Microfluidics and Nanofluidics

An electrokinetic mixer driven by oscillatory cross flow has been studied numerically as a means for generating chaotic mixing in microfluidic devices for both confined and throughput mixing configurations. The flow is analyzed using numerical simulation of the unsteady Navier–Stokes equations combined with the tracking of single and multi-species passive tracer particles. First, the case of confined flow mixing is studied in which flow in the perpendicular channels of the oscillatory mixing element is driven sinusoidally, and 90° out of phase. The flow is shown to be chaotic by means of positive effective (finite time) Lyapunov exponents, and the stretching and folding of material lines leading to Lagrangian tracer particle dispersion. The transition to chaotic flow in this case depends strongly on the Strouhal number (St), and weakly on the ratio of the cross flow channel length to width (L/W). For L/W = 2, the flow becomes appreciably chaotic as evidenced by visual particle dispersion at approximately St = 0.32, and the transitional value of St increases slightly with increasing aspect ratio. A peak degree of mixing on the order of 85% is obtained for the range of parameter values explored here. In the second phase of the analysis, the effect of combining a fixed throughput flow with the oscillatory cross channel motion for use in a continuous mixing operation is examined in a star cell geometry. Chaotic mixing is again observed, and the characteristics of the downstream dispersion patterns depend mainly on the Strouhal number and the (dimensionless) throughput rate. In the star cell, the flow becomes appreciably chaotic as evidenced by visual particle dispersion at approximately St = 1, slightly higher than for the case of cross cell. The star cell mixing behavior is marked by the convergence of the degree of mixing to a plateau level as the Strouhal number is increased at fixed flow rate. Degree of mixing values from 70 to 80% are obtained indicating that the continuous flow is bounded by the maximum degree of mixing obtained from the confined flow configuration.

Understanding drug extravasation from the leaky vasculature to tumour sites based on the enhanced permeability and retention effect (EPR) is of critical importance for designing and improving drug delivery efficiency. This paper reports a tumour–vasculature microfluidic device consisting of two microchannels (top channel and bottom channel) separated by a porous membrane. To investigate drug extravasation, a numerical two-phase mixture model was developed and validated using experimental results. This is the first time that a two-phase mixture model is used to investigate drug extravasation through the simulated leaky vasculature in a microfluidic device. After the flow structures and drug distribution were numerically examined, the effects of parameters including the velocity of blood flow, drug concentration, and the degree of blood vessel leakiness as represented by the membrane porosity were systematically investigated. This numerical model offers a powerful tool to study drug extravasation through leaky vasculature, and the simulated results provide useful insights into drug extravasation and drug accumulation at tumour sites.

Liquid–liquid flow profiles are central to the operation of microfluidic devices in a range of applications. We recently demonstrated a multi-stream solvent extraction (SX) chip that combines high-surface-to-volume ratios and volumetric throughput. Here, we study these flow profiles in detail using numerical simulations, with consideration of different boundary conditions. The two liquids differ in viscosity, modelled on platinum (aqueous) and extractant (organic) phases, and the position of the liquid–liquid interfaces (and therefore surface/volume and phase ratios) can be controlled by adjustment of flow rates. The prediction of the position of the interface requires the solution of the governing equations of fluid mechanics. The volume of fluid (VOF) method was used to simulate the dynamics of the organic and aqueous phases to reveal stable flow profiles. This experimentally validated computational model with the root-mean-square deviation of about 11 µm will be useful for simulation of microfluidic SX design and operation, particularly where process intensification is sought through scale-out.

Recently, the microwell has been widely used for cell trapping due to its simple design and enclosed microenvironment for on-chip cell culture and stimulation. In this paper, we investigated the effect of various geometrical factors on microwells for efficient particle analysis. We used the Arbitrary Lagrangian–Eulerian method to calculate the trajectory of particles entering circular and triangular microwells under various geometrical factors, particle size, and flow conditions. Our simulation results show that the W/L = 2 triangular microwell provides the best trapping efficiency due to a stronger recirculation vortex. A smaller particle size or slower flow rate also enhances particle trapping efficiency. To validate simulation results, we flowed 4.5, 6, and 10 µm diameter polystyrene beads into W/L = 1 circular, W/L = 1 and W/L = 2 triangular microwells under various flow rates. The experimental results agreed well with simulation results, showing that the occupancy of W/L = 2 triangular microwell was sevenfold and twofold higher than W/L = 1 circular and W/L = 1 triangular microwells, respectively. Overall, the above results can provide a useful guideline to design the microwell device for efficient hydrodynamic particle trapping, which can be applied to single cell analysis or rare cell capture.

