A mathematical study of peristaltic transport of a casson fluid

The peristaltic transport of a Casson fluid in a two — dimensional asymmetric channel is studied under long- wavelength and low-Reynolds number assumption The asymmetry in the channel is created by considering the peristaltic waves imposed on the boundary walls to possess different amplitude and phase The analysis of the flow is carried out in a wave frame of reference moving with the velocity of the wave Due to the asymmetry in the channel two yield planes exist and they are calculated by solving the transcendental equation in terms of the core width In an asymmetric channel the yield planes are skewed towards the boundary with higher amplitude or a phase difference in relation to the other boundary While in a symmetric channel the yield planes are located symmetrically on either side of the axis of the channel The phenomena of trapping and reflux have been discussed in the symmetric case of the channel It is noticed that trapping of fluid occurs and the trapping zone extends for an increase in the time average flux It is found that reflux occurs for higher values of amplitude of the peristaltic wave and the reflux zone extends for increased amplitudes

Peristaltic transport of a Casson fluid in an asymmetric channel.

The paper deals with the impact of non-linear viscoelastic fluid properties on the pumping characteristics of a peristaltic system For this purpose, a fluid dynamical model characterized by a long tube filled with a highly viscous liquid and by a periodic wave train traveling along the flexible wall is studied theoretically The wave shape may be arbitrary and is specified for illustration purposes only A asymptotic analysis of the axisymmetric, periodic, creeping flow has been performed under the condition that the wavelength is large compared to the mean tube radius Analytical findings show the influence of the aspect ratio, of the Weissenberg number, of the Deborah number and of the wave shape They allow also recognizing that the velocity field and the stress field are influenced by the fluid elasticity in a different way Symmetries observed with a Newtonian fluid remain valid within the approximation order as regards the kinematics of the peristaltic flow, but get lost concerning dynamic field quantities Under the condition of free pumping at small wave amplitude, the volume flux generated by the traveling wave may be a non-monotonic function of the wave frequency at otherwise constant parameters

Analysis of non-Newtonian effects in peristaltic pumping

Peristaltic motion of a non-Newtonian, incompressible power law fluid with suspension of small particles in a twodimensional channel is analyzed. A perturbation method has been employed to obtain the solution of the problem under the long wavelength approximation. The formation and growth of trapping zone are explained for variations in amplitude ratio and volume flow rate. The phenomenon of reflux has been studied. The behaviour of the axial velocity of fluid and solid particles has been discussed. The speed of the suspended particles is observed to be less than that of the fluid particles.

Peristaltic transport of small particles--power law fluid suspension in a channel.

The paper considers the phenomena of peristaltic transport of a non-Newtonian fluid represented as a power law fluid. The governing equations are the modified Navier-Stokes equations and the continuity equation in axisymmetric form. A solution is sought in terms of a perturbation series and it is shown the close proximity between analytical and numerical solutions when considering stream functions for various values of the flow behaviour index.

J. Mazumdar

Papers

Mathematical modelling of peristaltic transport of a non-Newtonian fluid.