Mixing by polymers: experimental test of decay regime of mixing

Microfluidics for Production of Particles: Mechanism, Methodology, and Applications

In the past two decades, microfluidics-based particle production is widely applied for multiple biological usages. Compared to conventional bulk methods, microfluidic-assisted particle production shows significant advantages, such as narrower particle size distribution, higher reproducibility, improved encapsulation efficiency, and enhanced scaling-up potency. Herein, an overview of the recent progress of the microfluidics technology for nano-, microparticles or droplet fabrication, and their biological applications is provided. For both nano-, microparticles/droplets, the previously established mechanisms behind particle production via microfluidics and some typical examples during the past five years are discussed. The emerging interdisciplinary technologies based on microfluidics that have produced microparticles or droplets for cellular analysis and artificial cells fabrication are summarized. The potential drawbacks and future perspectives are also briefly discussed.

Elastic turbulence in entangled semi-dilute DNA solutions measured with optical coherence tomography velocimetry

The flow instabilities of solutions of high molecular weight DNA in the entangled semi-dilute concentration regime were investigated using optical coherence tomography velocimetry, a technique that provides high spatial (probe volumes of 3.4 pL) and temporal resolution (sub μs) information on the flow behaviour of complex fluids in a rheometer. The velocity profiles of the opaque DNA solutions (high and low salt) were measured as a function of the distance across the gap of a parallel plate rheometer, and their evolution over time was measured. At lower DNA concentrations and low shear rates, the velocity fluctuations were well described by Gaussian functions and the velocity gradient was uniform across the rheometer gap, which is expected for Newtonian flows. As the DNA concentration and shear rate were increased there was a stable wall slip regime followed by an evolving wall slip regime, which is finally followed by the onset of elastic turbulence. Strain localization (shear banding) is observed on the boundaries of the flows at intermediate shear rates, but decreases in the high shear elastic turbulence regime, where bulk strain localization occurs. A dynamic phase diagram for non-linear flow was created to describe the different behaviours.

Oscillatory elastic instabilities in an extensional viscoelastic flow

Dilute polymer solutions are known to exhibit purely elastic instabilities even when the fluid inertia is negligible. Here we report the quantitative evidence of two consecutive oscillatory elastic instabilities in an elongation flow of a dilute polymer solution as realized in a T-junction geometry with a long recirculating cavity. The main result reported here is the observation and characterization of the first transition as a forward Hopf bifurcation resulted in a uniformly oscillating state due to breaking of time translational invariance. This unexpected finding is in contrast with previous experiments and numerical simulations performed in similar ranges of the Wi and Re numbers, where the forward fork-bifurcation into a steady asymmetric flow due to the broken spatial inversion symmetry was reported. We discuss the plausible discrepancy between our findings and previous studies that could be attributed to the long recirculating cavity, where the length of the recirculating cavity plays a crucial role in the breaking of time translational invariance instead of the spatial inversion. The second transition is manifested via time aperiodic transverse fluctuations of the interface between the dyed and undyed fluid streams at the channel junction and advected downstream by the mean flow. Both instabilities are characterized by fluid discharge-rate and simultaneous imaging of the interface between the dyed and undyed fluid streams in the outflow channel.

Microelectrokinetic turbulence in microfluidics at low Reynolds number

There is commonly no turbulence in microfluidics, and the flows are believed to be either laminar or chaotic, since Reynolds number (Re) in microflows is usually on the order of unity or lower. However, we recently demonstrated that it is possible to achieve turbulence with low Re (based on the measured flow velocity and the width of the channel entrance) when a pressure-driven flow is electrokinetically forced in a quasi T-microchannel. To be able to measure high frequency velocity fluctuations in microchannels, a velocimeter with submicrometer spatial resolution and microsecond temporal resolution, called a laser-induced fluorescence photobleaching anemometer, is developed. Here we characterize the microelectrokinetic turbulence and observe some typical and important features of high Re flows, such as Kolmogorov -5/3 spectrum of velocity fluctuation, which usually can be realized only at very high Re in macroturbulent flows.

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.

There can be turbulence in microfluidics at low Reynolds number

Turbulence is commonly viewed as a type of macroflow, where the Reynolds number (Re) has to be sufficiently high. In microfluidics, when Re is below or on the order of 1 and fast mixing is required, so far only chaotic flow has been reported to enhance mixing based on previous publications since turbulence is believed not to be possible to generate in such a low Re microflow. There is even a lack of velocimeter that can measure turbulence in microchannels. In this work, we report a direct observation of the existence of turbulence in microfluidics with Re on the order of 1 in a pressure driven flow under electrokinetic forcing using a novel velocimeter having ultrahigh spatiotemporal resolution. The work could provide a new method to control flow and transport phenomena in lab-on-a-chip and a new perspective on turbulence.

