Finite Length Microchannel Research Articles

Effect of a soluble surfactant on the linear stability of two-phase flows in a finite-length channel

We study numerically the effect of a soluble surfactant on the stability of two-phase flow in a finite-length microchannel. The two streams drag the surfactant molecules toward the downstream end of the interface against the action of the Marangoni stress. The sharp reduction of the interfacial tension at that end enhances the interface deformation and considerably destabilizes the system, translating into a sharp reduction of the critical capillary number even for very small surfactant volume concentrations.

Electrokinetic energy conversion in a finite length superhydrophobic microchannel

We investigated the effect of superhydrophobic walls on electrokinetics phenomena in a finite-length microchannel with superhydrophobic walls (in both transient and steady-state). We implemented the effect of superhydrophobicity using Navier’s slip-length. To include the importance of the electric double-layer, we scaled the slip-length with respect to Debye-length (κ-1). By increasing the slip-length from 0 to 144 nm (1.5κ-1), streaming-current, streaming-potential, flow-rate and electrokinetic energy conversion increased by 2.55, 2.44, 1.8, and 3.4 folds, accordingly. The electrokinetic energy conversion of each microchannel was in the order of picowatt. To produce more energy, an array of microchannels should be used.

Application of boundary element method to Stokes flows over a striped superhydrophobic surface with trapped gas bubbles

A slow steady flow of a viscous fluid over a superhydrophobic surface with a periodic striped system of 2D rectangular microcavities is considered. The microcavities contain small gas bubbles on the curved surface of which the shear stress vanishes. The general case is analyzed when the bubble occupies only a part of the cavity, and the flow velocity far from the surface is directed at an arbitrary angle to the cavity edge. Due to the linearity of the Stokes flow problem, the solution is split into two parts, corresponding to the flows perpendicular and along the cavities. Two variants of a boundary element method are developed and used to construct numerical solutions on the scale of a single cavity with periodic boundary conditions. By averaging these solutions, the average slip velocity and the slip length tensor components are calculated over a wide range of variation of governing parameters for the cases of a shear-driven flow and a pressure-driven channel flow. For a sufficiently high pressure drop in a microchannel of finite length, the variation of the bubble surface shift into the cavities induced by the streamwise pressure variation is estimated from numerical calculations.

Electrothermal Transport in Biological Systems: An Analytical Approach for Electrokinetically Modulated Peristaltic Flow

A mathematical model is presented to study the combined viscous electro-osmotic (EO) flow and heat transfer in a finite length microchannel with peristaltic wavy walls in the presence of Joule heating. The unsteady two-dimensional conservation equations for mass, momentum, and energy conservation with viscous dissipation, heat absorption, and electrokinetic body force, are formulated in a Cartesian co-ordinate system. Both single and train wave propagations are considered. The electrical field terms are rendered into electrical potential terms via the Poisson–Boltzmann equation, Debye length approximation, and ionic Nernst Planck equation. A parametric study is conducted to evaluate the impact of isothermal Joule heating and electro-osmotic velocity on axial velocity, temperature distribution, pressure difference, volumetric flow rate, skin friction, Nusselt number, and streamline distributions.

Numerical analysis of surface roughness effects on the Poiseuille flow caused by a small pressure drop

The rarefied gas flow caused by a pressure drop in a planar microchannel of finite length is analysed numerically to investigate the effect of surface roughness on thermal and hydrodynamic flow characteristics. The kinetic approach based on the nonlinear S-model of the Boltzmann kinetic equation coupled with the Maxwell’s diffuse gas-surface interaction model imposed at the wall is used. An implicit scheme for the solution of the S-model kinetic equation is applied and the algorithm has been optimised for the use of massive parallelization in the velocity space. A surface roughness is configured with series of triangular, semicircular, trapezoidal and rectangular obstructions. A competition between rarefaction and effects of roughness geometry is estimated by varying a rarefaction regime of flow from continuum up to free–molecular regime. The results indicate that the global flow performances in terms of the Poiseuille number, mass and thermal energy flow rates are affected by the wall roughness geometry when compared to the flow performances for a smooth channel. The triangular roughness produces the smallest impact on a gas flow, while the rectangular roughness the largest one. Rarefaction plays a significant role enhancing the effect of the surface roughness. In the continuum flow regime the roughness elements induce strong recirculation and flow separation regions. Moreover, the weakly rarefied flow strongly depends on the shape and the spacing of roughness elements. On the other hand, for the highly rarefied flow the global parameters are almost independent of the shape of elements. The increase in the spacing of roughness elements results in the reduction of the Poiseuille number and an enhancement of mass and thermal energy flow rates for all shapes of roughness elements.

