direct integral equation method for the creeping flow of a viscous incompressible fluid in the presence of a solid particle and a cylindrical interface is developed. The rigid obstacle and the cylindrical interface are immersed in another fluid, which is located in a domain bounded by two rigid walls. The integral formulation uses a combination between single-layer and the double-layer potentials, with the densities defined on the boundary of the rigid obstacle and the interface, respectively. The problem is reduced to the study of the existence and the uniqueness for a second-kind integral system of Fredholm equations.

7

Existence and uniqueness result for Stokes flows in a half-plane

Kohr M.

Archives of Mechanics

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1998

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Vol. 50, nr 4

791-803

EN

This paper is concerned with the study of the two-dimensional Stokes flow past a smooth obstacle near a plane wall. Using the bonduary integral formulation, the flow is represented in terms of a combined distribution of a single-laver and a double-layer potentials of Green's functions over the bonduary of the obstacle. The problem is formulated as a set of Fredholm integral equations of the second kind for the density of the potentials. The existence and uniqueness results of the solution are obtained. Numerical results are presented in the case of a rigid circular obstacle moving parallel or normal to the plane wall.

8

An integral method for two-dimensional stokes flows past rigid obstacles in the half-plane

Kohr M.

Applied Mechanics and Engineering

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1998

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Vol. 3, no 1

5-24

EN

The problem of determining the slow viscous flow of a fluid past a cylinder with an arbitrary cross section, in a domain with boundary limited by a plane wall, is formulated as a system of Fredholm linear integral equations of the second kind. We next complete the double-layer potentials of the system with some terms having singularities located inside the obstacle and which satisfy the nonslip boundary condition on the wall. We next prove that this system of integral equations has a unique continuous solution when the boundary of the particle is a Lyapunov curve. Also, the numerical results are given for the case of a fixed circular obstacle. For the numerical solution we use a standard boundary element technique.

9

An direct boundary integral equations method to Stokes flow past rigid bodies in ground effect

Kohr M.

Applied Mechanics and Engineering

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1998

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Vol. 3, no 2

217-232

EN

The aim of this paper is to give a direct boundary integral equations method for the slow motion of some rigid bodies of an arbitrary shape, near a plane wall in a viscous incompressible fluid. By using an integral representation of the velocity field as a sum between single-layer potentials and double-layer potentials, the problem is reduced to the study of a Fredholm integral system of the second kind. By following the properties of the single-layer and double-layer operators, the existence and uniqueness result of the corresponding solution is given. The numerical results are obtained by a standard boundary element method.