Groovy drops: effect of groove curvature on spontaneous capillary flow

Spontaneous capillary flow (SCF) of a drop in a groove with an ideally sharp corner is possible when the Concus-Fin (CF) condition is fulfilled. However, since ideally sharp corners do not exist in reality, it is important to understand the effect of finite corner curvature on SCF. This effect is analytically studied for long drops in a V-shaped groove with a curved corner, leading to a generalization of the CF condition for such drops. The generalized condition implies that SCF depends on the geometry of the corner as well as on the dimensionless length of the drop, in addition to its dependence on the opening angle and contact angle that is covered by the CF condition. Specific calculations are presented for rounded corners. In addition, this effect is numerically calculated for short drops in V-shaped grooves with rounded corners, using the Surface Evolver software. The results of both types of calculations show that even a relatively small corner radius strongly affects the possibility of SCF: when the corner is not ideally sharp, SCF requires conditions that are more difficult to achieve than predicted by the CF condition; also, the spreading of the drop stops at a finite length and does not proceed indefinitely.     

The pressure drop along rectangular microchannels containing bubbles

This paper derives the difference in pressure between the beginning and the end of a rectangular microchannel through which a flowing liquid (water, with or without surfactant, and mixtures of water and glycerol) carries bubbles that contact all four walls of the channel. It uses an indirect method to derive the pressure in the channel. The pressure drop depends predominantly on the number of bubbles in the channel at both low and high concentrations of surfactant. At intermediate concentrations of surfactant, if the channel contains bubbles (of the same or different lengths), the total, aggregated length of the bubbles in the channel is the dominant contributor to the pressure drop. The difference between these two cases stems from increased flow of liquid through the "gutters"-the regions of the system bounded by the curved body of the bubble and the corners of the channel-in the presence of intermediate concentrations of surfactant. This paper presents a systematic and quantitative investigation of the influence of surfactants on the flow of fluids in microchannels containing bubbles. It derives the contributions to the overall pressure drop from three regions of the channel: (i) the slugs of liquid between the bubbles (and separated from the bubbles), in which liquid flows as though no bubbles were present; (ii) the gutters along the corners of the microchannels; and (iii) the curved caps at the ends of the bubble.     

CFD modeling for flow and mass transfer in spacer-obstructed membrane feed channels

The effect of spacer geometry on fluid dynamics and mass transfer in feed channels of spiral wound membranes has been investigated. Three-dimensional computational fluid dynamics (CFD) simulations reveal significant influence of spacer geometric parameters such as filament spacing, thickness and flow attack angle on wall shear rates and mass transfer coefficients. The spacers with filaments in axial and transverse direction induce higher shear stresses at the top membrane surface when compared to the bottom; the mass transfer rates are almost equal. The distribution of mass transfer coefficients become uniform when the spacing between axial filaments is increased or transverse filament thickness is decreased. For spacers with filaments inclined to the channel axis, the flow structure depends on spacing and flow attack angle. The fluid follows a zigzag path when spacing is greater while it begins to line-up with the filaments when spacing is reduced or flow attack angle is increased. The flow when aligned with the filaments increases the wall shear stress but confines the region of higher mass transfer coefficient values to a narrower portion. The zigzag flow movement increases these values on a major portion of membrane surface which enhances the mass transfer rates.     

Thermal performance improvement in water nanofluid/GNP–SDBS in novel design of double-layer microchannel heat sink with sinusoidal cavities and rectangular ribs

In this numerical study, laminar flow of water nanofluid/GNP–SDBS (graphene nanoplatelet–sodium dodecylbenzene sulfonate) for 0–0.1% solid nanoparticles mass fraction was investigated for Reynolds numbers of 50–1000 in 3D space via finite volume method. In the newly proposed microchannel design, the cooling fluid is moving in countercurrent in the upper and lower layers of the microchannels, and there are cavities and sinusoidal routes on the solid walls of the microchannel, and the presence of rectangular ribs on the flow centerline along the fluid path enhances mixing for cooling fluid and creates better heat transfer for warm surfaces. The results of this study show that this special design of the microchannel can have a substantial increase in Nusselt number and heat transfer so that in the considered geometry by adding solid nanoparticles mass fraction it is possible to increase average Nusselt number for each Reynolds number by approximately 20%. Also, the mixing of the fluid because of formation of secondary flows has a strong effect on making the temperature distribution uniform in the cooling fluid and solid bed (wall) of the microchannel, especially in the lower layer. The upper layer of the microchannel always has a lower temperature due to indirect contact with heat flux compared with the lower layer. In this study, by increasing Reynolds number and mass fraction of solid nanoparticles the Nusselt number is increased and heat resistance of the lower wall of the microchannel is reduced. Based on the investigation of flow field and heat transfer, the use of the proposed design of the microchannel is recommended for Reynolds number less than 300.

