Liquid and gas flows in microchannels of varying cross section: a comparative analysis of the flow dynamics and design perspectives

This paper presents a comparative study of the flow of liquid and gases in microchannels of converging and diverging cross sections. Towards this, the static pressure across the microchannels is measured for different flow rates of the two fluids. The study includes both experimental and numerical investigations, thus providing several useful insights into the local information of flow parameters as well. Three different microchannels of varying angles of convergence/divergence (4°, 8° and 12°) are studied to understand the effect of the angle on flow properties such as pressure drop, Poiseuille number and diodicity. A comparison of the forces involved in liquid and gas flows shows their relative significance and effect on the flow structure. A diodic effect corresponds to a difference in the flow resistance in a microchannel of varying cross section, when the flow is subjected alternatively to converging and diverging orientations. In the present experiments, the diodic effect is observed for both liquid and gas as working fluids. The effect of governing parameters—Reynolds number and Knudsen number, on the diodicity is analysed. Based on these results, a comparison of design perspectives that may be useful in the design of converging/diverging microchannels for liquid and gas flows is provided.     

Two-Dimensional Analysis of Electrokinetically Driven Out-of-Plane Vortices in a Microchannel Liquid Flow Using Patterned Surface Charge

The technology developed for photolithographically patterning the electric surface charge to be negative, positive, or neutral enables the realization of complex liquid flows even in straight and uniform microchannels with extremely small Reynolds number. A theoretical model to analyze a steady incompressible electrokinetically driven two-dimensional liquid flow in a microchannel with an inhomogeneous surface charge under externally applied electric field is derived. The flow field is obtained analytically by solving the biharmonic equation with the Helmholtz-Smoluchowski slip boundary condition using the Fourier series expansion method. The model has been applied to study three basic out-of-plane vortical flow fields: single vortex and a train of corotating and a series of counterrotating vortex pairs. For model verification, the solution for the single vortex has been tested against numerical computations based on the full Navier-Stokes equations revealing the dominant control parameters. Two interesting phenomena have been observed in out-of-plane multivortex dynamics: merging of corotating vortices and splitting of counterrotating vortices. The criteria for the onset of both phenomena are discussed     

Pressure loss in constriction microchannels

Constriction devices contain elements inserted into the fluid stream, which change the local streamwise flow area. One such element is the orifice-like obstruction with sharp corners, a back-to-back abrupt contraction and expansion, which could trigger flow separation. A series of microchannels, 40 μm × 1 μm × 4000 μm in nominal dimensions, with constriction elements at the centers of the channels has been fabricated using standard micromachining techniques. The channel widths at the constriction sections varied from 10 μm to 34 μm, with pressure sensors integrated in each channel. Nitrogen gas was passed through the microdevices under inlet pressure up to 50 psi. The mass flow rates were measured for all the devices as a function of the pressure drop. A monotonic decrease of the flow rate with decreasing constriction-gap width was observed. The pressure distribution along the microchannel with the smallest constriction gap showed a pressure drop across the constriction element. Both mass flow rate and pressure measurements indicate that flow separation from the constriction sharp corners could occur     

Boundary domain integral method for high Reynolds viscous fluid flows in complex planar geometries

The article presents new developments in boundary domain integral method (BDIM) for computation of viscous fluid flows, governed by the Navier–Stokes equations. The BDIM algorithm uses velocity–vorticity formulation and is based on Poisson velocity equation for flow kinematics. This results in accurate determination of boundary vorticity values, a crucial step in constructing an accurate numerical algorithm for computation of flows in complex geometries, i.e. geometries with sharp corners. The domain velocity computations are done by the segmentation technique using large segments. After solving the kinematics equation the vorticity transport equation is solved using macro-element approach. This enables the use of macro-element based diffusion–convection fundamental solution, a key factor in assuring accuracy of computations for high Reynolds value laminar flows. The versatility and accuracy of the proposed numerical algorithm is shown for several test problems, including the standard driven cavity together with the driven cavity flow in an L shaped cavity and flow in a Z shaped channel. The values of Reynolds number reach 10,000 for driven cavity and 7500 for L shaped driven cavity, whereas the Z shaped channel flow is computed up to Re = 400. The comparison of computational results shows that the developed algorithm is capable of accurate resolution of flow fields in complex geometries.     

