Chaotic mixing in a steady flow in a microchannel

We report experiments on mixing of a passively advected fluorescent dye in a low Reynolds number flow in a microscopic channel. The channel is a chain of repeating segments with a custom designed profile that generates a steady three-dimensional flow with stretching and folding, and chaotic mixing. A few statistical characteristics of mixing in the flow are studied and are all found to agree with theoretical and experimental results for the flows in the Batchelor regime of mixing that are chaotic in time. The proposed microchannel provides fast and efficient mixing and is simple to fabricate.     

Resonant chaotic mixing in a cellular flow

This Letter presents a quantitative theory of resonant mixing in time-dependent volume-preserving 3D flows using a model cellular flow introduced in T. Solomon and I. Mezic, Nature (London) 425, 376 (2003), as an example. Specifically, we show that chaotic advection is dramatically enhanced by a time-dependent perturbation for certain resonant frequencies. We compute the fraction of the mixed volume as a function of the frequency of the perturbation and show that essentially complete mixing in 3D is achieved at every resonant frequency.     

On passage through resonances in volume-preserving systems

Resonance processes are common phenomena in multiscale (slow-fast) systems. In the present paper we consider capture into resonance and scattering on resonance in 3D volume-preserving multiscale systems. We propose a general theory of those processes and apply it to a class of kinematic models inspired by viscous Taylor-Couette flows between two counter-rotating cylinders. We describe the phenomena during a single passage through resonance and show that multiple passages lead to the chaotic advection and mixing. We calculate the width of the mixing domain and estimate a characteristic time of mixing. We show that the resultant mixing can be described using a diffusion equation with a diffusion coefficient depending on the averaged effect of the passages through resonances.     

Time-of-flight flow imaging of two-component flow inside a microfluidic chip

Here we report on using NMR imaging and spectroscopy in conjunction with time-of-flight tracking to noninvasively tag and monitor nuclear spins as they flow through the channels of a microfluidic chip. Any species with resolvable chemical-shift signatures can be separately monitored in a single experiment, irrespective of the optical properties of the fluids, thereby eliminating the need for foreign tracers. This is demonstrated on a chip with a mixing geometry in which two fluids converge from separate channels, and is generally applicable to any microfluidic device through which fluid flows within the nuclear spin-lattice relaxation time.     

Resonance phenomena and long-term chaotic advection in volume-preserving systems

Creating chaotic advection is the most efficient strategy to achieve mixing on microscale or in very viscous fluids. In this paper, we present a quantitative theory of the long-time resonant mixing in 3D near-integrable flows. We use the flow between two coaxial elliptic counter-rotating cylinders as a demonstrative model, where multiple scatterings on resonance result in mixing by causing the jumps of adiabatic invariants. We improve the existing estimates of the width of the mixing domain. We show that the resulting mixing both on short and long time scales can be described in terms of a single diffusion-type equation with a diffusion coefficient depending on the averaged effect of multiple passages through resonances. We discuss the exact location of the boundaries of the chaotic domain and show how it affects the properties of mixing.     

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

We develop a theory describing the transition to a spatially homogeneous regime in a mixing flow with a chaotic in time reaction. The transverse Lyapunov exponent governing the stability of the homogeneous state can be represented as a combination of Lyapunov exponents for spatial mixing and temporal chaos. This representation, being exact for time-independent flows and equal Pe clet numbers of different components, is demonstrated to work accurately for time-dependent flows and different Pe clet numbers.     

基于微泡共振的快速微流体声学混合方法研究

微流体在生物医学、化学工程等领域应用广泛,并具有重大意义.在预处理中,液体混合也是关键且最为必要的前序.为了提高微流控腔道内液体混合的效率,本文提出基于单微泡振动的声学混合器,通过微泡共振,产生声微流,声微流形成的剪切力将在流体中产生微扰动,实现液体的混合.设计了底面直径为40μm的微孔结构,由于液体表面张力作用形成微泡,在共振频率为165 kHz的压电换能器激励下,气泡发生共振产生声微流.通过对压电换能器输入不同能量,获取混合液体的最优参数,可在37.5 ms内实现混合效果,混合均匀度达到92.7%.本文设计的单微泡振动混合器结构简单、混合效率高、混合时间短、输入能量低,可为生物化学等方面的研究提供强有力的技术支撑.     

