Optimizing the Source Distribution in Fluid Mixing

A passive scalar is advected by a velocity field, with a nonuniform spatial source that maintains concentration inhomogeneities. For example, the scalar could be temperature with a source consisting of hot and cold spots, such that the mean temperature is constant. Which source distributions are best mixed by this velocity field? This question has a straightforward yet rich answer that is relevant to real mixing problems. We use a multiscale measure of steady-state enhancement to mixing and optimize it by a variational approach. We then solve the resulting Euler--Lagrange equation for a perturbed uniform flow and for simple cellular flows. The optimal source distributions have many broad features that are as expected: they avoid stagnation points, favor regions of fast flow, and their contours are aligned such that the flow blows hot spots onto cold and vice versa. However, the detailed structure varies widely with diffusivity and other problem parameters. Though these are model problems, the optimization procedure is simple enough to be adapted to more complex situations.Comment: 19 pages, 23 figures. RevTeX4 with psfrag macro

IHTC14-22470 EFFECT OF RAIN ON EVOLUTION OF DISTRIBUTION OF SOLUBLE GASEOUS POLLUTANTS IN THE ATMOSPHERE

ABSTRACT We suggest a model of rain scavenging of soluble gaseous pollutants in the atmosphere. It is shown that below-cloud gas scavenging is determined by non-stationary convective diffusion equation with the effective Peclet number. The obtained equation was analyzed numerically in the case of lognormal droplet size distribution. Calculations of scavenging coefficient and the rates of precipitation scavenging are performed for wet removal of ammonia (NH 3 ) and sulfur dioxide (SO 2 ) from the atmosphere. It is shown that scavenging coefficient is non-stationary and height-dependent. It is found also that the scavenging coefficient strongly depends on initial concentration distribution of soluble gaseous pollutants in the atmosphere. It is shown that in the case of linear distribution of the initial concentration of gaseous pollutants whereby the initial concentration of gaseous pollutants decreases with altitude, the scavenging coefficient increases with height in the beginning of rainfall. At the later stage of the rain scavenging coefficient decreases with height in the upper below-cloud layers of the atmosphere

Topological Chaos in Spatially Periodic Mixers

Topologically chaotic fluid advection is examined in two-dimensional flows with either or both directions spatially periodic. Topological chaos is created by driving flow with moving stirrers whose trajectories are chosen to form various braids. For spatially periodic flows, in addition to the usual stirrer-exchange braiding motions, there are additional topologically-nontrivial motions corresponding to stirrers traversing the periodic directions. This leads to a study of the braid group on the cylinder and the torus. Methods for finding topological entropy lower bounds for such flows are examined. These bounds are then compared to numerical stirring simulations of Stokes flow to evaluate their sharpness. The sine flow is also examined from a topological perspective.Comment: 18 pages, 14 figures. RevTeX4 style with psfrag macros. Final versio

Reduced models of chemical reaction in chaotic flows

A. Vikhansky and S. M. Co

Single-Phase Flow of Non-Newtonian Fluids in Porous Media

The study of flow of non-Newtonian fluids in porous media is very important and serves a wide variety of practical applications in processes such as enhanced oil recovery from underground reservoirs, filtration of polymer solutions and soil remediation through the removal of liquid pollutants. These fluids occur in diverse natural and synthetic forms and can be regarded as the rule rather than the exception. They show very complex strain and time dependent behavior and may have initial yield-stress. Their common feature is that they do not obey the simple Newtonian relation of proportionality between stress and rate of deformation. Non-Newtonian fluids are generally classified into three main categories: time-independent whose strain rate solely depends on the instantaneous stress, time-dependent whose strain rate is a function of both magnitude and duration of the applied stress and viscoelastic which shows partial elastic recovery on removal of the deforming stress and usually demonstrates both time and strain dependency. In this article the key aspects of these fluids are reviewed with particular emphasis on single-phase flow through porous media. The four main approaches for describing the flow in porous media are examined and assessed. These are: continuum models, bundle of tubes models, numerical methods and pore-scale network modeling.Comment: 94 pages, 12 figures, 1 tabl