Investigations on the flow behaviour in microfluidic device due to surface roughness: a computational fluid dynamics simulation

In the field of micro-fluidics device, as the cross section of micro-channel comes down to the scale of few tens of micro-meters, surface area to volume ratio increases significantly, and due to this, surface dependent phenomenon dominates during flow of the fluid. This surface dependent phenomenon is mainly governed by surface roughness as an important parameter which directly influences on flow and results in the loss of pressure head due to the building of localised pressure as well as eddy flow. To understand this mechanism, a computational fluid dynamics (CFD) simulation is carried out. In the present CFD simulation, fluid and solid interactions are modelled in two different types. The first is modelled as pure slip between them so that the effect of roughness can be investigated as a main source of friction factor. The second model consists the effect of the pure adhesion by maintain zero relative velocity on the surface of micro-channel. Behaviour of fluid flow and increase in pressure-drop are observed differently in the both types of model. It is observed that the rise in pressure-drop occurs exponentially as size of a channel reduces from 300 to 100 µm. This phenomenon reveals the science of the size effect on micro-channels. The surface roughness of micro-channel is simulated and it is also observed that the surface finish up to few tens of nanometers does not affect the fluid flow. However, the flow resistance increases as the surface roughness increases up to few hundreds of nanometers, and the pressure-drops along the channel length. In the present case, an elevated temperature of fluid mitigates the effect of surface roughness up to some extent for the efficient flow of fluid in a micro-fluidic device. Hence, micro-fluidic device with nano-finished micro-channel and elevated temperature of fluid is recommended for economic and efficient utilisation of the device.

     

Hydrodynamic dispersion in long microchannels under conditions of electroosmotic circulation: II. Electrolytes

This work describes the steady-state transport of an electrolyte due to a stationary concentration difference in straight long channels under conditions of electroosmotic circulation. The electroosmotic flow is induced due to the slip produced at the charged channel walls. This flow is assumed to be compensated by a pressure-driven counterflow so that the net volume flow through the channel is exactly zero. Owing to the concentration dependence of electroosmotic slip, there is an involved coupling between the solute transfer, hydrodynamic flow and charge conservation. Nevertheless, for such a system the Taylor–Aris dispersion (TAD) theory is shown to be approximately applicable locally within an inner part of the channel for a wide range of Péclet numbers (Pe) irrespective of the concentration difference. Numerical simulations reveal only small deviations from analytical solutions for the inner part of the channel. The breakdown of TAD theory occurs within boundary regions near the channel ends and is related to the variation of the dispersion mechanism from the purely molecular diffusion at the channel ends to the hydrodynamic dispersion within the inner part of the channel. This boundary region is larger at the lower-concentration channel edge and its size increases nearly linearly with Pe number. It is possible to derive a simple analytical approximation for the inner profile of cross-section-averaged electrolyte concentration in terms of only few parameters, determined numerically. Such analytical approximations can be useful for experimental studies of concentration polarization phenomena in long microchannels.     

Orbiting magnetic microbeads enable rapid microfluidic mixing

We use three-dimensional numerical simulations and experiments to examine microfluidic mixing induced by orbiting magnetic microbeads in a microfluidic channel. We show that orbiting microbeads can lead to rapid fluid mixing in low Reynolds number flow, and identify two distinct mixing mechanisms. Bulk advection of fluid across the channel occurs due to the flow pattern that is developed when the ratio of flow velocity to bead velocity is low, and leads to rapid mixing. At higher velocity ratios, dispersion of small amounts of fluid across the channel occurs and results in increased mixing. We use simulations to investigate the effect of system parameters on the distance required to achieve a desired mixing level. We develop an experimental continuous-flow device and use it to validate our simulations and to demonstrate rapid microfluidic mixing. This device has the flexibility to also be applied to a mixing chamber or to stop-flow applications for rapid and controllable mixing. In addition to rapid mixing, the use of orbiting magnetic microbeads has the added benefit that functionalized microbeads can be used to capture particles from the fluid solution during mixing, and that they can be extracted from the device for analysis, thus serving multiple functionalities in a single device.     

