Pressure-driven Liquid Flow Research Articles

Ion conduction property of track- etched conical nanopores modified by atom layer deposition method under applied pressure

In this work, single conical nanopores in Kapton films were fabricated using the etch-track and atomic layer deposition (ALD) methods. Nanopores with different tip sizes (34 nm, 123 nm, 194 nm, respectively) were used to investigate the effect of pressure on the ionic conduction rectification (ICR) of the nanopores. Results showed that the effect of pressure on the ICR of the nanopores is related to the tip size of the nanopore and the rectification coefficient of the nanopores in the electrolyte solution. When pressure was applied across the nanopore, a volumetric flow Q was engendered through the conical-shaped nanopore. Only when the tip size of the nanopore reached a certain size could the pressure-driven liquid flow eliminate the hydraulic resistance of the pore, changing the ion distribution in the nanopore and further altering the ICR of the nanopore. For nanopores with a tip size of 34 nm, the effect of pressure on ICR was almost negligible. Only when the tip size of the nanopore was greater than a certain extent did the applied pressure significantly affect the ICR. The influence of pressure on ICR was also related to the strength of the rectification coefficient of the nanopore in the electrolyte. Nanopores exhibiting smaller ion rectification coefficients were more susceptible to the effects of pressure on their ICR.

Oil-gated isoporous membrane with micro-apertures for controllable pressure-induced passive flow regulator.

The pressure-driven liquid flow controller is one of the key components in diverse applications including microfluidic systems, biomedical drug injection devices, and pressurized water supply systems. Electric feedback loop based flow controllers are fine-tunable but expensive and complex. The conventional safety valves based on spring force are simple and low cost, but their diverse application is limited due to their fixed pressure range, size, and shape. Herein, we propose a simple and controllable liquid-flowing system combining a closed liquid reservoir and an oil-gated isoporous membrane (OGIM). The ultra-thin and flexible OGIM acts as an immediately responsive and precisely controlled gas valve to maintain internal pneumatic pressure as designed to induce constant liquid flow. The oil filling apertures act as a gate for gas flow depending on the applied pressure and the threshold (gating) pressure of the gate is determined by the surface tension of the oil and the gate diameter. It is confirmed that the gating pressure is precisely controlled by varying the gate diameter, which agrees with the theoretically estimated pressures. Based on stably maintained pressure due to the function of OGIM, the constant liquid flow rate is achieved even with the high gas flow rate.

Fluid flow and interface motion in gels: A finite-strain theory and its application to a channel flow problem

We present a theory for coupled deformation and liquid permeation in polymer gels, allowing for large strains and rotations in conjunction with sharp interfaces separating regions of high and low polymer volume fraction. The theory is applied to pressure-driven liquid flow through a gel-filled rectangular channel, with the aim of investigating how the elastic and osmotic properties of the gel influence the resulting permeation process. Apart from streamwise flow in the direction of the applied pressure drop, the permeation process may involve transverse flow if the elastic response of the gel allows the normal stress acting on a plane parallel to the channel walls to be affected by the shear stress acting on the same plane. For certain elastic energy densities, including those of neo-Hookean and Mooney type, liquid permeation takes place exclusively in the direction of the applied pressure drop. Otherwise, spanwise permeation driven by the contribution to the normal stress distributed on planes parallel to the channel walls is also present. In contrast to the downstream flow, the transverse flow is transient and is accompanied by changes in composition leading to a nonuniform polymer distribution across the channel and thereby influencing the downstream flow profile. By analyzing the instantaneous response of the gel, we determine the driving force for the transverse flow and show that for strain-stiffening networks the transverse motion of the interstitial liquid is directed inward from the channel walls and that the polymer network motion spreads outward from the center of the channel toward the walls. The opposite occurs for strain-slackening networks. By analyzing the steady-state response, we demonstrate that the applied pressure gradient leads to nonuniform transverse distributions of polymer chains than can be continuous or discontinuous. Discontinuous distributions occur for an effective osmotic response involving attractive interactions and are accompanied by the formation of regions of high and low polymer volume fraction separated by sharp interfaces. Finally, we provide illustrative examples for a gel whose elastic and osmotic responses are modeled by the Gent elastic energy density and the Flory–Huggins mixing energy density, respectively.

