Quantification of the performance of chaotic micromixers on the basis of finite time Lyapunov exponents

Chaotic micromixers such as the staggered herringbone mixer developed by Stroock et al. allow efficient mixing of fluids even at low Reynolds number by repeated stretching and folding of the fluid interfaces. The ability of the fluid to mix well depends on the rate at which "chaotic advection" occurs in the mixer. An optimization of mixer geometries is a non trivial task which is often performed by time consuming and expensive trial and error experiments. In this paper an algorithm is presented that applies the concept of finite-time Lyapunov exponents to obtain a quantitative measure of the chaotic advection of the flow and hence the performance of micromixers. By performing lattice Boltzmann simulations of the flow inside a mixer geometry, introducing massless and non-interacting tracer particles and following their trajectories the finite time Lyapunov exponents can be calculated. The applicability of the method is demonstrated by a comparison of the improved geometrical structure of the staggered herringbone mixer with available literature data.Comment: 9 pages, 8 figure

Propagation of chaos for rank-based interacting diffusions and long time behaviour of a scalar quasilinear parabolic equation

We study a quasilinear parabolic Cauchy problem with a cumulative distribution function on the real line as an initial condition. We call 'probabilistic solution' a weak solution which remains a cumulative distribution function at all times. We prove the uniqueness of such a solution and we deduce the existence from a propagation of chaos result on a system of scalar diffusion processes, the interactions of which only depend on their ranking. We then investigate the long time behaviour of the solution. Using a probabilistic argument and under weak assumptions, we show that the flow of the Wasserstein distance between two solutions is contractive. Under more stringent conditions ensuring the regularity of the probabilistic solutions, we finally derive an explicit formula for the time derivative of the flow and we deduce the convergence of solutions to equilibrium.Comment: Stochastic partial differential equations: analysis and computations (2013) http://dx.doi.org/10.1007/s40072-013-0014-

Passive phloem loading and long-distance transport in a synthetic tree-on-a-chip

Vascular plants rely on differences of osmotic pressure to export sugars from regions of synthesis (mature leaves) to sugar sinks (roots, fruits). In this process, known as M\"unch pressure flow, the loading of sugars from photosynthetic cells to the export conduit (the phloem) is crucial, as it sets the pressure head necessary to power long-distance transport. Whereas most herbaceous plants use active mechanisms to increase phloem concentration above that of the photosynthetic cells, in most tree species, for which transport distances are largest, loading seems to occur via passive symplastic diffusion from the mesophyll to the phloem. Here, we use a synthetic microfluidic model of a passive loader to explore the nonlinear dynamics that arise during export and determine the ability of passive loading to drive long-distance transport. We first demonstrate that in our device, phloem concentration is set by the balance between the resistances to diffusive loading from the source and convective export through the phloem. Convection-limited export corresponds to classical models of M\"unch transport, where phloem concentration is close to that of the source; in contrast, diffusion-limited export leads to small phloem concentrations and weak scaling of flow rates with the hydraulic resistance. We then show that the effective regime of convection-limited export is predominant in plants with large transport resistances and low xylem pressures. Moreover, hydrostatic pressures developed in our synthetic passive loader can reach botanically relevant values as high as 10 bars. We conclude that passive loading is sufficient to drive long-distance transport in large plants, and that trees are well suited to take full advantage of passive phloem loading strategies

Geometric Mixing, Peristalsis, and the Geometric Phase of the Stomach

Mixing fluid in a container at low Reynolds number - in an inertialess environment - is not a trivial task. Reciprocating motions merely lead to cycles of mixing and unmixing, so continuous rotation, as used in many technological applications, would appear to be necessary. However, there is another solution: movement of the walls in a cyclical fashion to introduce a geometric phase. We show using journal-bearing flow as a model that such geometric mixing is a general tool for using deformable boundaries that return to the same position to mix fluid at low Reynolds number. We then simulate a biological example: we show that mixing in the stomach functions because of the "belly phase": peristaltic movement of the walls in a cyclical fashion introduces a geometric phase that avoids unmixing.Comment: Revised, published versio

Development and characterization of a microfluidic model of the tumour microenvironment

The physical microenvironment of tumours is characterized by heterotypic cell interactions and physiological gradients of nutrients, waste products and oxygen. This tumour microenvironment has a major impact on the biology of cancer cells and their response to chemotherapeutic agents. Despite this, most in vitro cancer research still relies primarily on cells grown in 2D and in isolation in nutrient- and oxygen-rich conditions. Here, a microfluidic device is presented that is easy to use and enables modelling and study of the tumour microenvironment in real-time. The versatility of this microfluidic platform allows for different aspects of the microenvironment to be monitored and dissected. This is exemplified here by real-time profiling of oxygen and glucose concentrations inside the device as well as effects on cell proliferation and growth, ROS generation and apoptosis. Heterotypic cell interactions were also studied. The device provides a live ‘window’ into the microenvironment and could be used to study cancer cells for which it is difficult to generate tumour spheroids. Another major application of the device is the study of effects of the microenvironment on cellular drug responses. Some data is presented for this indicating the device’s potential to enable more physiological in vitro drug screening

