H. Ramkissoon

Long-wave peristaltic transport of a compressible viscous fluid in a finite pipe subject to a time-dependent pressure drop

Axisymmetric viscous flow in a long pipe, driven by the pulsating pressure gradient and the wall deformation, is investigated. This kind of a flow is relevant to the peristaltic transport of blood due to the heart pumping along with the synchronic expansion/constriction of the vessel. Following the spirit of the lubrication theory, a reduced system of equations is derived. An obtained explicit solution demonstrates crucial role of peristalsis on the total fluid flux through the pipe. In order to account for the inertia effect, a model based on an averaging of the momentum equation using an a priori parabolic flow pattern across the pipe, is also derived.

Wall effects on a spherical particle

Abstract The motion of a solid spherical particle at the instant it passes the centre of a spheroidal container has been investigated using the no-slip condition at the surfaces. The shape of this spheroidal container is assumed to deviate slightly from that of a sphere at the surface. An expression for the stream function describing the flow field has been obtained to the first order in the parameter characterizing the deviation and this in turn has been utilized to evaluate the drag on the particle. Wall effects are then examined and special cases deduced.

Slip flow past an approximate spheroid

SummaryCreeping axisymmetric slip flow past a spheroid whose shape deviates slightly from that of a sphere is investigated. An exact solution is obtained to the first order in the small parameter characterizing the deformation. As an application, the case of flow past an oblate spheroid is considered and the drag experienced by it is evaluated. Special well-known cases are deduced and some observations made.

Unsteady flow of an elastico-viscous fluid in tubes of uniform cross-section

Abstract In this paper, the uniqueness of solution for internal bounded unsteady flows of a shortmemory fluid is first established. Closed-form solutions are then obtained for the equations characterizing flows of such fluids in circular and rectangular tubes of uniform cross-section under an arbitrary pressure gradient. Special cases including the oscillatory flow between two parallel plates are discussed.

Non-Newtonian fluid sphere in a spherical container

SummaryThe motion of an inner non-Newtonian fluid sphere at the instant it passes the centre of a rigid spherical container is investigated. The inner and outer fluid motions have been determined and the drag on the inner sphere evaluated. Well-known cases are deduced and wall effects then examined.

Longitudinal and torsional oscillation of a rod in a polar fluid

Abstract This paper examines the problem of an infinite rod undergoing both torsional and longitudinal oscillations in an unbounded incompressible fluid medium. With the aid of transform methods a class of exact solutions are obtained. Some numerical work is done to reveal the effect of micropolar parameters on the microrotation and velocity fields which are depicted graphically.

Flow due to the longitudinal and torsional oscillation of a cylinder

SummaryAn exact solution is obtained for the motion of a fluid contained in an infinité circular cylinder which is undergoing both torsional and longitudinal oscillations. An analytical expression is obtained for the viscous drag on the cylinder and the velocity is depicted graphically. Where possible, comparisons are made with corresponding results for the external problem.

Stokes flow past a slightly deformed fluid sphere

SummaryThe Stokes flow past a fluid spheroid whose shape deviates slightly from that of a sphere, is examined. To the first order in the small parameter characterizing the deformation, an exact solution is obtained. As an application, the case of a fluid oblate spheroid is considered and the drag experienced by it is evaluated. Special well-known cases are then deduced.ZusammenfassungDie Stokes-Strömung um einen Flüssigkeitstropfen, der nur leicht von einer perfekten Kugel abweicht, wird untersucht. Eine Lösung wird gefunden, die exakt ist bis zur ersten Ordnung im Deformations-Parameter. Als Beispiel wird der Strömungswiderstand eines abgeplatteten Flüssigkeits-Sphäroids berechnet. Die Methode liefert für bekannte Spezialfälle korrekte Lösungen.

Unsteady motion of a sphere in an elastico-viscous fluid

Abstract This paper examines the unsteady slow motion of a sphere in a short memory elastico-viscous Walters fluid. With the aid of a semi-direct variational approach, the flow field is determined and special cases of constant acceleration and exponentially decreasing acceleration are then investigated. To examine the effect of elasticity, streamlines have been plotted and compared with their classical counterparts.

Slow flow of a non-Newtonian liquid past a fluid sphere

SummaryThe motion of a non-Newtonian fluid past a Newtonian fluid sphere has been investigated using the Stokes approximation. The stream functions characterizing the internal and external flow fields have been determined and the special case of flow past a solid sphere is deduced. The drag experienced by the fluid sphere has been evaluated and found to be greater than the classical counterpart.