Fluid transport with suspended particles by means of dilating peristaltic waves
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Fluid transport with suspended particles by means of dilating peristaltic waves Sanjay Kumar Pandey1 · Shailendra Kumar Tiwari1 Received: 6 September 2019 / Accepted: 20 November 2019 © Springer Nature Switzerland AG 2020
Abstract In the present study, transport of a Newtonian fluid containing uniformly distributed tiny particles moving in a cylindrical tube is investigated when the peristaltic wave amplitude dilates exponentially. Long wavelength approximation is used to get rid of non-linear inertia terms. It is observed that dilation of wave-amplitude during propagation enhances pressure but reduces it with rising concentration of particulate suspension. Pressure rises with the amplitude dilation parameter in case solid particles are suspended in the fluid. Pressure is also observed to increase in the distal part of the tube. Keywords Peristalsis · Waves of dilating amplitude · Suspended particles–fluid mixture · Volume fraction of solid particles
1 Introduction In order to obtain qualitative and quantitative insight of the motion of suspended solid and rigid particles distributed uniformly in a homogeneous medium due to the passage of discrete peristaltic waves, Hung and Brown [1] employed a two-dimensional experimental model to investigate various geometries and dynamic effects on peristaltic transport. It was followed by Kaimal [2] who investigated peristaltic pumping of a Newtonian fluid with rigid solid particles suspended in it at low Reynolds number using long wavelength approximations. He discussed reflux and trapping but noted that the presence of the suspended particles does not lead to any significant disturbance to the flow field of the fluid. The governing equations had an additional term associated with the viscous part in terms of the difference of fluid and particulate velocities only. It was meant for modelling peristaltic pumping due to muscular contractions and also for engineering application of pumping solid–fluid mixtures.
Drew [3] studied the stability of a Stokes’ layer of a particle–fluid mixture. He obtained a set of coupled Orr-Sommerfeld equations governing the evolution of infinitesimal disturbances. He further found that for low concentration of course dust, flow can be stabilized by decreasing the particle relaxation time, which is otherwise unstable. The model suggested was potentially different from those used by Kaimal [2]. Using Drew’s model [3], Srivastava and Srivastava [4] investigated peristaltic transport of a particle–fluid suspension in a channel, which was further analysed by Misra and Pandey [5] for axi-symmetric flow. The contribution of the nonlinear convective acceleration terms in the flow equations were duly accounted for in the theoretical analyses. A perturbation technique was used to analyse the problem. The analysis was carried out for the situation in which the amplitude ratio was small. In order to illustrate the applicability of the theoretical analysis, numerical values of various physical quantities were computed for the flow of urine through the uret
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