Simulation of Viscoelastic Fluid Flows in Expansion Geometry Using Finite Volume Approach简

The simulation results on viscoelastic fluid flows in sudden expansion geometry with different expansion ratios are presented. Oldroyd-B, linear Phan-Thien-Tanner （L-PTT） and Finitely Extensible Nonlinear Elastic （FENE-P） based constitutive equations were applied in two-dimensional Cartesian coordinates. The governing equations in transient and fully developed regions were solved using open source software called OpenFOAM. The flow patterns, including velocity profiles, shear stresses and first normal stress differences in some horizontal and vertical sections are illustrated. In addition, effects of the fluid type, flow dynamics and expansion ratio on the flow and vortex patterns in transient and fully developed regions are presented and discussed. The presented results show that existences of vortices cause the inverse velocity and negative stresses in expansion regions of the channel which increase with increment of expansion ratio and Weissenberg number （We）. Furthermore, some dead spaces can be observed at channel expansion regions close to the wall which are also increased. The results also show that at low We numbers all fluids show close behavior while at high We numbers the FENE-P fluid behavior shows high divergence from that of the two other fluids.     

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.     

Secondary Flows of Simplified Phan-Thien Tanner (SPTT) Non-Linear Viscoelastic Fluid Between Parallel Rotating Disks

Summary: The steady state laminar flow of non-linear viscoelastic fluid with Simplified Phan-Thien Tanner (SPTT) model between coaxial rotating disks is studied analytically. With linearized stress coefficient in the constitutive equation (SPTT), primary flow and weak secondary flow have been investigated by perturbation techniques while the aspect ratio is very small. Axial and radial velocity profiles arising from secondary flow are completely analyzed for various boundary conditions and properties of the viscoelastic fluid. The results indicate the strong effects of the elasticity and boundary conditions on velocity profiles. The inertial secondary flow consists of a single vortex for co-rotating disks and two vortices for counter-rotating disks which is well represented by the approximate analytical solution.     

Simulation of a movement of dispersed particles in view of a second gas circulation in a cyclone

The gas flow in the cyclone was simulated in view of a constant component of a gas velocity directed from periphery to center of a cyclone. An influence of this component of the gas velocity makes it possible a judgment that with an increase in a value of the radial flowing off the particle velocity can shift and achieve outside wall of a vortex body. Its occurrence was not observed earlier and its forecast was difficult since the radial flowing off was directed to other side. As shown from computations at certain intensity of the second circulation such a critical size of the particles occurs that the particles transfer from suspension to rapid movement toward the outside wall of the vortex chamber.     

Elimination of edge effects in micro-thermal field-flow fractionation channel of low aspect ratio by splitting the carrier liquid flow into the main central stream and the thin stream layers at the side channel walls

An optimized construction of the separation channel for micro-thermal field-flow fractionation (FFF) was proposed and studied experimentally. The sample is injected in such a manner that its zone moves along the channel only in the main central stream where the flow velocity profile in the plane parallel to the main accumulation wall is practically flat. This central stream is separated from the contact with the side walls of the channel by thin flowing layers of the free carrier liquid. The retained species do not reach the thin liquid streams at the side walls where the flow rate decreases rapidly to achieve zero at the side wall according to the established 3D flow velocity profile. Such a construction of the channel allows one to reduce the aspect ratio (the ratio of the channel breadth b to its thickness w) without increasing the zone broadening. The hydrodynamic splitting of the outlet streams allows one not only to increase the concentration of the detected species but also the determination of the sign of Soret coefficient.     

A microfluidic mixer with grooves placed on the top and bottom of the channel

A new microfluidic mixer is presented consisting of a rectangular channel with grooves placed in the top and bottom. This not only increases the driving force behind the lateral flow, but allows for the formation of advection patterns that cannot be created with structures on the bottom alone. Chevrons, pointing in opposite directions on the top and bottom, are used to create a pair of vortices positioned side by side. Stripes running the width of the channel generate a pair of vertically stacked vortices. Computational fluid dynamics (CFD) simulations are used to model the behavior of the systems and provide velocity maps at cross-sections within the mixer. Experiments demonstrate the mixing that results when two segregated species enter the mixer side-by-side and pass through two cycles of the mixer (i.e., two alternating sets of four stripes and four chevrons).     

Field-flow fractionation in microfluidic channels of low aspect ratio

The shape of the steady-state three-dimensional flow velocity profile established in carrier liquid flowing inside the rectangular cross-sectional channel for field-flow fractionation should be taken into account to optimize the separation. The central parts of this profile in the planes parallel to the main channel walls are flat with almost identical flow velocities which drop down to zero at the side walls. The separated species transported by the flow in the close-to-side walls regions move with lower average velocities compared to the species transported in the central part of the channel and are undesirably broadened. The hydrodynamic splitting of the carrier liquid at the entry of the channel where the sample is injected only into the central part of the channel eliminates the excessive zone broadening. The aspect ratio of the breadth to the thickness of the channel ratio can thus be reduced. The effect of various aspect ratios on the shape of the flow velocity profile is calculated and the results are used to optimize the aspect ratio of microfluidic channels. The experiments carried out by microthermal field-flow fractionation confirmed that the aspect ratio cannot be reduced to a value of 1, proposed by other authors.     