     

Observation of fluidic behavior in a polymethylmethacrylate-fabricated microchannel by a simple spectroscopic analysis

An easy-to-use and low cost microreactor made of polymethylmethacrylate was mechanically fabricated with a microchannel (200 microm x 200 microm). The laminar flow behavior was investigated by visualizing the flow of red and green aqueous solutions. Digitized color images from a CCD camera were analyzed by resolving the color in RGB mode. Numeric data from red and green color components in the images could reveal the fluidic behavior in the microchannel because the spatial spectroscopic information corresponds to the color solution flows. Effects of corner shapes in a turn, flow rate and surface roughness were observed on the mixing of the laminar flows. A right angle turn and unevenness of +/-10% of the inner wall surface almost mixed the two color laminar flows.     

Electrokinetic-vortex formation near a two-part cylinder with same-sign zeta potentials in a straight microchannel

Vortex formation near a two-part cylinder with zeta potentials of different values but the same sign under an external DC electric field is numerically investigated in this paper. The cylinder, inserted in a straight microchannel filled with an aqueous solution, is composed of an upstream part and a downstream part. When a DC electric field is applied in the channel, under certain conditions, the vortex will form near the cylinder due to the different velocities of electroosmotic flow generated on the cylinder surface. The numerical results reveal that the larger the velocity difference of electroosmotic flow generated on the two-part cylinder and the smaller the channel width, the more conducive to vortex formation in the channel. In addition, if the zeta potential ratios of cylinder downstream part to upstream part and channel wall to cylinder upstream part are unchanged, the DC electric field strength and the zeta potential value do not affect the pattern of vortices formed in the channel. This study provides a way for vortex formation in microchannels and has the potential application in microfluidic devices.     

Surface-directed boundary flow in microfluidic channels

Channel geometry combined with surface chemistry enables a stable liquid boundary flow to be attained along the surfaces of a 12 microm diameter hydrophilic glass fiber in a closed semi-elliptical channel. Surface free energies and triangular corners formed by PDMS/glass fiber or OTS/glass fiber surfaces are shown to be responsible for the experimentally observed wetting phenomena and formation of liquid boundary layers that are 20-50 microm wide and 12 microm high. Viewing this stream through a 20 microm slit results in a virtual optical window with a 5 pL liquid volume suitable for cell counting and pathogen detection. The geometry that leads to the boundary layer is a closed channel that forms triangular corners where glass fiber and the OTS coated glass slide or PDMS touch. The contact angles and surfaces direct positioning of the fluid next to the fiber. Preferential wetting of corner regions initiates the boundary flow, while the elliptical cross-section of the channel stabilizes the microfluidic flow. The Young-Laplace equation, solved using fluid dynamic simulation software, shows contact angles that exceed 105 degrees will direct the aqueous fluid to a boundary layer next to a hydrophilic fiber with a contact angle of 5 degrees. We believe this is the first time that an explanation has been offered for the case of a boundary layer formation in a closed channel directed by a triangular geometry with two hydrophobic wetting edges adjacent to a hydrophilic surface.     

Electrokinetic mixing vortices due to electrolyte depletion at microchannel junctions

Due to electric field leakage across sharp corners, the irrotational character of Ohmic electroosmotic flow is violated. Instead, we demonstrate experimentally and theoretically evidence of electrolyte depletion and vortex separation in electroosmotic flow around a junction between wide and narrow channels. When the penetration length of the electric field exceeds the width of the narrow channel and if the electric field is directed from the narrow to the wide channel, the electromigration of ions diminishes significantly at the junction end of the narrow channel due to this leakage. Concentration depletion then develops at that location to maintain current balance but it also increases the corner zeta potential and the local electroosmotic slip velocity. A back pressure gradient hence appears to maintain flow balance and, at a sufficient magnitude, generates a pair of vortices.     