Electrokinetic power generation of non-Newtonian fluids in a finite length microchannel

In order to examine the effects of the fluid type as the electrolyte solvent on the efficiency of electrokinetic energy conversion, a comparative numerical study among three different fluid types of a transient electrokinetic flow through a single circular finite length microchannel has been conducted. The system was initially at an equilibrium non-flow state, and a step change in flow was applied and the calculation proceeding until steady state was achieved. The analysis was based on non-dimensional transport governing equations that were scaled using Debye length as the characteristic length scale and diffusion time as characteristic time scale. The fluid types considered were shear thinning, Newtonian, and shear thickening, and a power law modeled them with the scaled flow behavior index having values of 0.2, 1.0, and 1.8. In order to isolate the electrokinetic effects of the different relationships between the shear strain rate and shear stress, the flow consistency index was adjusted so that in all the cases the flow rate and total pressure drop matched that of water at 25 °C. All other fluid and interfacial properties were the same for all cases. The key observational difference between the various fluid types was that their different axial velocity profile acted on essential the same free charge density profiles. Consequently, the convection current density (i.e., the radial distribution of charge being advected along the channel) was strongly affected by the fluid type. Integration of this quantity to calculate the convection current showed that for the particular fluid properties chosen the shear thinning fluid was 20 % higher than the Newtonian fluid, while the shear thickening fluid was only 4 % lower than the Newtonian fluid. Combined with the effects, these different currents have on the streaming potential, the shear thinning fluid was 50 % more effective in converting flow work to electrical work than the Newtonian fluid, while the shear thickening fluid was only 16 % lower than the Newtonian fluid.

Coupled lattice Boltzmann method for simulating electrokinetic flows: A localized scheme for the Nernst–Plank model

We present a coupled lattice Boltzmann method (LBM) to solve a set of model equations for electrokinetic flows in micro-/nano-channels. The model consists of the Poisson equation for the electrical potential, the Nernst–Planck equation for the ion concentration, and the Navier–Stokes equation for the flows of the electrolyte solution. In the proposed LBM, the electrochemical migration and the convection of the electrolyte solution contributing to the ion flux are incorporated into the collision operator, which maintains the locality of the algorithm inherent to the original LBM. Furthermore, the Neumann-type boundary condition at the solid/liquid interface is then correctly imposed. In order to validate the present LBM, we consider an electro-osmotic flow in a slit between two charged infinite parallel plates, and the results of LBM computation are compared to the analytical solutions. Good agreement is obtained in the parameter range considered herein, including the case in which the nonlinearity of the Poisson equation due to the large potential variation manifests itself. We also apply the method to a two-dimensional problem of a finite-length microchannel with an entry and an exit. The steady state, as well as the transient behavior, of the electro-osmotic flow induced in the microchannel is investigated. It is shown that, although no external pressure difference is imposed, the presence of the entry and exit results in the occurrence of the local pressure gradient that causes a flow resistance reducing the magnitude of the electro-osmotic flow.

Feedback-induced oscillations in one-dimensional colloidal transport

We investigate a driven, one-dimensional system of colloidal particles in a periodically corrugated narrow channel subject to a time-delayed feedback control. Our goal is to identify conditions under which the control induces oscillatory, time-periodic states. The investigations are based on the Fokker-Planck equation involving the density distribution of the system. First, by using the numerical continuation technique, we determine the linear stability of a stationary density. Second, the nonlinear regimes are analyzed by studying numerically the temporal evolution of the first moment of the density distribution. In this way we construct a bifurcation diagram revealing the nature of the instability. Apart from the case of a system with periodic boundary conditions, we also consider a microchannel of finite length. Finally, we study the influence of (repulsive) particle interactions based on dynamical density functional theory.

Joule heating effect of electroosmosis in a finite-length microchannel made of different materials

This paper presents a numerical analysis of Joule heating effect of electroosmosis in a finite-length microchannel made of the glass and polydimethylsiloxane (PDMS) polymer. The Poisson-Boltzmann equation of electric double layer, the Navier-Stokes equation of liquid flow, and the liquid-solid coupled heat transfer equation are solved to investigate temperature behaviors of electroosmosis in a two-dimensional microchannel. The feedback effect of temperature variation on liquid properties (dielectric constant, viscosity, and thermal and electric conductivities) is taken into account. Numerical results indicate that there exists a heat developing length near the channel inlet where the flow velocity, temperature, pressure, and electric field rapidly vary and then approach to a steady state after the heat developing length, which may occupy a considerable portion of the microchannel in cases of thick chip and high electric field. The liquid temperature of steady state increases with the increase of the applied electric field, channel width, and chip thickness. The temperature on a PDMS wall is higher than that on a glass wall due to the difference of heat conductivities of materials. Temperature variations are found in the both longitudinal and transverse directions of the microchannel. The increase of the temperature on the wall decreases the charge density of the electric double layer. The longitudinal temperature variation induces a pressure gradient and changes the behavior of the electric field in the microchannel. The inflow liquid temperature does not change the liquid temperature of steady state and the heat developing length.

