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.

scholarly journals Slip Effects on Peristaltic Transport of a Particle-Fluid Suspension in a Planar Channel

2015 ◽  
Vol 2015 ◽  
pp. 1-14 ◽  
Author(s):  
Mohammed H. Kamel ◽  
Islam M. Eldesoky ◽  
Bilal M. Maher ◽  
Ramzy M. Abumandour
Keyword(s):  
Amplitude Ratio ◽  
Muscular Contraction ◽  
Slip Condition ◽  
Spherical Particles ◽  
Free Fluid ◽  
Mean Flow ◽  
Two Phase ◽  
Flow Process ◽  
Fluid Mixture ◽  
Slip Conditions

Peristaltic pumping induced by a sinusoidal traveling wave in the walls of a two-dimensional channel filled with a viscous incompressible fluid mixed with rigid spherical particles is investigated theoretically taking the slip effect on the wall into account. 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 analysis has been carried out by duly accounting for the nonlinear convective acceleration terms and the slip condition for the fluid part on the wavy wall. The governing equations are developed up to the second order of the amplitude ratio. The zeroth-order terms yield the Poiseuille flow and the first-order terms give the Orr-Sommerfeld equation. The results show that the slip conditions have significant effect within certain range of concentration. The phenomenon of reflux (the mean flow reversal) is discussed under slip conditions. It is found that the critical reflux pressure is lower for the particle-fluid suspension than for the particle-free fluid and is affected by slip condition. A motivation of the present analysis has been the hope that such theory of two-phase flow process under slip condition is very useful in understanding the role of peristaltic muscular contraction in transporting biofluid behaving like a particle-fluid mixture. Also the theory is important to the engineering applications of pumping solid-fluid mixture by peristalsis.

Investigation of the Flow Behavior of Participate Filled Fluids

1996 ◽  
Vol 445 ◽  
Author(s):  
T. E. Driscoll ◽  
P. C. Li ◽  
G. L. Lehmann ◽  
E. J. Cotts
Keyword(s):  
Large Particle ◽  
Capillary Flow ◽  
Flow Behavior ◽  
Solid Particles ◽  
Spherical Particles ◽  
Liquid Density ◽  
High Concentration ◽  
Flow Process ◽  
Fluid Mixture ◽  
Underfill Flow

AbstractUnderfill encapsulants, used in direct‐chip‐attachment (DCA) packaging of electronics, consist of an epoxy resin in which a high concentration of solid particles are suspended. As a fluid mixture key features of these encapsulants are their relatively large particle sizes and large particle‐to‐liquid density ratios (ρs/ρ0 ?2.4). Experiments have been conducted to characterize the flow behavior of model mixtures of negatively buoyant, spherical particles suspended in Newtonian liquids. Capillary flow in a parallel surface channel is used to simulate the underfill flow process. The effects of varying the channel spacing, particle size and liquid carrier are reported here. The flow behavior is contrasted with a linear fluid, effective viscosity model. Particle settling appears to be linked to the more complex behavior observed in both our model suspensions and measurements using an actual commercial encapsulant.

Direct Measurement of the Mean Flow Velocity Vector

1976 ◽  
Vol 98 (4) ◽  
pp. 736-739 ◽  
Author(s):  
R. H. Kirchhoff ◽  
R. M. Struziak
Keyword(s):  
Flow Velocity ◽  
Fundamental Frequency ◽  
Velocity Vector ◽  
Mean Flow ◽  
Two Phase ◽  
Response Equation ◽  
The Mean ◽  
Lock In ◽  
Mean Flow Velocity

The response of a single inclined rotating hot wire anemometer was analyzed. The mean flow anemometer response equation was expanded in a Fourier Series about the fundamental frequency of rotation. Utilizing the d-c level and the first two harmonics of the response it is possible to construct the mean flow velocity vector within a solid angle determined by the mounting angle of the wire. The rotating anemometer response was measured using the technique of two phase lock-in detection to determine the first two harmonics and their phases relative to the fundamental frequency of rotation. Determination of the mean flow velocity vector using this technique was found to be feasible.

Peristaltic Waves in Circular Cylindrical Tubes

1969 ◽  
Vol 36 (3) ◽  
pp. 579-587 ◽  
Author(s):  
F. Yin ◽  
Y. C. Fung
Keyword(s):  
Pressure Gradient ◽  
Wall Motion ◽  
Amplitude Ratio ◽  
Cylindrical Tube ◽  
Critical Value ◽  
Mean Flow ◽  
Navier Stokes Equation ◽  
Mean Pressure ◽  
The Mean ◽  
Set Up

Peristaltic pumping in a circular cylindrical tube is analyzed. The problem is a viscous fluid flow induced by an axisymmetric traveling sinusoidal wave of moderate amplitude imposed on the wall of a flexible tube. A perturbation method of solution is sought. The amplitude ratio (wave amplitude/tube radius) is chosen as a parameter. The nonlinear convective acceleration terms in the Navier-Stokes equation is retained. The governing equations are developed up to the second order in the amplitude ratio. The zeroth-order terms yield the classical Poiseuille flow, the first-order terms yield the Sommerfeld-Orr equation. If there is no pressure gradient in the absence of wall motion, the mean flow and mean pressure gradient (averaged over time) are both shown to be proportional to the square of the amplitude ratio. Numerical results are obtained for this simple case by approximating a complicated group of products of Bessel functions by a polynomial. The results show that the mean axial velocity is dominated by two terms. One term corresponds to a parabolic profile which is due to the mean pressure gradient set up by the wall motion. The other term arises from satisfying the no-slip boundary condition at the wavy wall rather than at the mean position of the wall. In addition, there are perturbations arising from the convective acceleration. If the mean pressure gradient set up by the wall motion itself reaches a certain positive critical value, the velocity becomes zero on the axis. Values of the mean pressure gradient larger than the critical value will induce backward flow in the fluid. Values of the critical pressure gradient for several cases are presented.

