# Interaction of Pulsatile and Peristaltic Transport Induced Flows of a Particle-Fluid Suspension

01 Mar 1998-Zamm-zeitschrift Fur Angewandte Mathematik Und Mechanik (WILEY‐VCH Verlag)-Vol. 78, Iss: 3, pp 207-212

About: This article is published in Zamm-zeitschrift Fur Angewandte Mathematik Und Mechanik.The article was published on 1998-03-01. It has received 3 citation(s) till now. The article focuses on the topic(s): Suspension (vehicle) & Pulsatile flow.

...read more

##### Citations

More filters

••

TL;DR: A perturbation solution to the complete set of Navier–Stokes equations is found for the case in which the frequency of the traveling wave and that of the imposed pressure gradient are equal and a first order steady flow is found to exist.

Abstract: The interaction of purely periodic mean flow with a peristaltic induced flow is investigated within the framework of a two-dimensional analogue. The mathematical model considers a viscous incompressible fluid under the effect of transverse magnetic field, taking into account the effect of Hall currents for a magneto-fluid with suspended particles between infinite parallel walls on which a sinusoidal traveling wave is imposed. A perturbation solution to the complete set of Navier–Stokes equations is found for the case in which the frequency of the traveling wave and that of the imposed pressure gradient are equal. The ratio of the traveling wave amplitude to channel width is assumed to be small. For this case a first order steady flow is found to exist, as contrasted to a second order effect in the absence of the imposed periodic pressure gradient. The effect of Hall parameter, Hartmann number and the various parameters included in the problem are discussed numerically.

44 citations

••

TL;DR: In this paper, a perturbation method is employed and the primitive variables are expanded in a series with the wall amplitude as the perturbations parameter, and the boundary conditions are applied at the mean surface of the channel and the first-order quantization quantities are numerically determined by solving the governing system of ordinary differential equations by shooting technique.

Abstract: The particulate suspension flow in a channel whose walls describe a travelling wave motion is examined numerically. A perturbation method is employed and the primitive variables are expanded in a series with the wall amplitude as the perturbation parameter. The boundary conditions are applied at the mean surface of the channel and the first-order perturbation quantities are numerically determined by solving the governing system of ordinary differential equations by shooting technique. The present approach does not impose any restriction on the Reynolds number of the flow and the wave number and frequency of the wavy-walled channel, although it is limited by the linear analysis. The wall shear stress and the positions of flow separation and reattachment points are computed and the influence of the volume fraction density of the particles is examined. The variations of velocity and pressure of the particulate suspension flow with frequency of excitation are also presented. Copyright © 2005 John Wiley & Sons, Ltd.

7 citations

••

TL;DR: In this article, a numerical study of the linear temporal stability characteristics of particulate suspension flow through a converging-diverging symmetric wavy-walled channel is considered.

Abstract: A numerical study of the linear temporal stability characteristics of particulate suspension flow through a converging-diverging symmetric wavy-walled channel is considered. The basic flow is a superposition of plane channel flow of particulate suspension and periodic flow components arising due to the small amplitude sinusoidal waviness of the channel walls. The disturbance equations are derived within the framework of Floquet theory and solved using the spectral collocation method. The effects of small amplitude sinusoidal waviness of the channel walls and those of the presence of particles on the initial growth of the disturbances are examined. Two-dimensional stability calculations for particulate suspensions indicate the presence of fast growing unstable modes that arise due to the waviness of the walls. Neutral stability calculations are performed in the disturbances wavenumber-Reynolds number (αs−Re) plane, for the wavy channel with representative values of wavenumber (λ) and the wall amplitude to semi-channel height ratio (∈w) for different values of volume fraction density of the particles (C). It is observed that the critical Reynolds number for transition decreases with increase of ∈w and C. However, the flow can be modulated by suitable wall excitation which in turn can stabilize the flow.

4 citations

### Cites methods from "Interaction of Pulsatile and Perist..."

...In view of this, as a first step towards understanding the stability characteristics of such flows, a simple model of particulate suspension employed by Nayfeh [26], Drew [24], Srivastava and Srivastava [16], and Usha and Prema [ 31 ] has been considered in this paper....

[...]

...The equations using the continuum approach are expressed as (Nayfeh [26], Drew [24], Srivastava and Srivastava [16], and Usha and Prema [30], [ 31 ]):...

[...]