Mixing of non-Newtonian fluids in wavy serpentine microchannel using electrokinetically driven flow

A numerical investigation is performed into the mixing performance of electrokinetically driven non-Newtonian fluids in a wavy serpentine microchannel. The flow behavior of the non-Newtonian fluids is described using a power-law model. The simulations examine the effects of the flow behavior index, the wave amplitude, the wavy-wall section length, and the applied electric field strength on the mixing performance. The results show that the volumetric flow rate of shear-thinning fluids is higher than that of shear-thickening fluids, and therefore results in a poorer mixing performance. It is shown that for both types of fluid, the mixing performance can be enhanced by increasing the wave amplitude, extending the length of the wavy-wall section, and reducing the strength of the electric field. Thus, although the mixing efficiency of shear-thinning fluids is lower than that of shear-thickening fluids, the mixing performance can be improved through an appropriate specification of the flow and geometry parameters. For example, given a shear-thinning fluid with a flow behavior index of 0.8, a mixing efficiency of 87% can be obtained by specifying the wave amplitude as 0.7, the wavy-wall section length as five times the characteristic length, the nondimensional Debye-Huckel parameter as 100, and the applied electric field strength as 43.5 V/cm.     

Electrokinetically-driven flow mixing in microchannels with wavy surface

This paper investigates the mixing characteristics of electrokinetically-driven flow in microchannels with different wavy surface configurations. Numerical simulations are performed to analyze the influence of the wave amplitude and the length of the wavy section on the mixing efficiency within the microchannel. Typically, straight channels have a poor mixing performance because the fluid flow is restricted to the low Reynolds number regime, and hence mixing takes place primarily as a result of diffusion effects. However, the wavy surfaces employed in the current microchannels increase the interfacial contact area between the two species in the microchannel and therefore improve the mixing efficiency. The mixing performance is further enhanced by the application of a heterogeneous charge pattern on the wavy surfaces. The numerical results show that the heterogeneous charge pattern generates flow circulations near the microchannel walls. These circulations are shown to provide an effective enhancement in the mixing performance. Overall, the present results show that the mixing performance is improved by increasing the magnitude of the heterogeneous surface zeta potential upon the wavy surface or by increasing the wave amplitude or the length of the wavy section in the microchannel.     

Pressure drop of slug flow in microchannels with increasing void fraction: experiment and modeling

Pressure drop in a gas-liquid slug flow through a long microchannel of rectangular cross-section was investigated. Pressure measurements in a lengthy (～0.8 m) microchannel determined the pressure gradient to be constant in a flow where gas bubbles progressively expanded and the flow velocity increased due to a significant pressure drop. Most of the earlier studies of slug flow in microchannels considered systems where the expansion of the gas bubbles was negligible in the channel. In contrast, we investigated systems where the volume of the gas phase increased significantly due to a large pressure drop (up to 1811 kPa) along the channel. This expansion of the gas phase led to a significant increase in the void fraction, causing considerable flow acceleration. The pressure drop in the microchannel was studied for three gas-liquid systems; water-nitrogen, dodecane-nitrogen, and pentadecane-nitrogen. Inside the microchannel, local pressure was measured using a series of embedded membranes acting as pressure sensors. Our investigation of the pressure drop showed a linear trend over a wide range of void fractions and flow conditions in the two-phase flow. The lengths and the velocities of the liquid slugs and the gas bubbles were also studied along the microchannel by employing a video imaging technique. Furthermore, a model describing the gas-liquid slug flow in a long microchannel was developed to calculate the pressure drop under conditions similar to the experiments. An excellent agreement between the developed model and the experimental data was obtained.     

Dissolution of carbon dioxide bubbles and microfluidic multiphase flows

We experimentally study the dissolution of carbon dioxide bubbles into common liquids (water, ethanol, and methanol) using microfluidic devices. Elongated bubbles are individually produced using a hydrodynamic focusing section into a compact microchannel. The initial bubble size is determined based on the fluid volumetric flow rates of injection and the channel geometry. By contrast, the bubble dissolution rate is found to depend on the inlet gas pressure and the fluid pair composition. For short periods of time after the fluids initial contact, the bubble length decreases linearly with time. We show that the initial rate of bubble shrinkage is proportional to the ratio of the diffusion coefficient and the Henry's law constant associated with each fluid pair. Our study shows the possibility to rapidly impregnate liquids with CO(2) over short distances using microfluidic technology.     