Micromixing and flow manipulation with polymer microactuators

Polymer actuators based on Gold/PolyPyrrole bilayers were microfabricated and their properties tested for flow promoting in the microdomain. When implemented in microchannels these actuators behaved as efficient micromixers for both, flow-through and stagnant conditions. Particle tracking experiments and numerical simulations of cross-sectional domains verified the capacity of these devices to promote complex, high velocity flows with chaotic advection properties in microscopic environments. Thinner devices could be actuated at higher frequencies than thicker devices, up to 10 Hz for 10 nm thick Gold layers with voltages not over 0.6 V (vs. Ag/AgCl), which led to enhanced flow generation properties. The results herein demonstrate that these actuators are practical candidates for fluid manipulation in the microdomain (for applications such as micromixing and pumping, and possibly even for propelling of swimming microdevices).     

Liquid flow through microchannels with grooved walls under wetting and superhydrophobic conditions

Recent developments in superhydrophobic surfaces have enabled significant reduction in the frictional drag for liquid flow through microchannels. There is an apparent risk when using such surfaces, however, that under some conditions the liquid meniscus may destabilize and, consequently, the liquid will wet the entire patterned surface. This paper presents analytical and experimental results that compare the laminar flow dynamics through microchannels with superhydrophobic walls featuring ribs and cavities oriented both parallel and transverse to the direction of flow under both wetting and non-wetting conditions. The results show the reduction in the total frictional resistance is much greater in channels when the liquid phase does not enter the cavity regions. Further, it is demonstrated that the wetting and non-wetting cavity results represent limiting cases between which the experimental data lie. Generalized expressions enabling prediction of the classical friction factor-Reynolds number product as a function of the relevant governing dimensionless parameters are also presented for both the superhydrophobic and wetting states. Experimental results are presented for a range of parameters in the laminar flow regime.     

Numerical study of the flow over shallow cavities

This paper reports on a series of numerical simulations of both laminar and turbulent flows over shallow cavities. For the turbulent case the influences of the following parameters were considered: (i) cavity aspect ratios, (ii) turbulence level of the oncoming flow, and (iii) Reynolds number. Several important results and conclusions are reported. We have found that for the turbulent case the external flow touches the floor of the cavity, and this depends on a specific value of each of these parameters. This condition has an important impact upon convective effects inside the cavity. The mathematical model corresponds to the incompressible, Reynolds-averaged, Navier-Stokes equations plus a high-Reynolds κ-ε model of turbulence, and the numerical computation is performed using the SIMPLER algorithm.     

Incompressible and compressible flows through rectangular microorifices entrenched in silicon microchannels

Incompressible and compressible flows through indispensable configurations such as rectangular microorifices entrenched in microchannels have been experimentally investigated. The current endeavor evaluates the effects of microorifice and microchannel size, estimates the discharge coefficients associated with both compressible and incompressible flows, examines the contraction coefficients, probes subsonic and supercritical gas flows, and explores the presence of any anomalous effects such as those reported for microchannels. The discharge coefficient in incompressible flow, using deionized (DI) water as the working fluid, rises and peaks at a critical Reynolds number, (200/spl les/Re/sub Crit//spl les/500). The reported range of the transitional Reynolds number compares favorably with the values observed in conventional scale studies and suggests the absence of any irregular scaling effects. Furthermore, nitrogen flows through various microorifices suggests that the constriction element rather than the microchannel area determines the flow rate. Additionally, the critical pressure ratio at choking is close to the isentropic value (0.47/spl les/(P/sub 2//P/sub 1/)/sub Crit//spl les/0.64) and no anomalous scale or slip effects have been observed. Unlike macroscale compressible flows through an orifice, the losses seem minimal and the discharge coefficients are close to unity. The geometry acts as a smooth converging-diverging nozzle and the mass flow rate trends appear similar to the data obtained in micronozzle flows.     

Fabrication and testing of bubble powered micropumps using embedded microheater

A bubble-powered micropump which consists of a pair of nozzle-diffuser flow controller and a pumping chamber was fabricated and tested in this study. The two-parallel micro line heaters were fabricated to be embedded in the silicon dioxide layer above a silicon wafer which serves as a base plate for the micropump. A pumping chamber, a pair of nozzle-diffuser unit and microchannels including the liquid inlet and outlet port were fabricated by etching through another silicon wafer. A glass wafer having two holes of inlet and outlet ports of liquid serve as upper plate of the pump. Sequential photographs of bubble nucleation, growth and collapse were visualized by CCD camera. The liquid flow through the nozzle during the period of bubble growth and slight back flow of liquid at the collapse period can be clearly seen. The volume flow rate was found to be dependent on the duty ratio and the operation frequency. The volume flow rate decreases as the duty ratio increases in the micropump with either circular or square pumping chamber.     