We developed a method of interfacing microfluidics with mass spectrometry (MS) using a robotic spotting system to automate the contact spotting process. We demonstrate that direct and automated spotting of analyte from multichannel microfluidic chips to a custom microstructured MALDI target plate was a simple, robust, and high-throughput method for interfacing parallel microchannels using matrix-assisted laser desorption/ionization mass spectrometry (MALDI-MS). Using thermoplastic cyclic olefin copolymer (COC) polymer microfluidic chips containing eight parallel 100 μm × 46 μm microchannels connected to a single input port, spotting volume repeatability and MALDI-MS signal uniformity are evaluated for a panel of sample peptides. The COC microfluidic chips were fabricated by hot embossing and solvent bonding techniques followed by chip dicing to create open ends for MS interfacing. Using the automatic robotic spotting approach, microfluidic chip-based reversed-phase liquid chromatography (RPLC) separations were interfaced with electrochemically etched nanofilament silicon (nSi) target substrate, demonstrating the potential of this approach toward chip-based microfluidic separation coupled with matrix-free laser desorption/ionization mass spectrometry.

It is now well established that for fluid flow at the micro- and nano-scales the standard no-slip boundary condition of fluid mechanics at fluid–solid interfaces is not applicable and must be replaced by a boundary condition that allows some degree of tangential fluid slip. Although molecular dynamics studies support this notion, an experimental verification of a slip boundary condition remains lacking, primarily due to the difficulty of performing accurate experimental observations at small scales. In this article, three simple fluid problems are studied in detail, namely a fluid near a solid wall that is suddenly set in motion (Stokes’ first problem), the long-time behavior of a fluid near an oscillating solid wall (Stokes’ second problem), and the long-time behavior of a fluid between two parallel walls one of which is oscillating (oscillatory Couette flow). The no-slip boundary condition is replaced with the Navier boundary condition, which allows a certain degree of tangential fluid slip via a constant slip length. The aim is to obtain analytical expressions, which may be used in an experimental determination of the constant slip length for any fluid–solid combination.

Molecular dynamics simulations of force-driven nano-channel gas flows show two distinct flow regions. While the bulk flow region can be determined using kinetic theory, transport in the near-wall region is dominated by gas–wall interactions. This duality enables definition of an inner-layer scaling, $$y^{*}$$ , based on the molecular dimensions. For gas–wall interactions determined by Lennard–Jones potential, the velocity distribution for $$y^{*} \le 3$$ exhibits a universal behavior as a function of the local Knudsen number and gas–wall interaction parameters, which can be interpreted as the “law of the nano-wall.” Knowing the velocity and density distributions within this region and using the bulk flow velocity profiles from Beskok–Karniadakis model (Beskok and Karniadakis in Microscale Thermophys Eng 3(1):43–77, 1999), we outline a procedure that can correct kinetic-theory-based mass flow rate predictions in the literature for various nano-channel gas flows.

A new computational method was developed to simulate a two-dimensional Eckart acoustic streaming field in an ultrasonic heptagonal chamber actuated by multiple acoustic transducers with different associated frequencies and acoustic incident pressures. Simulation was conducted using the superposition of multiple spatial gradients of the Reynolds stresses and the second mean sound pressures at different frequencies. The developed method extends beyond the capabilities of the conventional method that is restricted to uniform frequency and incident pressure. Various acoustic streaming patterns can be feasibly generated by tuning the frequency and incident pressure of each individual transducer. The implementation of multiple acoustic transducers offers flexibility to control acoustic flows in microfluidic devices for various applications. Furthermore, the developed simulation method for acoustic streaming fields provides an optimization tool for the frequency, incident pressure and location of each transducer.

This study presents a sheathless and portable microfluidic chip that is capable of high-throughput focusing bioparticles based on 3D travelling-wave dielectrophoresis (twDEP). High-throughput focusing is achieved by sustaining a centralized twDEP field normal to the continuous through-flow direction. Two twDEP electrode arrays are formed from upper and lower walls of the microchannel and extend to its center, which induce twDEP forces to provide the lateral displacements in two directions for focusing the bioparticles. Bioparticles can be focused to the center of the microchannel effectively by twDEP conveyance when the characteristic time due to twDEP conveying in the y direction is shorter than the residence time of the particles within twDEP electrode array. Red blood cells can be effectively focused into a narrow particle stream (~10 μm) below a critical flow rate of 10 μl/min (linear flow velocity ~5 mm/s), when under a voltage of 14 Vp–p at a frequency of 500 kHz is applied. Approximately 90% focusing efficiency for red blood cells can be achieved within two 6-mm-long electrode arrays when the flow rate is below 12 μl/min. Blood cells and Candida cells were also focused and sorted successfully based on their different twDEP mobilities. Compared to conventional 3D-paired DEP focusing, velocity is enhanced nearly four folds of magnitude. 3D twDEP provides the lateral displacements of particles and long residence time for migrating particles in a high-speed continuous flow, which breaks through the limitation of many electrokinetic cell manipulation techniques.