Gas Flow in Micro Channels-Experimental, Computational and Kinetic-Theoretical Investigations

The investigation of fluid flow in a tube or channel commenced from studying experimentally the liquid flow along a circular tube under the pressure difference imposed at both the ends, the results were verified by the exact solution of the Navier-Stokes Eq. under constant pressure gradient assumption (Poiseuille flow). The experimental work has been playing a pioneering role in the investigation of channel flows. In the case of gas for the tube (or channel) flow, according to the global mass conservation law, the pressure gradient is never a constant. The theoretical studies on rarefied gas Poiseuille flow based on constant pressure gradient assumption still compared well with the early experimental work because when pressure difference between the inlet and the outlet is small in comparison with the average pressure, the pressure distribution is approximately a linear one. Recently non-linear pressure distribution was experimentally found in the integrated micro- channel/pressure sensor systems with gas flow in the transitional regime. The mass flow rate of micro channel was exactly measured, challenging the rarefied gas dynamics community to put forward computation or simulation means for the calculation of micro-channel flow, and the flow characteristics in other micro devices. This paper reviews some of these computational efforts. It also presents a strict kinetic solution of the finite length micro-channel flow problem based on the global mass conservation and the exact kinetic theoretical solution of the Poiseuille flow at each section. Calculations and simulations are compared with reviewed experiments to check the agreement between the computational or theoretical results with experimental data. Keywords: Microchannel flow, Poiseuille flow, finite length channel flow, gas flow in channels, lattice Boltzmann method (LBM), information preservation (IP) method, kinetic theoretical solution of microchannel flow, global mass conservation for channel flow

Asymptotic Solutions for Low-Magnetic-Reynolds-Number Gas Flows Inside a Two-Dimensional Channel

This paper analyzes a near-continuum compressible magneto-gas-dynamic flow inside a two-dimensional microchannel or a two-dimensional channel of conventional dimensions, with a low-magnetic-Reynolds-number assumption. This work represents an extension from the classical Hartmann flow in a two-dimensional channel of infinite length to a microchannel of finite length. First, by comparing the magnitudes of different forces in the compressible gas flow, we obtain a nondimensional X momentum equation that relates the pressure ratio, Reynolds number, Mach number, magnetic Reynolds number, and magnetic force number. Second, for two cases of selected nondimensional parameters of comparable magnitude, we solve for asymptotic solutions of velocities, pressure, temperature, and mass flow rate of compressible gas flow based on the velocity-slip and temperature-jump wall boundary conditions while maintaining a consistent quasi-isothermal assumption. It is found that even with a small magnetic Reynolds number, the electric and magnetic field effects on the flow properties can be significant. Numerical solutions of the same formulation are obtained for validation of the present analytical solutions. The major work in this study is theoretical and the solutions are obtained in closed forms that can provide physical insights into flows inside a microchannel or a channel of conventional dimensions.

Transient Electrokinetic Transport in a Finite Length Microchannel: Currents, Capacitance, and an Electrical Analogy

Numerical simulations with the fluid mechanics based on the unsteady Navier-Stokes equations and the Poisson-Nernst-Planck formulation of electrostatics and ion transport were used to explore the transient transport of charge through a finite length cylindrical microchannel that is driven by a pressure difference. The evolution of the transcapillary potential from a no-flow equilibrium to the steady-state-steady-flow streaming potential was analyzed by following the convection, migration, and net currents. Observations of the unsteady characteristics of the streaming current, electrical resistance, and capacitance led to an electrical analogy. This electrical analogy was made from a current source (to represent convection current), which was placed in parallel with a capacitor (to allow the accumulation of charge) and a resistor (to permit a migration current). A parametric study involving a range of geometries, fluid mechanics, electrostatics, and mass transfer states allowed predictive submodels for the current source, capacitor, and resistor to be developed based on a dimensional analysis.

Kinetic modeling of temperature driven flows in short microchannels

The temperature driven gas flows in both a two-dimensional finite length microchannel and a cylindrical tube have been studied numerically, with a goal of investigating performance optimization for a nanomembrane-based Knudsen Compressor. The numerical solutions were obtained using the direct simulation Monte Carlo (DSMC) method and a discrete ordinate method for the ellipsoidal statistical and Bhatnagar–Gross–Krook models. The Knudsen number was 0.2 and the length-to-height ratio 5. Three different wall temperature distributions were considered: linear, step-wise, and a non-monotonic profile typical for a radiantly heated Knudsen Compressor's membrane. The short channel end effects are characterized, and the sensitivity of the mass flow to a non-monotonic temperature distribution is shown.

Transient streaming potential in a finite length microchannel

Pressure-driven flow of an electrolyte solution in a microchannel with charged solid surfaces induces a streaming potential across the microchannel. Such a flow also causes rejection of ions by the microchannel, leading to different concentrations in the feed and permeate reservoirs connecting the capillary, which forms the basis of membrane based separation of electrolytes. Modeling approaches traditionally employed to assess the streaming potential development and ion rejection by capillaries often present a confusing picture of the governing electrochemical transport processes. In this paper, a transient numerical simulation of electrochemical transport process leading to the development of a streaming potential across a finite length circular cylindrical microchannel connecting two infinite reservoirs is presented. The solution based on finite element analysis shows the transient development of ionic concentrations, electric fields, and the streaming potential over the length of the microchannel. The transient analysis presented here resolves several contradictions between the two types of modeling approaches employed in assessing streaming potential development and ion rejection. The simulation results show that the streaming potential across the channel is predominantly set up at the timescale of the developing convective transport, while the equilibrium ion concentrations are developed over a considerably longer duration.