Flow-induced waterway in a heterogeneous granular material

In a heterogeneous granular material, viscous flow concentrates to regions with lower particle number density, or higher permeability region, denoted here by “macroscopic cavity”. This in turn enhances the normal stress toward the fluid region on the upstream boundary, which destroys the boundary if the local stress exceeds a certain magnitude. The latter may further enhance the concentration of flow into the cavity region, which is repeated to form a large scale fluidized region toward upstream direction. These processes have been elucidated in our previous experiment using glass beads layer confined between two parallel plane walls. In this paper, a numerical simulation taking into account of the global flow field on the basis of the generalized Darcy?s equation as well as the local stick-slip equation on the basis of the Newton?s equation of motion is performed. Our numerical simulation can successfully reproduce our experimental findings by imposing a suitable pressure gradient and frictional coefficient. The present numerical method can be applied to more general distribution of cavities, including three-dimensional ones, which may predict the formation of long underground waterways or creation of the passage of blood flows (angiogenesis).     

Planar CMOS compatible process for the fabrication of buried microchannels in silicon, using porous-silicon technology

This work presents a new method for the fabrication of buried microchannels, covered with porous silicon (PS). The specific method is a two-step electrochemical process, which combines PS formation and electropolishing. In a first step a PS layer with a specific depth is created at a predefined area and in the following step a cavity underneath is formed, by electropolishing of silicon. The shape of the microchannel is semi-cylindrical due to isotropic formation. The method allows accurate control of the dimensions of both PS and the cavity. The formation conditions of the PS layer and the cavity were optimized so as to obtain smooth microchannel walls. In order to obtain stable structures the area underneath the PS masking layer was transformed into n-type by implantation, taking advantage of the selectivity of PS formation between n- and p-type silicon. With this technique, a monocrystalline support for the PS layer is formed on top of the cavity. Various microchannel diameters with different thickness of capping PS layer were obtained. The process is CMOS compatible and it uses only one lithographic step and leaves the surface of the wafer unaffected for further processing. A microfluidic thermal flow sensor was fabricated using this technology, the experimental evaluation of which is in progress.     

A Numerical Method for Simulation of Microflows by Solving Directly Kinetic Equations with WENO Schemes

A numerical method for simulation of transitional-regime gas flows in microdevices is presented. The method is based on solving relaxation-type kinetic equations using high-order shock capturing weighted essentially non-oscillatory (WENO) schemes in the coordinate space and the discrete ordinate techniques in the velocity space. In contrast to the direct simulation Monte Carlo (DSMC) method, this approach is not subject to statistical scattering and is equally efficient when simulating both steady and unsteady flows. The presented numerical method is used to simulate some classical problems of rarefied gas dynamics as well as some microflows of practical interest, namely shock wave propagation in a microchannel and steady and unsteady flows in a supersonic micronozzle. Computational results are compared with Navier–Stokes and DSMC solutions.     

Mapping low-Reynolds-number microcavity flows using microfluidic screening devices

Low-Reynolds-number flows in cavities, characterized by separating and recirculating flows are increasingly used in microfluidic applications such as mixing and sorting of fluids, cells, or particles. However, there is still a lack of guidelines available for selecting the appropriate or optimized microcavity configuration according to the specific task at hand. In an effort to provide accurate design guidelines, we investigate quantitatively low-Reynolds-number cavity flow phenomena using a microfluidic screening platform featuring rectangular channels lined with cylindrical cavities. Using particle image velocimetry (PIV), supported by computational fluid dynamics (CFD) simulations, we map the entire spectrum of flows that exist in microcavities over a wide range of low-Reynolds numbers (Re = 0.1, 1, and 10) and dimensionless geometric parameters. Comprehensive phase diagrams of the corresponding microcavity flow regimes are summarized, capturing the gradual transition from attached flow to a single vortex and crossing through two- and three-vortex recirculating systems featuring saddle-points. Finally, we provide design insights into maximizing the rotational frequencies of recirculating single-vortex microcavity systems. Overall, our results provide a complete and quantitative framework for selecting cavities in microfluidic-based microcentrifuges and vortex mixers.     

Multi relaxation time lattice Boltzmann simulations of deep lid driven cavity flows at different aspect ratios

In this paper, the multi relaxation time (MRT) lattice Boltzmann equation (LBE) was used to compute lid driven cavity flows at different Reynolds numbers (100–7500) and cavity aspect ratios (1–4 cavity width depth). Steady solutions were obtained for square cavity flows, however for deep cavity flows at 1.5 and 4 cavity width depth, unsteady solutions prevail at Re = 7500, where periodic flow exists manifested by the rapid changes of the shapes and locations of the corner vortices in strong contrast of the stationary primary vortex. The merger of the bottom corner vortices into a primary vortex and the reemergence of the corner vortices as the Reynolds number increases are more evident for the deep cavity flows. For the four cavity width depth cavity, four primary vortices were predicted by MRT model for Reynolds number beyond 1000, which were not predicted by previous single relaxation time (SRT) BGK LBE model, and this was verified by complementary Navier–Stokes simulations. Also, MRT model is more suitable for parallel computations than its BGK counterpart, due to the more intense local computations of the multi relaxation time procedure.     

