Boundary effects on chaotic advection-diffusion chemical reactions

Rotation of Liquid Metal Droplets Solely Driven by the Action of Magnetic Fields

The self-rotation of liquid metal droplets (LMDs) has garnered potential for numerous applications, such as chip cooling, fluid mixture, and robotics. However, the controllable self-rotation of LMDs utilizing magnetic fields is still underexplored. Here, we report a novel method to induce self-rotation of LMDs solely utilizing a rotating magnetic field. This is achieved by rotating a pair of permanent magnets around a LMD located at the magnetic field center. The LMD experiences Lorenz force generated by the relative motion between the droplet and the permanent magnets and can be rotated. Remarkably, unlike the actuation induced by electrochemistry, the rotational motion of the droplet induced by magnetic fields avoids the generation of gas bubbles and behaves smoothly and steadily. We investigate the main parameters that affect the self-rotational behaviors of LMDs and validate the theory of this approach. We further demonstrate the ability of accelerating cooling and a mixer enabled by the self-rotation of a LMD. We believe that the presented technique can be conveniently adapted by other systems after necessary modifications and enables new progress in microfluidics, microelectromechanical (MEMS) applications, and micro robotics.

Active mixing of complex fluids at the microscale

Mixing of complex fluids at low Reynolds number is fundamental for a broad range of applications, including materials assembly, microfluidics, and biomedical devices. Of these materials, yield stress fluids (and gels) pose the most significant challenges, especially when they must be mixed in low volumes over short timescales. New scaling relationships between mixer dimensions and operating conditions are derived and experimentally verified to create a framework for designing active microfluidic mixers that can efficiently homogenize a wide range of complex fluids. Active mixing printheads are then designed and implemented for multimaterial 3D printing of viscoelastic inks with programmable control of local composition.

Scaling laws of peripheral mixing of passive scalar in a wall-shear layer

The scaling laws governing the concentration moments of a passive scalar released from a ground-level localized source in a neutrally stratified wall-shear layer are investigated using a theoretical framework recently formulated by Lebedev and Turitsyn [Phys. Rev. E 69, 036301 (2004)]. For the current application, this theoretical framework is generalized from the smooth random velocity field applicable in the viscous sublayer to the nonsmooth random velocity field that applies to the bulk of the wall-shear layer. Theoretical relationships for the passive scalar concentration moments are compared to a water-channel simulation of turbulent diffusion from a ground-level source in a wall-shear layer. The diffusion measurements in the wall-shear layer are shown to be consistent with the theoretical description and also imply the robustness of the identified scaling laws for the scalar concentration moments.

Predicting the evolution of fast chemical reactions in chaotic flows

We study the fast irreversible bimolecular reaction in a two-dimensional chaotic flow. The reactants are initially segregated and together fill the whole domain. Simulations show that the reactant concentration decays exponentially with rate lambda and then crosses over to the algebraic law of chemical kinetics in the final stage of the reaction. We estimate the crossover time from the reaction rate constant and the flow parameters. The exponential decay phase of the reaction can be described in terms of an equivalent passive scalar problem, allowing us to predict lambda using the theory of passive scalar advection. Depending on the relative length scale between the velocity and the concentration fields, lambda is either related to the distribution of the finite-time Lyapunov exponent of the flow or given in terms of an effective diffusivity which is independent of the small-scale stretching properties of the flow. For the former case, we suggest an optimal choice of flow parameters at which lambda is maximum.

Predicting the progress of diffusively limited chemical reactions in the presence of chaotic advection

The effects of chaotic advection and diffusion on fast chemical reactions in two-dimensional fluid flows are investigated using experimentally measured stretching fields and fluorescent monitoring of the local concentration. Flow symmetry, Reynolds number, and mean path length affect the spatial distribution and time dependence of the reaction product. A single parameter lambdaN , where lambda is the mean Lyapunov exponent N and is the number of mixing cycles, can be used to predict the time-dependent total product for flows having different dynamical features.

Passive scalar evolution in peripheral regions

We consider the evolution of a passive scalar (concentration of pollutants or temperature) in a chaotic (turbulent) flow. A universal asymptotic behavior of the passive scalar decay (homogenization) related to peripheral regions (near walls) is established. The passive scalar moments and their pair correlation function in the peripheral region are analyzed. A special case investigated in our paper is the passive scalar decay along a pipe.