Universal behavior of entrainment due to coherent structures in turbulent shear flow

A solution is suggested for a persistent mystery in the physics of turbulent flows: cumulus clouds rise to towering heights, practically without entraining the ambient medium, while apparently similar turbulent jets quickly lose their identity through entrainment and mixing. Dynamical system computations on a model vortical flow show that entrainment due to coherent structures depends sensitively on relative speeds of fluid parcels. Local heating, for example, can alter drastically the sizes of Kolmogorov-Arnol'd-Moser tori and chaotic mixing regions. The entrainment rate and, hence, the lifetime of a turbulent shear flow show a universal, nonmonotone dependence on the heating.     

Microfluidic mixing enhancement using electrokinetic instability under electric field perturbations in a double T-shaped microchannel

The electrokinetic instability (EKI) phenomenon occurs when microfluidic flows with an electrical conductivity gradient are driven by a high-intensity external electrical field. Although EKI limits the robust performance of complex electrokinetic bioanalytical systems, it can be actively exploited to achieve the rapid mixing of micro- and nanoliter volume solutions in microscale devices. This paper investigates the EKI phenomenon in a double T-shaped microchannel, in which two aqueous electrolyte solutions with a 3.5:1 conductivity ratio are driven electrokinetically into the mixing channel via the application of a DC electrical field. A stratified flow condition is formed when the intensity of the applied DC electrical field is below a certain threshold value. However, as the intensity is increased, a series of flow circulations forms at the interfaces of neighboring solutions flows, and then propagates in the downstream direction when the intensity of the electrical field is increased beyond a certain critical threshold value. Electrical field intensity perturbations aligned in the direction of the conductivity gradient are then added to the DC electrical field at the upper inlet of the double T-shaped microchannel near the main mixing channel. It is found that these perturbations can stir the microfluidic instability and the induced flow instability conditions can enhance the mixing efficiency. Support by the National Science Council of Taiwan (Grant Nos. NSC 96-2221-E- 167-031-MY2, NSC 96-2622-E-167-006-CC3, and NSC97-3114-E-167-001)     

Control methods for problems of mixing and coherence in chaotic maps and flows

We review a variety of control methods which are capable of enhancing the chaoticity and mixing properties of chaotic flows and also methods which work towards promoting the coherence properties of such flows. We discuss a parameter control method which can enhance the chaoticity and the rate of mixing of dissipative as well as conservative flows and outline methods which promote global mixing by the addition of noise and by preventing island formation. As the inverse side of this problem, we summarize methods which can create coherent structures in chaotic dynamical flows. We also discuss the utility of these methods from the point of view of applications as well as for understanding phenomena which occur in natural systems.     

Transient chaotic mixing during a baroclinic life cycle

We discuss how atmospheric eddies affect transport and mixing of tracers at midlatitudes. To this purpose, we study baroclinic life cycles in a simple dynamical model of the atmosphere. We consider the trapping properties of the developing eddies and the characteristics of meridional transport, and we identify regions of increased mixing. Although the flow is in principle three-dimensional, we illustrate how some of the concepts developed in the study of two-dimensional chaotic advection provide useful information on tracer dynamics in more complicated flows. (c) 2000 American Institute of Physics.     

Design,Implementation, Simulation,and Visualization of a Highly Efficient RIM Microfluidic Mixer for Rapid Freeze-Quench of Biological Samples

Abstract  

Rapid freeze-quench (RFQ) trapping of short-lived reaction intermediates for spectroscopic study plays an important role in the characterization of biological reactions. Recently, there has been considerable effort to achieve sub-millisecond reaction deadtimes. We present here a new, robust, high-velocity microfluidic mixer that enables such rapid freeze-quenching. It is a based on the mixing method of two impinging jets commonly used in reaction injection molding of plastics. This method achieves efficient mixing by inducing chaotic flow at relatively low Reynolds numbers (Re = 140). We present the first mathematical simulation and microscopic visualization of mixing in such RFQ micromixers, the results of which show that the impinging solutions efficiently mix within the mixing chamber. These tests, along with a practical demonstration in an RFQ setup that involves copper wheels, show that this new mixer can in practice provide reaction deadtimes as low as 100 μs.     