Elasto-inertial turbulence

Turbulence is ubiquitous in nature, yet even for the case of ordinary Newtonian fluids like water, our understanding of this phenomenon is limited. Many liquids of practical importance are more complicated (e.g., blood, polymer melts, paints), however; they exhibit elastic as well as viscous characteristics, and the relation between stress and strain is nonlinear. We demonstrate here for a model system of such complex fluids that at high shear rates, turbulence is not simply modified as previously believed but is suppressed and replaced by a different type of disordered motion, elasto-inertial turbulence. Elasto-inertial turbulence is found to occur at much lower Reynolds numbers than Newtonian turbulence, and the dynamical properties differ significantly. The friction scaling observed coincides with the so-called "maximum drag reduction" asymptote, which is exhibited by a wide range of viscoelastic fluids.

Linear conversion of pressure into concentration, rapid switching of concentration, and generation of linear ramps of concentration in a microfluidic device

Mixing of liquids to produce solutions with different concentrations is one of the basic functionalities of microfluidic devices. Generation of specific temporal patterns of concentration in microfluidic devices is an important technique to study responses of cells and model organisms to variations in the chemical composition of their environment. Here, we present a simple microfluidic network that linearly converts pressure at an inlet into concentration of a soluble reagent in an observation region and also enables independent concurrent linear control of concentrations of two reagents. The microfluidic device has an integrated mixer channel with chaotic three-dimensional flow that facilitates rapid switching of concentrations in a continuous range. A simple pneumatic setup generating linear ramps of pressure is used to produce smooth linear ramps and triangular waves of concentration with different slopes. The use of chaotic vs. laminar mixers is discussed in the context of microfluidic devices providing rapid switching and generating temporal waves of concentration.

Elastic turbulence in a curvilinear channel flow

We report detailed quantitative studies of elastic turbulence in a curvilinear channel flow in a dilute polymer solution of high molecular weight polyacrylamide in a high viscosity water-sugar solvent. Detailed studies of the average and rms velocity and velocity gradients profiles reveal the emergence of a boundary layer associated with the nonuniform distribution of the elastic stresses across the channel. The characteristic boundary width is independent of the Weissenberg number Wi and proportional to the channel width, which is consistent with the findings our early investigations of the boundary layer in elastic turbulence in different flow geometries. The nonuniform distribution of the elastic stresses across the channel and appearance of the characteristic spatial scales of the order of the boundary layer width of both velocity and velocity gradient in the correlation functions of the velocity and velocity gradient fields in a bulk flow may suggest that excessive elastic stresses, concentrated in the boundary layer, are ejected into the bulk flow similar to jets observed in passive scalar mixing in elastic turbulence observed recently. Finally, the experimental results show that one of the main predictions of the theory of elastic turbulence, namely, the saturation of the normalized rms velocity gradient in the bulk flow of elastic turbulence contradicts the experimental observations both qualitatively and quantitatively in spite of the fact that the theory explains well the observed sharp power-law decay of the velocity power spectrum. The experimental findings call for further development of theory of elastic turbulence in a bounded container, similar to what was done for a passive scalar problem.

Scalar decay in a three-dimensional chaotic flow

The decay of a passive scalar in a three-dimensional chaotic flow is studied using high-resolution numerical simulations. The (volume-preserving) flow considered is a three-dimensional extension of the randomized alternating sine flow employed extensively in studies of mixing in two dimensions. It is used to show that theoretical predictions for two-dimensional flows with small diffusivity carry over to three dimensions even though the stretching properties differ significantly. The variance decay rate, scalar field structure, and time evolution of statistical moments confirm that there are two distinct regimes of scalar decay: a locally controlled regime, which applies when the domain size is comparable to the characteristic length scale of the velocity field, and a globally controlled regime, which applies when the domain is larger. Asymptotic predictions for the variance decay rate in both regimes show excellent agreement with the numerical results. Consideration of both the forward flow and its time reverse makes it possible to compare the scalar evolution in flows with one or two expanding directions; simulations confirm the theoretical prediction that the decay rate of the scalar is the same in both flows, despite the very different scalar field structures.

Flow pattern transition accompanied with sudden growth of flow resistance in two-dimensional curvilinear viscoelastic flows

We numerically find three types of steady solutions of viscoelastic flows and flow pattern transitions between them in a two-dimensional wavy-walled channel for low to moderate Weissenberg (Wi) and Reynolds (Re) numbers using a spectral element method. The solutions are called "convective," "transition," and "elastic" in ascending order of Wi. In the convective region in the Wi-Re parameter space, convective effect and pressure gradient balance on average. As Wi increases, elastic effect becomes comparable, and the first transition sets in. Through the transition, a separation vortex disappears, and a jet flow induced close to the wall by the viscoelasticity moves into the bulk; the viscous drag significantly drops, and the elastic wall friction rises sharply. This transition is caused by an elastic force in the streamwise direction due to the competition of the convective and elastic effects. In the transition region, the convective and elastic effects balance. When the elastic effect becomes greater than the convective effect, the second transition occurs but it is relatively moderate. The second transition seems to be governed by the so-called Weissenberg effect. These transitions are not sensitive to driving forces. By a scaling analysis, it is shown that the stress component is proportional to the Reynolds number on the boundary of the first transition in the Wi-Re space. This scaling coincides well with the numerical result.