Peristaltic Transport

1968 ◽  
Vol 35 (4) ◽  
pp. 669-675 ◽  
Author(s):  
Y. C. Fung ◽  
C. S. Yih
Keyword(s):  
Velocity Profile ◽  
Pressure Gradient ◽  
Amplitude Ratio ◽  
Critical Value ◽  
Positive Pressure ◽  
Peristaltic Motion ◽  
Mean Flow ◽  
Peristaltic Pumping ◽  
Order Of Magnitude ◽  
The Mean

Peristaltic pumping (viscous fluid flow induced by a sinusoidal traveling wave motion of the walls of a tube) at moderate amplitudes of motion is analyzed in the two-dimensional case. The nonlinear convective acceleration is considered and the nonslip condition is applied on the wavy wall (rather than on the mean position) in order to account for the mean flow induced by the wall motion. In the case in which there is no other cause of flow, the mean flow induced by the peristaltic motion of the wall is proportional to the square of the amplitude ratio (wave amplitude/half width of channel). The velocity profile depends on the mean pressure gradient. In this paper only those cases in which the pressure gradient will produce a flow of the same order of magnitude as that induced by the peristaltic motion are considered. If the pressure gradient is positive and equal to a certain critical value, then the velocity is zero on the center line. Pumping against a positive pressure gradient greater than the critical value would induce a backward flow (reflux) in the core region of the stream. There will be no reflux if the pressure gradient is smaller than the critical value. The velocity profile and the value of the critical pressure gradient are presented in this paper.

Statistical hydromechanics of disperse systems. Part 2. Solution of the kinetic equation for suspended particles

1972 ◽  
Vol 52 (2) ◽  
pp. 345-355 ◽  
Author(s):  
Yu. A. Buyevich
Keyword(s):  
Kinetic Equation ◽  
Successive Approximations ◽  
Method Of Successive Approximations ◽  
Mean Flow ◽  
Time And Space ◽  
Two Phase ◽  
The Mean ◽  
Derivatives Of ◽  
Dynamic Variables

To solve the kinetic equation for particles of a monodisperse two-phase mixture the method of successive approximations is developed; this resembles in its main features the well-known Chapman-Enskog method in the kinetic theory of gases. This method is applicable for a mixture whose state differs slightly from the equilibrium, i.e., when time and space derivatives of the dynamic variables describing the mean flow of both phases of the mixture are sufficiently small. Accordingly, the solution obtained is valid when the time and space scales of the mean flow exceed considerably those for random pseudo-turbulent motion of particles and a fluid. The conservation equations for determination of all the dynamic variables are formulated in approximations which have the same meaning as those of Euler and Navier & Stokes in hydromechanics of one-phase media.

scholarly journals Wave–Mean Flow Interactions and the Maintenance of Superrotation in a Terrestrial Atmosphere

2016 ◽  
Vol 73 (8) ◽  
pp. 3181-3196 ◽  
Author(s):  
João Rafael Dias Pinto ◽  
Jonathan Lloyd Mitchell
Keyword(s):  
Large Scale ◽  
Low Frequency ◽  
Zonal Flow ◽  
Equatorial Region ◽  
Rossby Number ◽  
Kelvin Wave ◽  
Mean Flow ◽  
Flow Process ◽  
Dynamical Interaction ◽  
The Mean

Abstract The interplay between mean meridional circulation and transient eddies through wave–mean flow interaction processes defines the general behavior of any planetary atmospheric circulation. Under a higher-Rossby-number regime, equatorward momentum transports provided by large-scale disturbances generate a strong zonal flow at the equatorial region. At intermediate Rossby numbers, equatorial Kelvin waves play a leading role in maintaining a superrotating jet over the equator. However, at high Rossby numbers, the Kelvin wave only provides equatorward momentum fluxes during spinup, and the wave–mean flow process that maintains this strongly superrotating state has yet to be identified. This study presents a comprehensive analysis of the tridimensional structure and life cycle of atmospheric waves and their interaction with the mean flow, which maintains the strong, long-lived superrotating state in a higher-Rossby-number-regime atmosphere. The results show that the mean zonal superrotating circulation is maintained by the dynamical interaction between mixed baroclinic–barotropic Rossby wave modes via low-frequency variations of the zonal-mean state in short and sporadic periods of stronger instability. The modulation of amplitude of the equatorial and extratropical Rossby waves suggests a nonlinear mechanism of eddy–eddy interaction between these modes.

Production and Dissipation of Energy in the Turbulent Flow of a Particle-Fluid Mixture, With Some Results on Drag Reduction

1976 ◽  
Vol 43 (4) ◽  
pp. 543-547 ◽  
Author(s):  
D. A. Drew
Keyword(s):  
Energy Balance ◽  
Turbulent Flow ◽  
Drag Reduction ◽  
Large Reynolds Number ◽  
Motion Model ◽  
Mean Flow ◽  
Two Phase ◽  
Dissipation Energy ◽  
Fluid Mixture ◽  
Dissipation Of Energy

The production and dissipation of energy in a two-phase model for particle-fluid turbulent flow is considered. For plane parallel mean flow use of several scaling arguments yields a balance between production and drag dissipation for the particles, and between production and viscous dissipation for the fluid. A simple particle motion model is used to obtain estimates of the drag dissipation. Energy balance considerations are made for situations where drag reduction by the addition of particles is observed. Significant drag reduction is found to occur for sufficiently large Reynolds number. Discussion of the extra effectiveness of polymers for drag reduction is given within the framework of energy balance.

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