Folding of viscous threads in diverging microchannels

We study the folding instability of a viscous thread surrounded by a less viscous miscible liquid flowing from a square to a diverging microchannel. Because of the change in the flow introduced by the diverging channel, the viscous thread minimizes viscous dissipation by oscillating to form bends rather than by simply dilating. The folding frequency and the thread diameter can be related to the volume flow rates and thus to the characteristic shear rate. Diffusive mixing at the boundary of the thread can significantly modify the folding flow morphologies. This microfluidic system enables us to control the bending of the thread and to enhance mixing between liquids having significantly different viscosities.     

Fluorescence lifetime imaging of mixing dynamics in continuous-flow microdroplet reactors

Water-in-oil microdroplets within fluidic channels have the potential to serve as isolated reaction compartments for monitoring real-time dynamics with high efficiency and repeatability. Droplets, usually generated from aqueous and oil solutions using standard microfluidic formats, can be produced at frequencies in excess of 1 kHz. Although mixing within such microdroplets is normally enhanced by chaotic advection, the mixing pattern from droplet to droplet is almost identical and reproducible in form. Herein, we demonstrate that fluorescence lifetime imaging can be used to reconstruct mixing patterns within a droplet with a time resolution of 5 micros.     

Determination of the optimal excitation frequency range in background flows

The chaotization of a vortical flow caused by a nonstationary incident flow is studied by the examples of several dynamically consistent models. It is shown that for relatively small values of excitation amplitude, the chaotization of such flows and, correspondingly, chaotic transport of passive scalars is determined by a small number of nonlinear resonances with frequencies close to the excitation frequency. Hence, the analysis of locations and overlaps of these resonances in the considered models makes it possible to derive fairly good estimates of excitation frequencies that are optimal for the chaotic transport.     

Mixing of non-Newtonian fluids in steadily forced systems

We investigate mixing in a viscoelastic and shear-thinning fluid-a very common combination in polymers and suspensions. We find that competition between elastic and viscous forces generates self-similar mixing, lobe transport, and other characteristics of chaos. The mechanism by which chaos is produced is evaluated both in experiments and in a simple model. We find that chaotic flow is generated by spontaneous oscillations, the magnitude and frequency of which govern the extent of chaos and mixing.     

Experimental studies of pattern formation in a reaction-advection-diffusion system

Experiments are presented on pattern formation in the Belousov-Zhabotinsky (BZ) reaction in a blinking vortex flow. Mixing in this flow is chaotic, with nearby tracers separating exponentially with time. The patterns that form in this flow with the BZ reaction mimic chaotic mixing structures seen in passive transport. The behavior is analyzed in terms of a mixing time taum and a characteristic decorrelation time TBZ for the BZ system. Flows with taum comparable to or smaller than TBZ generate large-scale patterns whose features are captured by simulations of mixing fields for the flow.     

Onset of Chaotic Kolmogorov Flows Resulting from Interacting Oscillatory Modes

On the basis of rigorous analysis supported by numerical computation, a systematic study is presented to locate and examine chaotic Kolmogorov flows resulting from the interaction of a basic steady-state flow and oscillatory modes. Referenced to suitably chosen initial conditions of the Kolmogorov flow model, these oscillatory modes are derived from the equation linearized around the basic steady-state flow. The numerical experiments provide insight into the transition process from secondary self-oscillation flows or secondary steady-state flows to chaotic Kolmogorov flows.     

Modelling of flows in micromixers

A method is proposed for modelling fluid flows in microchannels. The method is tested on the known experimental data on studying the flows in microchannels with the aid of the micro-PIV. The flow regimes in micromixers of the Y- and T-types are studied. The passive and active mixers are considered. The dependence of the mixing efficiency on the Reynolds and Péclet numbers as well as the possibility of using the hydrophobic and ultra-hydrophobic coatings are analysed. A T-mixer is proposed as an active technique of mixing, in which the flow rate in one of the inlet channels varied according to the harmonic law. The dependence of the mixing efficiency on the frequency of the variation of the flow rate and its amplitude is established.     

Multiscale laminar flows with turbulentlike properties

By applying fractal electromagnetic force fields on a thin layer of brine, we generate steady quasi-two-dimensional laminar flows with multiscale stagnation point topology. This topology is shown to control the evolution of pair separation (Delta) statistics by imposing a turbulentlike locality based on the sizes and strain rates of hyperbolic stagnation points when the flows are fast enough, in which case Delta(2) approximately t(gamma) is a good approximation with gamma close to 3. Spatially multiscale laminar flows with turbulentlike spectral and stirring properties are a new concept with potential applications in efficient and microfluidic mixing.