PARTICULATE SUSPENSION FLOW INDUCED BY SINUSOIDAL PERISTALTIC WAVES THROUGH ECCENTRIC CYLINDERS: THREAD ANNULAR

2013 ◽  
Vol 06 (04) ◽  
pp. 1350026 ◽  
Author(s):  
KH. S. MEKHEIMER ◽  
Y. ABD ELMABOUD ◽  
A. I. ABDELLATEEF
Keyword(s):  
Particle Concentration ◽  
Surgical Trauma ◽  
Medical Implants ◽  
Flexible Cylinder ◽  
Fluid Mixture ◽  
Friction Forces ◽  
Eccentric Cylinders ◽  
Peristaltic Pumping ◽  
Flow Through ◽  
Eccentric Annuli

This paper describes a new model for obtaining analytical solutions of peristaltic flow through eccentric annuli. A mathematical model of peristaltic pumping of a fluid mixture (as blood model) in a circular eccentric cylinders is presented and it is motivated due to the fact that thread injection is a promising method for placing medical implants within the human body with minimum surgical trauma. For the eccentric annuli, the inner cylinder is rigid and moving with a constant velocity V, and the outer one is hollow flexible cylinder that has a sinusoidal wave traveling down its wall. The coupled differential equations for both the fluid and the particle phases have been solved by using two methods and the expressions for the velocity distribution of fluid and particle phase, flow rate, pressure drop, friction forces at the inner and outer cylinders have been derived. The results obtained are discussed in brief. The significance of the particle concentration and the eccentricity parameter as well as the nature of the basic flow has been well explained.

Slip Flow in Eccentric Annuli

2017 ◽  
Vol 139 (4) ◽  
Author(s):  
R. S. Alassar
Keyword(s):  
Aspect Ratio ◽  
Average Velocity ◽  
Slip Flow ◽  
Small Aspect Ratio ◽  
Channel Geometry ◽  
Bipolar Coordinates ◽  
Cylindrical Annulus ◽  
Velocity Flow ◽  
Flow Through ◽  
Eccentric Annuli

A solution of the problem of Poiseuille slip flow through an eccentric cylindrical annulus is obtained in bipolar coordinates. The solution is in excellent agreement with the two published limiting cases of slip flow through concentric annuli and no-slip flow through eccentric annuli. It is shown that for a fixed aspect ratio, fully eccentric channels sustain the maximum average velocity (flow rate) under the same pressure gradient and slip conditions. For a given channel geometry, the average velocity varies linearly with Knudsen number except for small aspect ratio. It is also shown that the extrema of the friction factor Reynolds number product is determined by how this product is defined or scaled.

A theoretical study of viscous effects in peristaltic pumping

1994 ◽  
Vol 279 ◽  
pp. 177-195 ◽  
Author(s):  
Alden M. Provost ◽  
W. H. Schwarz
Keyword(s):  
Wave Propagation ◽  
Pressure Gradient ◽  
Flow Rate ◽  
Mean Flow ◽  
Viscous Effects ◽  
Transverse Waves ◽  
Peristaltic Pumping ◽  
Mean Pressure ◽  
Flow Through ◽  
The Mean

Intuition and previous results suggest that a peristaltic wave tends to drive the mean flow in the direction of wave propagation. New theoretical results indicate that, when the viscosity of the transported fluid is shear-dependent, the direction of mean flow can oppose the direction of wave propagation even in the presence of a zero or favourable mean pressure gradient. The theory is based on an analysis of lubrication-type flow through an infinitely long, axisymmetric tube subjected to a periodic train of transverse waves. Sample calculations for a shear-thinning fluid illustrate that, for a given waveform, the sense of the mean flow can depend on the rheology of the fluid, and that the mean flow rate need not increase monotonically with wave speed and occlusion. We also show that, in the absence of a mean pressure gradient, positive mean flow is assured only for Newtonian fluids; any deviation from Newtonian behaviour allows one to find at least one non-trivial waveform for which the mean flow rate is zero or negative. Introduction of a class of waves dominated by long, straight sections facilitates the proof of this result and provides a simple tool for understanding viscous effects in peristaltic pumping.