Coil-stretch transition in an ensemble of polymers in isotropic turbulence

We study the statistical properties of ensembles of polymers in isotropic turbulence numerically in the one-way coupling regime. A linear polymer chain passively convected by turbulence is modeled by a line of beads, each of which is connected by a finitely extensible nonlinear elastic force and subject to Brownian motion. We find that when the Weissenberg number Wi(η)<1, the polymer chain has a coiled configuration, while for Wi(η)>10, it remains stretched for a much longer time than the typical time scale of the fluctuating turbulent velocity gradient. Various statistical quantities characterizing the ensemble of polymers, such as the mean, variance, autocorrelation time, and probability density function of the end-to-end vector distance, indicate that the coil-stretch transition occurs at Wi(η)=3-4. We also find that this trend is insensitive to the number of beads N(b) ( N(b)=20 or N(b)=2), provided that the parameters in the model with a small number of beads are properly generated from the one with a large number of beads (i.e., using the formula of Jin and Collins). Finally, the Wi(η) effects on the alignment of the end-to-end vector versus the principal axis of the rate of strain tensor and on the polymer elongation are examined from the viewpoint of local flow topology.

Influence of micromixer characteristics on polydispersity index of block copolymers synthesized in continuous flow microreactors

The influence of interdigital multilamination micromixer characteristics on monomer conversions, molecular weights and especially on the polydispersity index of block copolymers synthesized continuously in two microtube reactors is investigated. The micromixers are used to mix, before copolymerization, a polymer solution with different viscosities and the second monomer. Different geometries of micromixer (number of microchannels, characteristic lengths) have been studied. It was found that polydispersity indices of the copolymers follow a linear relationship with the Reynolds number in the micromixer, represented by a form factor. Thus, beside the operating conditions (nature of the first block and comonomer flow rate), the choice of the micromixer geometry and dimension is essential to control the copolymerization in terms of molecular weights and polydispersity indices. This linear correlation allows the prediction of copolymer features. It can also be a new method to optimize existing micromixers or design other geometries so that mixing could be more efficient.

Slow decay of concentration variance due to no-slip walls in chaotic mixing

Chaotic mixing in a closed vessel is studied experimentally and numerically in different two-dimensional (2D) flow configurations. For a purely hyperbolic phase space, it is well known that concentration fluctuations converge to an eigenmode of the advection-diffusion operator and decay exponentially with time. We illustrate how the unstable manifold of hyperbolic periodic points dominates the resulting persistent pattern. We show for different physical viscous flows that, in the case of a fully chaotic Poincaré section, parabolic periodic points at the walls lead to slower (algebraic) decay. A persistent pattern, the backbone of which is the unstable manifold of parabolic points, can be observed. However, slow stretching at the wall forbids the rapid propagation of stretched filaments throughout the whole domain, and hence delays the formation of an eigenmode until it is no longer experimentally observable. Inspired by the baker's map, we introduce a 1D model with a parabolic point that gives a good account of the slow decay observed in experiments. We derive a universal decay law for such systems parametrized by the rate at which a particle approaches the no-slip wall.

Role of elastic stress in statistical and scaling properties of elastic turbulence

The role of elastic stress in statistical and scaling properties of elastic turbulence in a polymer solution flow between two disks is discussed. The analogy with a small-scale magnetodynamics and a passive scalar turbulent advection in the Batchelor regime is used to explain the experimentally observed statistical properties, the flow structure, and the scaling of elastic turbulence. The emergence of a new length scale, namely, the boundary layer thickness, is observed and studied.

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.

Chaotic flow and efficient mixing in a microchannel with a polymer solution

Microscopic flows are almost universally linear, laminar, and stationary because the Reynolds number, Re, is usually very small. That impedes mixing in microfluidic devices, which sometimes limits their performance. Here, we show that truly chaotic flow can be generated in a smooth microchannel of a uniform width at arbitrarily low Re, if a small amount of flexible polymers is added to the working liquid. The chaotic flow regime is characterized by randomly fluctuating three-dimensional velocity field and significant growth of the flow resistance. Although the size of the polymer molecules extended in the flow may become comparable to the microchannel width, the flow behavior is fully compatible with that in a macroscopic channel in the regime of elastic turbulence. The chaotic flow leads to quite efficient mixing, which is almost diffusion independent. For macromolecules, mixing time in this microscopic flow can be three to four orders of magnitude shorter than due to molecular diffusion.