Numerical simulation of heat transfer enhancement by elastic turbulence in a curvy channel

Although many investigations on elastic turbulence have been conducted in recent years, two major research topics still call for in-depth mechanistic investigations. Specifically, one is heat transfer performance affected by elastic turbulence; the other is so-called high Weissenberg number problem (HWNP) in numerical simulation of viscoelastic fluid flow. Taking these two topics into account simultaneously, the coupled problem becomes heat transfer characteristic of viscoelastic fluid in elastic turbulence at high Weissenberg number (Wi) and very low Reynolds number (Re). In this work, we implement numerical simulations by embedding log-conformation reformulation algorithm into the open-source software OpenFOAM. The heat transfer process of viscoelastic fluid flow in a three-dimensional (3D) curvy channel is simulated over a wide range of Wi. For the first time, significant heat transfer enhancement induced by elastic turbulence in a curvy channel at high Wi was identified numerically. When Wi is above the critical value of O(1), the heat transfer performance is found to be dramatically improved by elastic turbulence and then approaches a saturation. From the transient analysis of flow motions in the axial and cross sections, it can be seen that the flow twists and wiggles in the curvy channel and the field synergy effect of viscoelastic fluid flow becomes more intensive than that of Newtonian fluid flow. These effects give rise to the extremely irregular flow motions in the cross section and consequently lead to heat transfer enhancement.     

How does wall slippage affect hydrodynamic dispersion?

How hydrodynamic dispersion is affected by wall slip remains to be fully understood. An attempt is made in this article looking into this issue for dispersion in some elementary pressure-driven flows. Both the long-time Taylor–Aris dispersion and the early-phase convection-dominated dispersion are investigated, analytically and numerically, respectively. The mean and the variance of the residence time distribution are also examined. In the basic case where the walls of a parallel-plate channel have equal slip lengths, the slip is in general to reduce the spread of a solute cloud in a finite channel by either increasing the convection speed or decreasing the dispersivity. However, the decreasing effect of slip on dispersion can be diminished or even reversed by unequal slip lengths and/or phase exchange with the wall. The convection-dominated regime is investigated, following a recently proposed transport-based method, to determine how the mean residence time and variance of elution profiles may change with axial positions depending on the slip.     

Design and simulation of a thermo transfer type MEMS based micro flow sensor for arterial blood flow measurement

Thermo transfer type MEMS (Micro Electro Mechanical System) based micro flow sensing device have promising potential to solve the limitation of implantable arterial blood flow rate monitoring. The present paper emphasizes on modeling and simulation of MEMS based micro flow sensing device, which will be capable of implantable arterial blood flow rate measurement. It describes the basic design and model architecture of thermal type micro flow sensor. A pair of thin film micro heaters is designed through MEMS micro machining process and simulated using CoventorWare; a finite element based numerical code. A rectangular cross section micro channel has been modeled where in micro heater and thermal sensors are embedded using the same CoventorWare tools. Some promising and interesting results of thermal dissipation depending upon very small amount of flow rate through the micro channel are investigated. It is observed that measuring the variation of temperature difference between downstream and upstream, the variation of fluid flow rate in the micro channel can be measured. The numerical simulation results also shows that the temperature distribution profile of the heated surface depends upon microfluidic flow rate i.e. convective heat transfer is directly proportional to the microfluidic flow rate on the surface of the insulating membrane. The simplified analytical model of the thermo transfer type flow sensor is presented and verified by simulation results, which are very promising for application in arterial blood flow rate measuring in implantable micro devices for continuous monitoring of cardiac output.     

Modeling of 2D density-dependent flow and transport in porous media using finite volume method

A two-dimensional finite volume unstructured mesh method (FVUM) based on a triangular mesh is developed for modeling density-dependent flow and transport through saturated-unsaturated porous media. The combined flow and transport model can handle a wide range of real-word problems, including the simulation of flow alone, contaminant transport alone, and combined flow and transport. Saltwater intrusion problems and instability caused by denser water on the top were investigated in this paper. Because the fundamental mechanism causing saltwater intrusion most likely is caused by density-induced convection and dispersion, the developed model is used to assess the interplay between density-driven flow and subsurface media through which the saltwater intrusion occurs.The mathematical formulation of the model is comprised of fluid flow and solute transport equations, coupled by fluid density. In the specific case of saltwater intrusion and unstable brine transport problems, this set of governing equation is non-linear and requires iterative methods to solve them simultaneously. Three case studies, which include a wide range of physical conditions, are used for verification of presented model and comparison with previously published solutions from other researchers presents encouraging agreements.     