A Note on Leakage Jet Forces: Application in the Modelling of Digital Twins of Hydraulic Valves

2021 ◽  
Author(s):  
Zoufiné Lauer-Baré ◽  
Erich Gaertig ◽  
Johannes Krebs ◽  
Christian Arndt ◽  
Christian Sleziona ◽  
...  
Keyword(s):  
Shear Force ◽  
Analytical Approximation ◽  
Analytical Relation ◽  
Large Set ◽  
Simulation Tools ◽  
Eccentric Cylinders ◽  
Digital Twins ◽  
Numerical Instabilities ◽  
Flow Through ◽  
Hydraulic Valves

The proper modelling of fluid flow through annular gaps is of great interest in leakage calculations for many applications in fluid power technology. However, while detailed numerical simulations are certainly possible, they are very time consuming, in various cases prone to numerical instabilities and may not even include all physically relevant effects. This is an issue especially in system simulations, where a large set of computations is needed in order to prepare the lookup-tables for the required input fields. In this work, an analytical approximation for the shear force, which is induced by viscous flow between two eccentric cylinders, is presented. This relation, and its derivation, mimics and enhances the well-known Piercy-relation for the corresponding volume flow that is utilized in state-of-the-art system simulation tools. To determine its range of validity, the analytical relation for the shear force is compared to 3D-simulations. Additionally, an application of this approximation for creating digital twins of hydraulic valves is also discussed in this work.

scholarly journals Pressure Drop Measurements of the Flow through Eccentric Cylinders with Rotating Inner Cylinders

1969 ◽  
Vol 12 (53) ◽  
pp. 1032-1040 ◽  
Author(s):  
Yutaka YAMADA ◽  
Koichi NAKABAYASHI ◽  
Kozo MAEDA
Keyword(s):  
Pressure Drop ◽  
Eccentric Cylinders ◽  
Flow Through

ALTERATION IN ELECTRO-OSMOTIC FLOW THROUGH A NON-DARCY POROUS MEDIUM DUE TO MHD AND PERISTALTIC PUMPING

2019 ◽  
Vol 22 (13) ◽  
pp. 1639-1650
Author(s):  
Saima Noreen ◽  
Qurat-ul-Ain ◽  
Muhammad Qasim ◽  
Dharmendra Tripathi
Keyword(s):  
Porous Medium ◽  
Osmotic Flow ◽  
Peristaltic Pumping ◽  
Flow Through ◽  
Electro Osmotic Flow

scholarly journals Rotational and Axial Flow through the Gap between Eccentric Cylinders, of which the Outer One Rotates

1974 ◽  
Vol 17 (114) ◽  
pp. 1564-1571 ◽  
Author(s):  
Koichi NAKABAYASHI ◽  
Yutaka YAMADA ◽  
Kaname SEO
Keyword(s):  
Axial Flow ◽  
Eccentric Cylinders ◽  
Flow Through

Peristaltic Transport of a Particle-Fluid Suspension

1989 ◽  
Vol 111 (2) ◽  
pp. 157-165 ◽  
Author(s):  
L. M. Srivastava ◽  
V. P. Srivastava
Keyword(s):  
Particle Concentration ◽  
Amplitude Ratio ◽  
Flow Reversal ◽  
Spherical Particles ◽  
Free Fluid ◽  
Mean Flow ◽  
Two Phase ◽  
Flow Process ◽  
Fluid Mixture ◽  
The Mean

Peristaltic pumping by a sinusoidal traveling wave in the walls of a two-dimensional channel filled with a viscous incompressible fluid in which are distributed identical rigid spherical particles, is investigated theoretically. A perturbation solution is obtained which satisfies the momentum equations for the case in which amplitude ratio (wave amplitude/channel half width) is small. The results show that the fluid phase mean axial velocity decreases with increase in the particle concentration. The phenomenon of reflux (the mean flow reversal) is discussed. A reversal of velocity in the neighborhood of the centerline occurs when the pressure gradient is greater than that of the critical reflux condition. It is found that the critical reflux pressure is lower for the particle-fluid suspension than for the particle-free fluid. It is further observed that the mean flow reversal is strongly dependent on the particle concentration and the presence of particles in the fluid favors the reversal flow. A motivation of the present analysis has been the hope that such a theory of two-phase flow process is very useful in understanding the role of peristaltic muscular contraction in transporting bio-fluid behaving like a particle-fluid mixture. Also the theory is important to the engineering applications of pumping solid-fluid mixtures by peristalsis.

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