Cluster formation and growth in microchannel flow of dilute particle suspensions

The lifetime of microfluidic devices depends on their ability to maintain flow without interruption. Certain applications require microdevices for transport of liquids containing particles. However, microchannels are susceptible to blockage by solid particles. Therefore, in this study, the phenomenon of interest is the formation and growth of clusters on a microchannel surface in the flow of a dilute suspension of hard spheres. Based on the present experiments, aggregation of clusters was observed for particle-laden flows in microchannels with particle void fraction as low as 0.001 and particle diameter to channel height ratio as low as 0.1. The incipience and growth of a single cluster is discussed, and the spatial distribution and time evolution of clusters along the microchannel are presented. Although the cluster size seems to be independent of location, more clusters are found at the inlet/outlet regions than in the microchannel center. Similarly as for an individual cluster, as long as particle–cluster interaction is the dominant mode, the total cluster area in the microchannel grows almost linearly in time. The effects of flow rate, particle size, and concentration are also reported.     

Node flows in graphs with conservative flow

Summary In analyzing graphs with conservative flow where the node flows are of interest (e.g. algorithm flowcharts) the practice has been to measure or to analytically determine the flows in the independent edges, and to calculate all other edge flows using Kirchhoff's law of flow conservation. The node flows are then obtained as the sum of edge flows entering each node.This paper presents a transformation on such graphs whereby the transformed graph, if analyzed for its edge flows, will directly yield the node flows of the original graph.A proof is also given that the number of node flow measurements determined by the transformed graph never exceeds the number of edge flow measurements that would be required if the transformation were not applied.     

A robust low speed preconditioning formulation for viscous flow computations

A modification of a low speed preconditioning formulation is proposed to perform robust computations for both internal and external flows. This formulation is based on the isentropic Mach number to derive an efficient scheme for viscous flows. The preconditioning technique is coupled with a point-implicit symmetric Gauss-Seidel relaxation scheme in conjunction with a finite volume discretization for structured mesh topologies. Results of computations of standard test cases with attached and separated boundary layers are presented to validate and assess the method in terms of convergence, accuracy and robustness. The robustness and the effectiveness of the preconditioning formulation is then demonstrated by presenting crosswind air intake computations. This application features a strong acceleration of the flow field around the inlet lips combined with complex three-dimensional separations and therefore it constitutes a challenging test case for preconditioning simulations. It is found that the separation line is better predicted with the preconditioning procedure and good agreement between measured and computed data of flow topology is obtained.     

Fabrication of silicon and oxide membranes over cavities usingion-cut layer transfer

Silicon and oxide membranes were fabricated using an ion-cut layer transfer process, which is suitable for sub-micron-thick membrane fabrication with good thickness uniformity and surface micro-roughness. After hydrogen ions were implanted into a silicon wafer, the implanted wafer was bonded to another wafer that has patterned cavities of various shapes and sizes. The bonded pair was then heated until hydrogen-induced silicon layer cleavage occurred along the implanted hydrogen peak concentration, resulting in the transfer of the silicon layer from one wafer to the other. Using this technique, we have been able to form sealed cavities and channels of various shapes and sizes up to 50-μm wide, with a 1.6-μm-thick silicon membrane. As a process variation, we have also fabricated silicon dioxide membranes for optically transparent applications     

Experimental investigations of liquid flow in rib-patterned microchannels with different surface wettability

The effects of rib-patterned surfaces and surface wettability on liquid flow in microchannels were experimentally investigated in this study. Microchannels were fabricated on single-crystal silicon wafers by photolithographic and wet-etching techniques. Rib structures were patterned in the silicon microchannel, and the surface was chemically treated by trichlorosilane to create hydrophobic condition. Experiments with water as the working fluid were performed with these microchannels over a wide range of Reynolds numbers between 110 and 1914. The results for the rib-patterned microchannels showed that the friction factor with the hydraulic diameter based on the rib-to-upper-wall height was lower than that predicted from incompressible theory with the same height. The friction factor-Reynolds number products for the hydrophobic condition increased as Reynolds number increased in the laminar flow regime. The experimental results were also compared with the predictive expressions from the literature, and it was found that the experimental data for the small rib/cavity geometry was in good agreement with those in the literature.