Transient response analysis and modeling of near wall flow conditions in a micro channel: evidence of slip flow

An experimental tool for determination of the near wall transport parameters in a micro channel, supported by flow simulation, is presented. The method is based on the transient flow response due to convective diffusion, in absence of specific adsorption. An approximately step-function type temporal solute concentration variation serves as the input signal. The associated response signal of a surface plasmon resonance sensor, acting as an integral part of a micro channel, has been taken as the output signal. It provides the flow-dependent change of the NaOH solute concentration in the channel within the optical detection and near wall distance interval 0 < d < 0.5 μm. The temporal signal evolution and response time, until an initially plain aqueous solution is replaced by the solute, varies inversely with solute concentration and flow rate. In the asymptotic limits, the near wall forced convective and diffusive channel transit times, along with the associated velocities, can be extracted and separated. A low convective near wall flow speed would account for 100% adsorption efficiency. The validity of the scaling relation for Fickian diffusive transport has been confirmed by experiments. Convective near wall flow reveals a distorted parabolic flow profile. This indicates relaxation of the no-slip condition, and presence of slip flow. Neither boundary layer formation, nor near wall micro turbulences have been observed. Eventually, a compact mathematical transient flow model, outlined in the Laplace domain for the electrical equivalent analogue circuit and applicable to the convective diffusion equation, has been developed for the flow transients.     

Hydrodynamic dispersion of neutral solutes in nanochannels: the effect of streaming potential

An analytical model is developed to account for the effect of streaming potential on the hydrodynamic dispersion of neutral solutes in pressure-driven flow. The pressure-driven flow and the resulting electroosmotic backflow exhibit coupled dispersion effects in nanoscale channels where the hydraulic diameter is on the order of the electrical double layer thickness. An effective diffusion coefficient for this regime is derived. The influence of streaming potential on hydrodynamic dispersion is found to be mainly dependent on an electrokinetic parameter, previously termed the “figure of merit”. Results indicate that streaming potential decreases the effective diffusion coefficient of the solute, while increasing the dispersion coefficient as traditionally defined. This discrepancy arises from the additional effect of streaming potential on average solute velocity, and discussed herein.     

Broadening of neutral analyte band in electroosmotic flow through slit channel with different zeta potentials of the walls

The study is concerned with addressing hydrodynamic dispersion of an electroneutral non-adsorbed solute being transported by electroosmotic flow through a slit channel formed by walls with different zeta potentials. The analysis is conducted in terms of the plate height which, using the Van Deemter equation, can be expressed through the cross-sectional mean flow velocity, the solute molecular diffusion coefficient and a length scale parameter having meaning of the minimum achievable plate height and depending on the velocity distribution within the channel cross-section. The minimum plate height is determined by substituting distribution of electroosmotic velocity into the preliminary derived integral expression that is valid for any given velocity distribution within a slit channel cross-section. The electroosmotic velocity distribution within the slit channel cross-section is obtained by solving one-dimensional version of the Stokes equation accounting for electric force exerted on the local equilibrium electric space charge. The major obtained result is an analytical expression which represents the minimum plate height normalized by half of channel width as a function of two dimensionless parameters, namely, half of channel width normalized by the Debye length, and the ratio of the wall zeta potentials. The obtained result reveals a substantial increase in the minimum plate height compared with the case of equal wall zeta potentials. Different limiting cases of the obtained relationships are analyzed and possible applications are discussed.     

DSMC investigation of rarefied gas flow through diverging micro- and nanochannels

Direct simulation Monte Carlo (DSMC) method with simplified Bernoulli trials (SBT) collision scheme has been used to study the rarefied pressure-driven nitrogen flow through diverging micro- and nanochannels. The fluid behaviours flowing between two plates with different divergence angles ranging between 0° and 17° are described at different pressure ratios (1.5 ≤ Π ≤ 2.5) and Knudsen numbers (0.03 ≤ Kn ≤ 12.7). The primary flow field properties, including pressure, velocity, and temperature, are presented for divergent micro- and nanochannels and are compared with those of a micro- and nanochannel with a uniform cross section. The variations of the flow field properties in divergent micro- and nanochannels which are influenced by the area change, the channel pressure ratio, and the rarefication are discussed. The results show no flow separation in divergent micro- and nanochannels for all the range of simulation parameters studied in the present work. It has been found that a divergent channel can carry higher amounts of mass in comparison with an equivalent straight channel geometry. A correlation between the mass flow rate through micro- and nanochannels, the divergence angle, the pressure ratio, and the Knudsen number has been suggested. The present numerical findings prove the occurrence of Knudsen minimum phenomenon in micro- and nanochannels with non-uniform cross sections.     

