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The analysis of Taylor dispersion in a fluid flowing through a narrow pipe is of considerable interest among the scientific community. Most of the studies on dispersion primarily considered a transversely uniform release of contaminant at the initial moment, while only a few have addressed the influence of the initial condition on the dispersion process in a tube flow. The present work investigates the transient dispersion process with a ring-source release of solute by means of an unsteady two-dimensional transport model. An irreversible absorptive type of a first-order reaction is also considered. The transport model is solved using the series expansion technique of W. N. Gill [“A note on the solution of transient dispersion problems,” Proc. R. Soc. A 298, 335 (1967)], known as the generalized dispersion technique. The whole transport model is explained using the transport coefficients obtained from the first four terms of Gill's series expansion. Meanwhile, the concept of statistical moments is also used for finding the transport coefficients. The study outcomes are well established, satisfying the result of existing literature under limiting conditions. The inclusion of the ring-source release of solute in the study of dispersion has a significant effect at the initial time. In addition, the view of the cross-sectional distribution of solute concentration gives more detailed information on solute scattering under the proposed model.

This study aims at investigating the dispersion process in an oscillatory flow of a layered liquid. The liquid is considered as a three-layer liquid where the center region is the Casson liquid surrounded by a Newtonian liquid layer flowing through a narrow pipe under the wall reaction. The perturbation technique has been used for solving the momentum equations. In order to assist the analysis of solute transport behavior, Aris-Barton’s method of moments has been utilized, where different molecular diffusivities were assumed for different respective regions, yet to be constant. The effects of finite yield stress, viscosity ratio, density ratio, peripheral layer thickness, and irreversible absorption at the tube wall on dispersion are investigated in detail. In the cases of steady, unsteady, and combined flow situations, dispersion coefficient is found to be diminished by absorption parameter, viscosity ratio, and yield stress, respectively. In the case of a steady flow and unsteady convective diffusion of a reactive solute, dispersion coefficient is independent of density ratio. For both the unsteady and combined flows, density ratio provides a pulsatile behaviour of the dispersion process though an increase in the density ratio may faster the dispersion process. Dispersion at early times is not affected by absorption though a considerable effect is observed for large time. The presence of a peripheral layer enhances the value of the dispersion coefficient and is higher than the single layer Casson liquid flow. As strong as the non-Newtonian effect is considered, the dispersion process becomes slower. Larger values of molecular diffusivity at different layers are the reason for less dispersion coefficient. This study may be useful for understanding the dispersion process in the blood-like liquid flow analysis for microcirculation.

We have studied the effect of addition of (a) mica, (b) silane coupling agent, and (c) silane-treated mica on the ambient dielectric properties of vulcanized styrene-butadiene rubber. It is observed that both dielectric constant and dielectric loss increase as mica, silane, and silane-treated mica are added. The increase is more pronounced in the case of silane-treated mica than for the untreated mica systems. The observed values of dielectric constants are in close agreement with the calculated ones obtained from different theories of heterogeneous dielectrics. Dielectric strength shows an increasing trend in the presence of mica. At higher mica loading, D.C. conductivity decreases slightly.