Investigating enhanced mass flow rates in pressure-driven liquid flows in nanotubes

Over the past two decades, several researchers have presented experimental data from pressure-driven liquid flows through nanotubes. They quote flow velocities which are four to five orders of magnitude higher than those predicted by the classical theory. Thus far, attempts to explain these enhanced mass flow rates at the nanoscale have focused mainly on introducing wall-slip boundary conditions on the fluid mass velocity. In this paper, we present a different theory. A change of variable on the velocity field within the classical Navier–Stokes equations is adopted to transform the equations into physically different equations. The resulting equations, termed re-casted Navier–Stokes equations, contain additional diffusion terms whose expressions depend upon the driving mechanism. The new equations are then solved for the pressure driven flow in a long nano-channel. Analogous to previous studies of gas flows in micro- and nano-channels, a perturbation expansion in the aspect ratio allows for the construction of a 2D analytical solution. In contrast to slip-flow models, this solution is specified by a no-slip boundary condition at the channel walls. The mass flow rate can be calculated explicitly and compared to available data. We conclude that the new re-casting methodology may provide an alternative theoretical physical explanation of the enhanced mass flow phenomena.

Electrical Double Layer Effect on Pressure-driven Liquid Flow and Heat Transfer in Microchannels

The effect of the electrical double layer(EDL) on pressure-driven liquid flow and heat transfer in a flat microchannel are investigated under asymmetric boundary conditions including unequal zeta potentials and unequal heat fluxes on two walls.A mathematical model of pressure-driven liquid flow in microchannels is constructed.Electrical potential of EDL,liquid flow and thermal characteristics is determined using the Poisson-Boltzmann,the modified Navier-Stokes and the energy equations,respectively.The analytical solutions of the electrical potential,the velocity field and the temperature field are obtained by solving these three coupled equations.The influences of electrokinetic parameter(K),zeta potential,ratio of two zeta potentials and heat flux ratio on electrical potential,velocity distributions,temperature distributions and heat transfer rate are discussed in detail.Results show that the wall zeta potential strongly affects the electrical potential distributions in microchannels,then the change of flow-induced streaming potential will affect the velocity profile,thereby affecting the temperature distributions and heat transfer.Therefore,EDL has a significant effect on electrokinetic flow in microchannels,compared with that in conventional Poiseuille flow without EDL effect,there is an apparent difference in the flow and heat transfer characteristics between them.

Boundary velocity slip of pressure driven liquid flow in a micron pipe

The velocity slip of gas flow in a micron channel has been widely recognized. For pressure driven liquid flow in a macro pipe, the minute velocity slip at the wall boundary is usually neglected. With a decreasing scale in the cross section of the flow passage, the effect of velocity slip on flow and heat transfer behaviors becomes progressively more noticeable. Based on the three Hamaker homogeneous material hypotheses, the method for calculating the acting force between the solid and liquid molecular groups is established. By analyzing the forces exerted on the liquid group near the pipe wall, it is found that the active force arising from the rough solid wall can provide the component force to resist the shearing force and keep the liquid group immobile. Based on this a velocity slip criterion is proposed. Considering the force balance of a slipping liquid group, the frictional force caused by the solid wall can be obtained and then the velocity of the liquid group can be calculated using the derived coefficient of friction. The investigation reveals that, in a micron pipe, a small velocity slip may occur when the flow pressure gradient is relatively large, and will cause errors in the pipe flow estimates.