PDMS microfluidics developed for polymer based photonic biosensors

In this work, advances in the fabrication technology and functional analysis of a polymer microfluidic system-as a significant part of a developed polymer photonic biosensor-are reported. Robust and cost-effective microfluidics in PDMS including sample preparation functions is designed and realized by using SU-8 moulding replica. Surface modification strategies using Triton X-100 and PDMS-PEO and their effect on device sealing and non-specific protein adsorption are investigated by contact angle measurement and in situ fluorescence microscopy. © 2014 Springer-Verlag Berlin Heidelberg

Fabrication of Functionalized Double-Lamellar Multifunctional Envelope-Type Nanodevices Using a Microfluidic Chip with a Chaotic Mixer Array

Multifunctional envelope-type nanodevices (MENDs) are very promising non-viral gene delivery vectors because they are biocompatible and enable programmed packaging of various functional elements into an individual nanostructured liposome. Conventionally MENDs have been fabricated by complicated, labor-intensive, time-consuming bulk batch methods. To avoid these problems in MEND fabrication, we adopted a microfluidic chip with a chaotic mixer array on the floor of its reaction channel. The array was composed of 69 cycles of the staggered chaotic mixer with bas-relief structures. Although the reaction channel had very large Péclet numbers (>105) favorable for laminar flows, its chaotic mixer array led to very small mixing lengths (<1.5 cm) and that allowed homogeneous mixing of MEND precursors in a short time. Using the microfluidic chip, we fabricated a double-lamellar MEND (D-MEND) composed of a condensed plasmid DNA core and a lipid bilayer membrane envelope as well as the D-MEND modified with trans-membrane peptide octaarginine. Our lab-on-a-chip approach was much simpler, faster, and more convenient for fabricating the MENDs, as compared with the conventional bulk batch approaches. Further, the physical properties of the on-chip-fabricated MENDs were comparable to or better than those of the bulk batch-fabricated MENDs. Our fabrication strategy using microfluidic chips with short mixing length reaction channels may provide practical ways for constructing more elegant liposome-based non-viral vectors that can effectively penetrate all membranes in cells and lead to high gene transfection efficiency

An integrated, self-contained microfluidic cassette for isolation, amplification, and detection of nucleic acids

A self-contained, integrated, disposable, sample-to-answer, polycarbonate microfluidic cassette for nucleic acid-based detection of pathogens at the point of care was designed, constructed, and tested. The cassette comprises on-chip sample lysis, nucleic acid isolation, enzymatic amplification (polymerase chain reaction and, when needed, reverse transcription), amplicon labeling, and detection. On-chip pouches and valves facilitate fluid flow control. All the liquids and dry reagents needed for the various reactions are pre-stored in the cassette. The liquid reagents are stored in flexible pouches formed on the chip surface. Dry (RT-)PCR reagents are pre-stored in the thermal cycling, reaction chamber. The process operations include sample introduction; lysis of cells and viruses; solid-phase extraction, concentration, and purification of nucleic acids from the lysate; elution of the nucleic acids into a thermal cycling chamber and mixing with pre-stored (RT-)PCR dry reagents; thermal cycling; and detection. The PCR amplicons are labeled with digoxigenin and biotin and transmitted onto a lateral flow strip, where the target analytes bind to a test line consisting of immobilized avidin-D. The immobilized nucleic acids are labeled with up-converting phosphor (UCP) reporter particles. The operation of the cassette is automatically controlled by an analyzer that provides pouch and valve actuation with electrical motors and heating for the thermal cycling. The functionality of the device is demonstrated by detecting the presence of bacterial B.Cereus, viral armored RNA HIV, and HIV I virus in saliva samples. The cassette and actuator described here can be used to detect other diseases as well as the presence of bacterial and viral pathogens in the water supply and other fluids

Ensemble Analysis of Angiogenic Growth in Three-Dimensional Microfluidic Cell Cultures

We demonstrate ensemble three-dimensional cell cultures and quantitative analysis of angiogenic growth from uniform endothelial monolayers. Our approach combines two key elements: a micro-fluidic assay that enables parallelized angiogenic growth instances subject to common extracellular conditions, and an automated image acquisition and processing scheme enabling high-throughput, unbiased quantification of angiogenic growth. Because of the increased throughput of the assay in comparison to existing three-dimensional morphogenic assays, statistical properties of angiogenic growth can be reliably estimated. We used the assay to evaluate the combined effects of vascular endothelial growth factor (VEGF) and the signaling lipid sphingoshine-1-phosphate (S1P). Our results show the importance of S1P in amplifying the angiogenic response in the presence of VEGF gradients. Furthermore, the application of S1P with VEGF gradients resulted in angiogenic sprouts with higher aspect ratio than S1P with background levels of VEGF, despite reduced total migratory activity. This implies a synergistic effect between the growth factors in promoting angiogenic activity. Finally, the variance in the computed angiogenic metrics (as measured by ensemble standard deviation) was found to increase linearly with the ensemble mean. This finding is consistent with stochastic agent-based mathematical models of angiogenesis that represent angiogenic growth as a series of independent stochastic cell-level decisions