Flow over a membrane-covered,fluid-filled cavity

The flow-induced response of a membrane covering a fluid-filled cavity located in a section of a rigid-walled channel was explored using finite element analysis. The membrane was initially aligned with the channel wall and separated the channel fluid from the cavity fluid. As fluid flowed over the membrane-covered cavity, a streamwise-dependent transmural pressure gradient caused membrane deformation. This model has application to synthetic models of the vocal fold cover layer used in voice production research. In this paper, the model is introduced and responses of the channel flow, the membrane, and the cavity flow are summarized for a range of flow and membrane parameters. It is shown that for high values of cavity fluid viscosity, the intracavity pressure and the beam deflection both reached steady values. For combinations of low cavity viscosity and sufficiently large upstream pressures, large-amplitude membrane vibrations resulted. Asymmetric conditions were introduced by creating cavities on opposing sides of the channel and assigning different stiffness values to the two membranes. The asymmetry resulted in reduction in or cessation of vibration amplitude, depending on the degree of asymmetry, and in significant skewing of the downstream flow field.     

Induced mixing electrokinetics in a charged corrugated nano-channel: towards a controlled ionic transport

To perform a fluid analysis for electroosmotic flows in micro- and nano-channels, it is necessary to mix various fluid contents in micro- and nano-scales. It is observed that fluids in electroosmotic flow exhibits Reynolds number effect as the flow exerts very weak inertial force and it requires long channel for mixing of different layers and species through diffusion process. Hence, if the desired length scale of mixing is large, an enormous time is needed for the molecules to be thoroughly mixed by diffusion. The theory of dynamic equations on time scale is used to study the stability of these systems. It is found that such a system may exhibits an unstable nature for overlapping electric double layer field with fluctuating velocities and stability is preserved for zero linear growth coefficient. To obtain an improved understanding of mixing performance, a numerical study is performed with the variation of channel height when more than one ionic species with channels patterned with heterogeneity is considered. The wall heterogeneity may be created by placing some blocks of unequal size (with or without charged) close to the channel wall or some external potential patches. The analytical results for the transport characteristics of electroosmotic flow obtained are compared with the direct numerical simulation of the Navier–Stokes equation, Nernst–Plank equation, and Poisson equation, simultaneously. It is shown that heterogeneous potential could generate complex flow structures and the increment of species layers at different levels of the channel cross section from inlet to outlet significantly improve the mixing rate.     

Implications of variable fluid resistance caused by start-up flow in microfluidic networks

Electrical circuit analogies are often used to design microfluidic systems because they simplify device design, providing simple relationships between fluid flow rate, driving forces, and channel dimensions. However, such approximations often significantly overestimate flow rates in situations where start-up energy losses from establishing kinetic head are similar in magnitude to the energy required to overcome viscous shear stresses, as is often the case within complex microfluidic networks. These reduced flows can be more accurately predicted within an electrical analogy framework that accounts for the nonlinear flow resistance generated on the transient regime of start-up flow. In this work, standard flow resistance expressions are modified to account for such effects, and the onset of nonlinear resistance is predicted by a dimensionless parameter, $\xi = Re\frac{D}{L},$ which is dependent on the Reynolds number and the channel length. As a demonstration, variable fluid resistance is shown to dramatically affect the flow performance of common microfluidic units such as T-junctions and serpentine channels, and the change in performance is accurately predicted. Experimental and theoretical analysis of T-junctions further shows that variable flow resistance causes the ratio of flows through the junction to converge toward unity with respect to an increasing total flow rate. In addition, serpentine channels are shown to exaggerate these start-up effects, owing to compounded energetic demand associated with changing a flow’s direction. As a result, serpentine channels cause the ratio of flow rates exiting a T-junction to diverge from unity with respect to an increasing flow rate.     

Dispersion in electroosmotic flow generated by oscillatory electric field interacting with oscillatory wall potentials

An analytical study is presented in this article on the dispersion of a neutral solute released in an oscillatory electroosmotic flow (EOF) through a two-dimensional microchannel. The flow is driven by the nonlinear interaction between oscillatory axial electric field and oscillatory wall potentials. These fields have the same oscillation frequency, but with disparate phases. An asymptotic method of averaging is employed to derive the analytical expressions for the steady-flow-induced and oscillatory-flow-induced components of the dispersion coefficient. Dispersion coefficients are functions of various parameters representing the effects of electric double-layer thickness (Debye length), oscillation parameter, and phases of the oscillating fields. The time–harmonic interaction between the wall potentials and electric field generates steady as well as time-oscillatory components of electroosmotic flow, each of which will contribute to a steady component of the dispersion coefficient. It is found that, for a thin electric double layer, the phases of the oscillating wall potentials will play an important role in determining the magnitude of the dispersion coefficient. When both phases are zero (i.e., full synchronization of the wall potentials with the electric field), the flow is nearly a plug flow leading to very small dispersion. When one phase is zero and the other phase is π,?the flow will be sheared to the largest possible extent at the center of the channel, and such a sharp velocity gradient will lead to the maximum possible dispersion coefficient.     