Mass Transport through Carbon Nanotube Membranes in Three Different Regimes: Ionic Diffusion and Gas and Liquid Flow

Transport phenomena through the hollow conduits of carbon nanotubes (CNTs) are subjects of intense theoretical and experimental research. We have studied molecular transport over the large spectrum of ionic diffusion to pressure-driven gaseous and liquid flow. Plasma oxidation during the fabrication of the membrane introduces carboxylic acid groups at the CNT entrance, which provides electrostatic "gatekeeper" effects on ionic transport. Diffusive transport of ions of different charge and size through the core of the CNT is close to bulk diffusion expectations and allows estimation of the number of open pores or porosity of the membrane. Flux of gases such as N(2), CO(2), Ar, H(2), and CH(4) scaled inversely with their molecular weight by an exponent of 0.4, close to expected kinetic theory velocity expectations. However, the magnitude of the fluxes was ∼15- to 30-fold higher than predicted from Knudsen diffusion kinetics and consistent with specular momentum reflection inside smooth pores. Polar liquids such as water, ethanol, and isopropyl alcohol and nonpolar liquids such as hexane and decane were dramatically enhanced, with water flow over 4 orders of magnitude larger than "no-slip" hydrodynamic flow predictions. As direct experimental proof for the mechanism of near perfect slip conditions within CNT cores, a stepwise hydrophilic functionalization of CNT membranes from as-produced, tip-functionalized, and core-functionalized was performed. Pressure-driven water flow through the membrane was reduced from 5 × 10(4) to 2 × 10(2) to less than a factor of 5 enhancement over conventional Newtonian flow, while retaining nearly the same pore area.

Single-cell manipulation on microfluidic chip by dielectrophoretic actuation and impedance detection

This paper presents the design, fabrication, and characterization of a microfluidic biochip with integrated actuation electrodes used to manipulate a cell and a microbead by dielectrophoresis and sensing electrodes to detect the trapping by using the impedance detection method. Combining deflective dielectrophoretic barriers with controlled pressure-driven liquid flows allows the accurate control of a cell/microbead in suspensions. The threshold voltage for microbead trapping was experimentally verified at various flow rates. The impedance change caused by the blockage of the electrical conducting path between sensing electrodes with the trapping of an MCF7 cell and a polystyrene microbead was measured. The impedance before the trapping of an MCF7 cell was 10.9 MΩ at 1 kHz and increased to 12 MΩ when the cell was placed between sensing electrodes.

Flow behavior in microchannel made of different materials with wall slip velocity and electro-viscous effects

In a microfluidic system, flow slip velocity on a solid wall can be the same order of magnitude as the average velocity in a microchannel. The flow-electricity interaction in a complex microfluidic system subjected to joint action of wall slip and electro-viscous effect is an important topic. This paper presents an analytic solution of pressure-driven liquid flow velocity and flow-induced electric field in a two-dimensional microchannel made of different materials with wall slip and electro-viscous effects. The Poisson- Boltzmann equation and the Navier-Stokes equation are solved for the analytic solutions. The analytic solutions agree well with the numerical solutions. It was found that the wall slip amplifies the flow-induced electric field and enhances the electro-viscous effect on flow. Thus the electro-viscous effect can be significant in a relatively wide microchannel with relatively large κh, the ratio of channel width to thickness of electric double layer, in comparison with the channel without wall slip.

Pressure Drop in Rectangular Microchannels as Compared With Theory Based on Arbitrary Cross Section

Pressure driven liquid flow through rectangular cross-section microchannels is investigated experimentally. Polydimethylsiloxane microchannels are fabricated using soft lithography. Pressure drop data are used to characterize the friction factor over a range of aspect ratios from 0.13 to 0.76 and Reynolds number from 1 to 35 with distilled water as working fluid. Results are compared with the general model developed to predict the fully developed pressure drop in arbitrary cross-section microchannels. Using available theories, effects of different losses, such as developing region, minor flow contraction and expansion, and streaming potential on the measured pressure drop, are investigated. Experimental results compare well with the theory based on the presure drop in channels of arbitrary cross section.

