Shear dispersion along circular pipes is affected by bends, but the torsion of the pipe is negligible

The flow of a viscous fluid along a curving pipe of fixed radius is driven by a pressure gradient. For a generally curving pipe it is the fluid flux which is constant along the pipe and so I correct fluid flow solutions of Dean (1928) and Topakoglu (1967) which assume constant pressure gradient. When the pipe is straight, the fluid adopts the parabolic velocity profile of Poiseuille flow; the spread of any contaminant along the pipe is then described by the shear dispersion model of Taylor (1954) and its refinements by Mercer, Watt et al (1994,1996). However, two conflicting effects occur in a generally curving pipe: viscosity skews the velocity profile which enhances the shear dispersion; whereas in faster flow centrifugal effects establish secondary flows that reduce the shear dispersion. The two opposing effects cancel at a Reynolds number of about 15. Interestingly, the torsion of the pipe seems to have very little effect upon the flow or the dispersion, the curvature is by far the dominant influence. Lastly, curvature and torsion in the fluid flow significantly enhance the upstream tails of concentration profiles in qualitative agreement with observations of dispersion in river flow

Three-dimensional aspects of fluid flows in channels. II. Effects of Meniscus and Thin Film regimes on Viscous Fingers

We perform a three-dimensional study of steady state viscous fingers that develop in linear channels. By means of a three-dimensional Lattice-Boltzmann scheme that mimics the full macroscopic equations of motion of the fluid momentum and order parameter, we study the effect of the thickness of the channel in two cases. First, for total displacement of the fluids in the channel thickness direction, we find that the steady state finger is effectively two-dimensional and that previous two-dimensional results can be recovered by taking into account the effect of a curved meniscus across the channel thickness as a contribution to surface stresses. Secondly, when a thin film develops in the channel thickness direction, the finger narrows with increasing channel aspect ratio in agreement with experimental results. The effect of the thin film renders the problem three-dimensional and results deviate from the two-dimensional prediction.Comment: 9 pages, 10 figure

Characteristics of liquids lugs in gas–liquid Taylor flow in microchannels

The hydrodynamics of liquid slugs in gas–liquid Taylor flow in straight and meandering microchannels have been studied using micro Particle Image Velocimetry. The results confirm a recirculation motion in the liquid slug, which is symmetrical about the center line of the channel for the straight geometry and more complex and three-dimensional in the meandering channel. An attempt has also been made to quantify and characterize this recirculation motion in these short liquid slugs (Ls/w<1.5) by evaluating the recirculation rate, velocity and time. The recirculation velocity was found to increase linearly with the two-phase superficial velocity UTP. The product of the liquid slug residence time and the recirculation rate is independent of UTP under the studied flow conditions. These results suggest that the amount of heat or mass transferred between a given liquid slug and its surroundings is independent of the total flow rate and determined principally by the characteristics of the liquid slug

A flexible error estimate for the application of centre manifold theory

In applications of centre manifold theory we need more flexible error estimates than that provided by, for example, the Approximation Theorem 3 by Carr [4, 6]. Here we extend the theory to cover the case where the order of approximation in parameters and that in dynamical variables may be completely different. This allows, for example, the effective evaluation of low-dimensional dynamical models at finite parameter values

Microfluidics: Fluid physics at the nanoliter scale

Microfabricated integrated circuits revolutionized computation by vastly reducing the space, labor, and time required for calculations. Microfluidic systems hold similar promise for the large-scale automation of chemistry and biology, suggesting the possibility of numerous experiments performed rapidly and in parallel, while consuming little reagent. While it is too early to tell whether such a vision will be realized, significant progress has been achieved, and various applications of significant scientific and practical interest have been developed. Here a review of the physics of small volumes (nanoliters) of fluids is presented, as parametrized by a series of dimensionless numbers expressing the relative importance of various physical phenomena. Specifically, this review explores the Reynolds number Re, addressing inertial effects; the Péclet number Pe, which concerns convective and diffusive transport; the capillary number Ca expressing the importance of interfacial tension; the Deborah, Weissenberg, and elasticity numbers De, Wi, and El, describing elastic effects due to deformable microstructural elements like polymers; the Grashof and Rayleigh numbers Gr and Ra, describing density-driven flows; and the Knudsen number, describing the importance of noncontinuum molecular effects. Furthermore, the long-range nature of viscous flows and the small device dimensions inherent in microfluidics mean that the influence of boundaries is typically significant. A variety of strategies have been developed to manipulate fluids by exploiting boundary effects; among these are electrokinetic effects, acoustic streaming, and fluid-structure interactions. The goal is to describe the physics behind the rich variety of fluid phenomena occurring on the nanoliter scale using simple scaling arguments, with the hopes of developing an intuitive sense for this occasionally counterintuitive world

Effect of microchannel aspect ratio on residence time distributions and the axial dispersion coefficient

The effect of microchannel aspect ratio (channel depth/channel width) on residence time distributions and the axial dispersion coefficient have been investigated for Newtonian and shear thinning non-Newtonian flow using computational fluid dynamics. The results reveal that for a fixed cross sectional area and throughput, there is a narrowing of the residence time distribution as the aspect ratio decreases. This is quantified by an axial dispersion coefficient that increases rapidly for aspect ratios less than 0.3 and then tends towards an asymptote as the aspect ratio goes to 1. The results also show that the axial dispersion coefficient is related linearly to the Reynolds number when either the aspect ratio or the mean fluid velocity is varied. However, the fluid Péclet number is a linear function of the Reynolds number only when the aspect ratio (and therefore hydraulic diameter) is varied. Globally, the results indicate that microchannels should be designed with low aspect ratios (≤ 0.3) for reduced axial dispersion