An electrokinetic mixer driven by oscillatory cross flow

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.

DEPOSIM: A Macintosh computer model for two-dimensional simulation of transport, deposition, erosion, and compaction of clastic sediments

DEPOSIM is a dynamic deterministic two-dimensional simulation model implemented on an Apple Macintosh 512 kbyte computer, that represents the interaction between transport, deposition, erosion, and compaction of clastic sediments. Sediment particles, transported within a fluid medium, are represented in a cross section through a sedimentary basin. The cross section is separated into discrete columns. The behavior of particles depends on velocity of the fluid in each column of the cross section, as well as on the basin's configuration, particularly on the steepness of slope of the seafloor. Fluid velocity depends on the velocity of the fluid newly supplied to the basin in each time increment, and on the depth of water in each column. Input parameters were taken from actual sedimentological and oceanographic literature that is concerned with clastic sediments. DEPOSIM takes into account up to three different particle sizes. Graphics subroutines display the cross sections and frequency distributions of particle sizes on a column-by-column basis. Resolution of cross sections on the computer screen or in hardcopies can be improved by using an “enlarging” subroutine. Preparation of data input for the model is interactive completely and uses mouse and window techiques. DEPOSIM is well suited for computer-aided instruction.     

Three-dimensional simulations of viscous folding in diverging microchannels

Three-dimensional simulations on the viscous folding in diverging microchannels reported by Cubaud and Mason (Phys Rev Lett 96(11):114,501, 2006a) are performed using the parallel code BLUE for multiphase flows (Shin et al. in A solver for massively parallel direct numerical simulation of three-dimensional multiphase flows. arXiv:1410.8568). The more viscous liquid \(L_1\) is injected into the channel from the center inlet, and the less viscous liquid \(L_2\) from two side inlets. Liquid \(L_1\) takes the form of a thin filament due to hydrodynamic focusing in the long channel that leads to the diverging region. The thread then becomes unstable to a folding instability, due to the longitudinal compressive stress applied to it by the diverging flow of liquid \(L_2\). Given the long computation time, we were limited to a parameter study comprising five simulations in which the flow rate ratio, the viscosity ratio, the Reynolds number, and the shape of the channel were varied relative to a reference model. In our simulations, the cross section of the thread produced by focusing is elliptical rather than circular. The initial folding axis can be either parallel or perpendicular to the narrow dimension of the chamber. In the former case, the folding slowly transforms via twisting to perpendicular folding, or it may remain parallel. The direction of folding onset is determined by the velocity profile and the elliptical shape of the thread cross section in the channel that feeds the diverging part of the cell. Due to the high viscosity contrast and very low Reynolds numbers, direct numerical simulations of this two-phase flow are very challenging and to our knowledge these are the first three-dimensional direct parallel numerical simulations of viscous threads in microchannels. Our simulations provide good qualitative comparison of the early time onset of the folding instability, however, since the computational time for these simulations is quite long, especially for such viscous threads, long-time comparisons with experiments for quantities such as folding amplitude and frequency are limited.     

Analysis of Stokes flow in microchannels with superhydrophobic surfaces containing a periodic array of micro-grooves

Superhydrophobic surfaces have been demonstrated to be capable of reducing fluid resistance in micro- and nanofluidic applications. The objective of this paper is to present analytical solutions for the Stokes flow through microchannels employing superhydrophobic surfaces with alternating micro-grooves and ribs. Results are presented for both cases where the micro-grooves are aligned parallel and perpendicular to the flow direction. The effects of patterning the grooves on one or both channel walls are also analyzed. The reduction in fluid resistance has been quantified in terms of a dimensionless effective slip length, which is found to increase monotonically with the shear-free fraction and the periodic extent of each groove–rib combination normalized by the channel half-height. Asymptotic relationships have been derived for the normalized effective slip length corresponding to large and small limiting values of the shear-free fraction and the normalized groove–rib period. A detailed comparison has been made between transverse and longitudinal grooves, patterned on one or both channel walls, to assess their effectiveness in terms of enhancing the effective slip length. These comparisons have been carried out for small and large limiting values, as well as finite values of the shear-free fraction and normalized groove–rib period. Results for the normalized effective slip length corresponding to transverse and longitudinal grooves are further applied to model the Stokes flow through microchannels employing superhydrophobic surfaces containing a periodic array of micro-grooves inclined at an angle to the direction of the applied pressure gradient. Results are presented for the normalized effective slip lengths parallel to the direction of the applied pressure gradient and the normalized cross flow rate perpendicular to the direction of the applied pressure gradient.