Electroviscous Effects in Low Reynolds Number Flow through a Microfluidic Contraction with Rectangular Cross-Section

The electrokinetic flow resistance (electroviscous effect) is predicted for steady state, pressure-driven liquid flow at low Reynolds number in a microfluidic contraction of rectangular cross-section. Calculations of the three dimensional flow are performed in parallel using a finite volume numerical method. The channel walls are assumed to carry a uniform charge density and the liquid is taken to be a symmetric 1:1 electrolyte. Predictions are presented for a single set of flow and electrokinetic parameters. It is shown that the magnitude of the streaming potential gradient and the charge density of counter-ions in the liquid is greater than that in corresponding two-dimensional slit-like contraction geometry. The apparent viscosity is found to be very close to the value for a rectangular channel of uniform cross-section at the chosen Reynolds number (Re = 0.1). It is speculated that the apparent viscosity for the contraction geometry will increase as the Reynolds number is reduced.

Monitoring of liquid flow through microtubes using a micropressure sensor

The pressure-driven liquid flow through microtubes was studied in a range of very low Reynolds numbers (<0.15) by monitoring the pressure change in situ. Cylindrical microtubes with diameters ranging from 50 μm to 500 μm were examined and two types of tube material, namely PEEK polymer and fused silica were compared. A good linear relation for the pressure drop versus flow rate was obtained. Apparent deviations between the measured slopes with those calculated using conventional theory were attributed to uncertainties in the calculated values which are dominated by the uncertainties in the microtube diameters. It was found that a period of stabilisation time was required for reaching a steady flow after the syringe pump was switched on/off or to a different flow rate. The stabilisation time was likely due to the compressibility of the fluid. Insignificant difference between PEEK polymer and fused silica microtubes in terms of flow resistance was observed. The in-situ measurement of pressure drops provides a convenient approach for monitoring fluid flow through microtubes and detecting dimensional changes within microchannels in Lab-on-a-Chip and microreactor systems.

Analysis of the electro-viscous effects on pressure-driven liquid flow in a two-section heterogeneous microchannel

In this paper, the electro-viscous effects on pressure-driven liquid flow through a microchannel which is composed of two heterogeneous sections are analyzed. The Poisson–Boltzmann equation, Navier–Stokes equations and a set of constrained equations are solved analytically to obtain the velocity profiles and the streaming potentials in each section. Effects of the zeta potential and length ratio of the two sections on the flow resistance are discussed by means of the apparent viscosity ratio and the Poiseuille number.

Solute transport and separation in nanochannel chromatography

An analytical model is developed to study the solute transport and separation in pressure-driven liquid flow through cylindrical nanochannels. The flow-induced streaming potential is found to significantly affect the solute speed, retention and dispersion in nanochannel chromatography. These effects are sensitive to the solute charge, and found to be mainly dependent on an electrokinetic “figure of merit”.

Electroviscous effects in low Reynolds number liquid flow through a slit-like microfluidic contraction

A finite volume numerical method is used to predict electroviscous effects in steady state, pressure-driven liquid flow in a slit-like microfluidic contraction at low Reynolds number. A uniform charge density is assumed on the channel walls and the liquid is taken to be a symmetric 1:1 electrolyte. It is shown that predicted profiles of electrical potential, charge, and velocity across the channel at locations half way along the contraction and outlet sections are almost coincident with their uniform slit counterparts. A simple theory is developed that calculates the pressure drop along the channel by adding the pressure losses in the inlet, contraction and outlet sections (based on the classical fully developed electrokinetic flow solution in a uniform slit) to the entry and exit losses due to the contraction, approximated using the low Reynolds number analytical solution for a slit orifice without electrokinetic effects. For the parameter range investigated, the simple theory overestimates the apparent viscosity by up to 5–10%, compared with that determined by the numerical solution, but the differences are smaller when the surface charge density or EDL thickness is small, or the overall pressure drop is large (as occurs for long contractions).