Analysis of geometry effects on band spreading of microchip electrophoresis

The geometry and the flow field conditions in the separation microchannel of an electrophoresis chip system may have important impact on the system's separation efficiency. Understanding the geometry effect on the flow field physics in the separation microchannel is beneficial to the design or operation of an electrophoresis system. The turns in a microfabricated separation microchannel generally results in degraded separation quality. To avoid this limitation, channels are constructed with different types of turns to determine the optimum design that minimizes turn-induced band broadening. We have designed and tested various geometric bend ratios to greatly reduce this so-called "racetrack" effect. The effects of the separation channel geometry, fluid velocity profile and bend ratio on the band distribution in the detection area are discussed. Results show that the folded square U-shaped channel is better for miniaturization and simplification. The band tilting was corrected and the racetrack effect reduced in the detection area when the bend ratio is 4:1. The detection time obtained from the present numerical solution matches very well with the experimental data.     

Shape Factor Correlations of Hydraulic Conductance in Noncircular Capillaries

In Part I of this paper, we introduced the Mason-Morrow shape factor and the corner half-angles to capture the part of geometry of angular capillaries essential in pore network calculations of single- and two-phase flow in drainage and imbibition. We then used this shape factor to obtain simple expressions for the hydraulic conductance in single-phase flow through triangular, rectangular, and oval capillaries. In Part II, we study two-phase fluid flow along angular capillaries. The nonwetting fluid occupies the central part of the capillary, whereas the wetting liquid fills the corners. First, we verify the numerical solution obtained by Ransohoff-Radke for concave corner menisci by using a high-resolution finite element method with zero and infinite surface shear viscosity. We present new numerical results for corner flow domains bounded by convex menisci, i.e., for pinned contact lines and forced imbibition. We also present numerical solutions for two-phase flow with momentum transfer across the interface. We introduce a dimensionless hydraulic conductance of wetting fluid in the corners and correlate it with the corner filament shape factor, corner half-angle, and contact angle. By appropriate scaling, we obtain an accurate universal curve for flow conductance in the corners of an arbitrary angular capillary and for arbitrary contact angles. We give error estimates of the Ransohoff-Radke flow resistance factors, of the Zhou et al. analytical expressions for the resistance factors, and of our universal curves for the hydraulic conductance with no-slip and perfect-slip boundary conditions at the interface. Our expressions for the hydraulic conductance in corner flow of wetting liquid not only are valid for both concave and convex fluid interfaces but also are more accurate than any other published correlation. Copyright 2001 Academic Press.     

Influence of the three-dimensional heterogeneous roughness on electrokinetic transport in microchannels

Surface roughness has been considered as a passive means of enhancing species mixing in electroosmotic flow through microfluidic systems. It is highly desirable to understand the synergetic effect of three-dimensional (3D) roughness and surface heterogeneity on the electrokinetic flow through microchannels. In this study, we developed a three-dimensional finite-volume-based numerical model to simulate electroosmotic transport in a slit microchannel (formed between two parallel plates) with numerous heterogeneous prismatic roughness elements arranged symmetrically and asymmetrically on the microchannel walls. We consider that all 3D prismatic rough elements have the same surface charge or zeta potential, the substrate (the microchannel wall) surface has a different zeta potential. The results showed that the rough channel's geometry and the electroosmotic mobility ratio of the roughness elements' surface to that of the substrate, epsilon(mu), have a dramatic influence on the induced-pressure field, the electroosmotic flow patterns, and the electroosmotic flow rate in the heterogeneous rough microchannels. The associated sample-species transport presents a tidal-wave-like concentration field at the intersection between four neighboring rough elements under low epsilon(mu) values and has a concentration field similar to that of the smooth channels under high epsilon(mu) values.     

Design and simulation of the micromixer with chaotic advection in twisted microchannels

