Temporal chaos versus spatial mixing in reaction-advection-diffusion systems

Flow-induced arrest of spatiotemporal chaos and transition to a stationary pattern in the Gray-Scott model

We examine the prototypical Gray-Scott model, which mimics cubic autocatalytic reaction with linear decay of the autocatalyst, to model the kinetics of a reaction-diffusion system subjected to advective streamline flow. For a proper choice of boundary conditions and parameter space, the system admits wave-induced spatiotemporal chaos in the absence of flow. We show that flow above a critical value leads to an arrest of the spatiotemporal chaos due to a change in the instability from absolute to convective type. Furthermore, stationary spatial structures are borne out of a second successive bifurcation for yet another critical flow value. The theoretical formulations are corroborated by extensive numerical simulation of the full reaction-diffusion-advection system in one dimension.

Filtration at the microfluidic level: enrichment of nanoparticles by tunable filters

We present an electrohydrodynamic device for filtration of nanometre-sized particles from suspensions. A high-frequency electric field is locally generated through the action of mutually parallel microelectrodes integrated into a microfluidic channel. Due to the mechanism of ohmic heating, a thermal gradient arises above these electrodes. In conjunction with temperature-sensitive properties of the fluid, an eddy flow behaviour emerges in the laminar environment. This acts as an adjustable filter. For quantification of the filtration efficiency, we tested a wide range of particle concentrations at different electric field strengths and overall external flow velocities. Particles with a diameter of 200 nm were retained in this manner at rates of up to 100%. Numerical simulations of a model taking into account the hydrodynamic as well as electric conditions, but no interactions between the point-shaped particles, yield results that are similar to the experiment in both the flow trajectories and the particle accumulation. Our easy technique could become a valuable tool that complements conventional filtration methods for handling nanometre-scaled particles in medicine and biotechnology, e.g. bacteria and viruses.

Small-scale particle advection, manipulation and mixing: beyond the hydrodynamic scale

In this paper we discuss the problems of particle advection, manipulation and mixing at small scales. We start by considering reaction-advection-diffusion systems with the focus on mixing. We show how mixing advection affects the processes of reaction-diffusion and discuss mixing-induced instabilities. Further, we consider the problem of particle manipulation and discuss collective effects in systems comprising solid and compressible particles. We particularly discuss mechanisms of particle entrapment, the role of compressibility in the dynamics of bubbly liquids and nonequilibrium colloidal explosion. Finally, we address two issues related to the problem of wetting. First, we study the role of contact line motion for a sessile droplet (or a bubble) on an oscillating substrate. Second, we discuss an instability of a thin film leading to the formation of a fractal structure of droplets.

Effective dimensions and chemical reactions in fluid flows

We show that chemical activity in hydrodynamical flows can be understood as the outcome of three basic effects: the stirring protocol of the flow, the local properties of the reaction, and the global folding dynamics which also depends on the geometry of the container. The essence of each of these components can be described by simple functional relations. In an ordinary differential equation approach, they determine a new chemical rate equation for the concentration, which turns out to be coupled to the dynamics of an effective fractal dimension. The theory predicts an exponential convergence to the asymptotic chemical state. This holds even in flows characterized by a linear stirring protocol where transient fractal patterns are shown to exist despite the lack of any chaotic set of the advection dynamics. In the exponential case the theory applies to flows of chaotic time dependence (chaotic flows) as well.

Chemical transients in closed chaotic flows: the role of effective dimensions

We investigate chemical activity in hydrodynamical flows in closed containers. In contrast to open flows, in closed flows the chemical field does not show a well-defined fractal property; nevertheless, there is a transient filamentary structure present. We show that the effect of the filamentary patterns on the chemical activity can be modeled by the use of time-dependent effective dimensions. We derive a new chemical rate equation, which turns out to be coupled to the dynamics of the effective dimension, and predicts an exponential convergence. Previous results concerning activity in open flows are special cases of this new rate equation.