Towards a generalized representation of surface effects on pressure-driven liquid flow in microchannels

This letter postulates a generalized fundamental formulation to model the influence of surface characteristics on pressure-driven liquid transport through microchannels. Probabilistic effects pertaining to the influence of roughness elements and uncertainties in wall conditions due to the presence of a random distribution of nanobubbles are represented spectrally by employing a stochastic version of the Navier-Stokes equations. A generalized mathematical expression is eventually arrived at, by normalizing these characteristics, which can act as a fundamental scientific guideline towards the design of microfluidic channels.

Experimental Study on Band Dispersion in Channels Structured with Micropillars

The band dispersion in channels with an orderly pillar structure with a pressure-driven liquid flow was determined. Several channels with different geometries were etched in a silicon wafer and enclosed by a glass wafer. The microchannels obtained had the same depth, pillar disposition, and overall porosity, but different pillar diameters and channel widths. The broadening of narrow bands of a fluorescent sample solution flowing through the channels was measured using a fluorescence microscope. It was shown that the peak dispersion occurring in the channels can be much lower than in conventional packed columns, as a consequence of the higher degree of order of the solid structure. Reduced plate heights of approximately 0.2 could be obtained for (nonretained) bands. No correlation was found between the aspect ratio (the ratio of the channel width and the pillar diameter) and band dispersion. The geometrical construction of the sidewall region was shown to play a critical role for channel performance. A good agreement was found with predictions for the optimal sidewall geometry obtained previously with simulation studies.

Effect of shape factor on the electrokinetic response of slot-like capillaries

The effect of the shape factor on the electrokinetic response of pressure-driven liquid flow through slot-like capillaries is analyzed in this work. The electrokinetic response is found by first solving for the electrical potential using the Poisson–Boltzmann equation, and then using it as an input to construct an external force term in the Navier–Stokes equation. It is found that flow properties are significantly modified for small pore sizes with hydraulic radius in the range of microns and submicrons, according to the properties of the electrolyte solution. The modified flow rate in the presence of such electrokinetic effects can be less than 50% of the predictions expected with conventional flow models such as Darcy's equation. Apparent viscosities larger than expected are calculated using the reduced flow. Actual values are dependent on the capillary dimensions, pressure gradient, solid-surface conductivity, and properties of the electrolyte fluid. For a rectangular capillary cross-sectional geometry the apparent viscosity and friction coefficients values decrease with the shape factor in a nontrivial way. These results are relevant for the modelling of certain porous formations of interest to the oil industry.

Fluid flows in microchannels with cavities

Pressure-driven gas and liquid flows through microchannels with cavities have been studied using both experimental measurements and numerical computations. Several microchannels with cavities varying in shape, number and dimensions have been fabricated. One set of microdevices, integrated with sensors on a silicon wafer, is used for flow rate and pressure distribution measurements in gas flows. Another set of microdevices, fabricated using glass-to-silicon wafer bonding, is utilized for visualization of liquid flow patterns. The cavity effect on the flow in the microchannel is found to be very small, with the mass flow rate increasing slightly with increasing number of cavities. The flow pattern in the cavity depends on two control parameters; it is fully attached only if both the reduced Reynolds number and the cavity number are small. A flow regime map has been constructed, where the critical values for the transition from attached to separated flow are determined. The numerical computations reveal another control parameter, the cavity aspect ratio. The flow in the cavity is similar only if all three control parameters are the same. Finally, the vorticity distribution and related circulation in the cavity are analyzed. [1546].

Streaming Currents in a Single Nanofluidic Channel

We report measurements of the streaming current, an electrical current generated by a pressure-driven liquid flow, in individual rectangular silica nanochannels down to 70 nm in height. The streaming current is observed to be proportional to the pressure gradient and increases with the channel height. As a function of salt concentration, it is approximately constant below approximately 10 mM, whereas it strongly decreases at higher salt. Changing the sign of the surface charge is found to reverse the streaming current. The data are best modeled using a nonlinear Poisson-Boltzmann theory that includes the salt-dependent hydration state of the silica surface.