Chaotic mixers with twisted microchannels were designed and simulated numerically in the present study. The phenomenon whereby a simple Eulerian velocity field may generate a chaotic response in the distribution of a Lagrangian marker is termed chaotic advection. Dynamic system theory indicates that chaotic particle motion can occur when a velocity field is either two-dimensional and time-dependent, or three-dimensional. In the present study, micromixers with three-dimensional structures of the twisted microchannel were designed in order to induce chaotic mixing. In addition to the basic T-mixer, three types of micromixers with inclined, oblique and wavelike microchannels were investigated. In the design of each twisted microchannel, the angle of the channels' bottoms alternates in each subsection. When the fluids enter the twisted microchannels, the flow sways around the varying structures within the microchannels. The designs of the twisted microchannels provide a third degree of freedom to the flow field in the microchannel. Therefore, chaotic regimes that lead to chaotic mixing may arise. The numerical results indicate that mixing occurs in the main channel and progressively larger mixing lengths are required as the Peclet number increased. The swaying of the flow in the twisted microchannel causes chaotic advection. Among the four micromixer designs, the micromixer with the inclined channel most improved mixing. Furthermore, using the inclined mixer with six subsections yielded optimum performance, decreasing the mixing length by up to 31% from that of the basic T-mixer.     

Fabrication of microfluidic mixers and artificial vasculatures using a high-brightness diode-pumped Nd:YAG laser direct write method

This paper describes a direct write laser technology, which is fast and flexible, for fabricating multiple-level microfluidic channels. A high brightness diode-pumped Nd-YAG laser with slab geometry was used for its excellent beam quality. Channels with flat walls and staggered herringbone ridges on the floor have been successfully fabricated and their ability to perform passive mixing of liquid is discussed. Also, a multi-width multi-depth microchannel has been fabricated to generate biomimetic vasculatures whose channel diameters change according to Murray's law, which states that the cube of the radius of a parent vessel equals the sum of the cubes of the radii of the daughters. The multi-depth architecture allows for flow patterns to resemble physiological vascular systems with lower overall resistance and more uniform flow velocities throughout the network compared to planar patterning techniques which generate uniformly thin channels. The ability to directly fabricate multiple level structures using relatively straightforward laser technology enhances our ability to rapidly prototype complex lab-on-a-chip systems and to develop physiological microfluidic structures for tissue engineering and investigations in biomedical fluidics problems.     

Band spreading control in electrophoresis microchips by localized zeta-potential variation using field-effect

The paper proposes a new technique, which varies the zeta potential along the channel walls in the vicinity of the microchannel corners in such as a way as to minimize the effects of turn-induced dispersion within U-shaped separation channels. The effects of the separation channel geometry, the fluid velocity profile, and boundary control of the zeta potential on the band distribution in the detection area are all discussed within this paper. The results for the folded square U-shaped separation channel indicate that boundary control of the zeta potential by field-effect significantly reduces the band dispersion induced by the 90[degree] turns. Finally, the results confirm that application of the proposed localized zeta potential variation method results in a correction of the band tilting phenomenon and a reduction in the racetrack effect.     

Micromixing of miscible liquids in segmented gas-liquid flow

We present an integrated microfluidic system that achieves efficient mixing between two miscible liquid streams by introducing a gas phase, forming a segmented gas-liquid (slug) flow, and completely separating the mixed liquid and gas streams in a planar capillary separator. The recirculation motion associated with segmented flow enhances advection in straight microchannels without requiring additional fabrication steps. Instantaneous velocity fields are quantified by microscopic particle image velocimetry (muPIV). Velocities in the direction normal to the channel amount to approximately 30% of the bulk liquid velocity inside a liquid segment. This value depends only weakly on the length of a liquid segment. Spatial concentration fields and the extent of mixing (EOM) are obtained from pulsed-laser fluorescence microscopy and confocal scanning microscopy measurements. The mixing length is reduced 2-3-fold in comparison with previously reported chaotic micromixers that use three-dimensional microchannel networks or patterned walls. Segmented gas-liquid microflows allow mixing times to be varied over several orders of magnitude between milliseconds and second time scales.     

Toolbox for the design of optimized microfluidic components

A computational "toolbox" for the a priori design of optimized microfluidic components is presented. These components consist of a microchannel under low-Reynolds number, pressure-driven flow, with an arrangement of grooves cut into the top and bottom to generate a tailored cross-channel flow. An advection map for each feature (i.e., groove of a particular shape and orientation) predicts the lateral transport of fluid within the channel due to that feature. We show that applying these maps in sequence generates an excellent representation of the outflow distribution for complex designs that combine these basic features. The effect of the complex three-dimensional flow field can therefore be predicted without solving the governing flow equations through the composite geometry, and the resulting distribution of fluids in the channel is used to evaluate how well a component performs a specified task. The generation and use of advection maps is described, and the toolbox is applied to determine optimal combinations of features for specified mixer sizes and mixing metrics.