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.     

Focusing particles by induced charge electrokinetic flow in a microchannel

A novel method of sheathless particle focusing by induced charge electrokinetic flow in a microchannel is presented in this paper. By placing a pair of metal plates on the opposite walls of the channel and applying an electrical field, particle focusing is achieved due to the two pairs of vortex that constrain the flow of the particle solution. As an example, the trajectories of particles under different electrical fields with only one metal plate on one side channel wall were numerically simulated and experimentally validated. Other flow focusing effects, such as the focused width ratio (focused width/channel width) and length ratio (focused length/half‐length of metal plate) of the sample solution, were also numerically studied. The results show that the particle firstly passes through the gaps between the upstream vortices and the channel walls. Afterwards, the particle is focused to pass through the gap between the two downstream vortices that determine the focused particle position. Numerical simulations show that the focused particle stream becomes thin with the increases in the applied electrical field and the length of the metal plates. As regards to the focused length ratio of the focused stream, however, it slightly increases with the increase in the applied electrical field and almost keeps constant with the increase in the length of the metal plate. The size of the focused sample solution, therefore, can be easily adjusted by controlling the applied electrical field and the sizes of the metal plates.     

Electrokinetic flow through an elliptical microchannel: effects of aspect ratio and electrical boundary conditions

The electrokinetic flow of an electrolyte solution through an elliptical microchannel is studied theoretically. The system under consideration simulates the flow of a fluid, for example, in vein. We show that, for a constant cross-sectional area, both the electroosmotic volumetric flow rate and the streaming potential increase monotonically with an increase in the aspect ratio, and both the total electric current and the electroviscous effect may exhibit a local minimum as the aspect ratio varies. Also, for a constant average potential on the channel wall, the difference between the results based on three kinds of boundary conditions, which include constant surface charge, constant surface potential, and charge-regulated surface, is inappreciable if the hydraulic diameter is larger than 1 mum.     

DC-biased AC-electrokinetics: a conductivity gradient driven fluid flow

This paper studies the principles of fluid flow manipulation based on DC-biased AC-electrokinetics. This method makes use of planar parallel electrodes in a microfluidic channel in contact with an electrolyte solution, with a DC biased AC electrical signal applied to the electrode pair. Due to the application of DC bias, incipient Faradaic electrolytic reactions take place resulting in an increase of the ionic content of the bulk solution. The ionic content was found to be dissimilar at the cathodic and anodic sides of the channel and a conductivity difference of approximately 10% was measured for 2 V(DC). Fluid flow is generated by the action of the DC biased AC electric signal acting on the transverse conductivity gradient generated across the microchannel. The induced flow in the form of vortex was characterized experimentally and the results substantiated theoretically. The velocity of the induced flow vortex under the employed experimental conditions was ~600 to 700 μm s(-1) which is faster than those obtained in conventional AC-electroosmosis and AC-electrothermal types of flows.     

Numerical study of the vortex-induced electroosmotic mixing of non-Newtonian biofluids in a nonuniformly charged wavy microchannel: Effect of finite ion size

We propose a micromixer for obtaining better efficiency of vortex induced electroosmotic mixing of non-Newtonian bio-fluids at a relatively higher flow rate, which finds relevance in many biomedical and biological applications. To represent the rheology of non-Newtonian fluid, we consider the Carreau model in this study, while the applied electric field drives the constituent components in the micromixer. We show that the spatial variation of the applied field, triggered by the topological change of the bounding surfaces, upon interacting with the non-uniform surface potential gives rise to efficient mixing as realized by the formation of vortices in the proposed micromixer. Also, we show that the phase-lag between surface potential leads to the formation of asymmetric vortices. This behavior offers better mixing performance following the appearance of undulation on the flow pattern. Finally, we establish that the assumption of a point charge in the paradigm of electroosmotic mixing, which is not realistic as well, under-predicts the mixing efficiency at higher amplitude of the non-uniform zeta potential. The inferences of the present analysis may guide as a design tool for micromixer where rheological properties of the fluid and flow actuation parameters can be simultaneously tuned to obtain phenomenal enhancement in mixing efficiency.     

Mapping vortex-like hydrodynamic flow in microfluidic networks using fluorescence correlation spectroscopy

The ability to quickly measure flow parameters in microfluidic devices is critical for micro total analysis system (μTAS) applications. Macrofluidic methods to assess flow suffer from limitations that have made conventional methods unsuitable for the flow behavior profiling. Single molecule fluorescence correlation spectroscopy (FCS) has been employed in our study to characterize the fluidic vortex generating at a T-shape junction of microscale channels. Due to its high spatial and temporal resolution, the corresponding magnitudes relative to different flow rates in the main channel can be quantitatively differentiated using flow time (τ_F) measurements of dye molecules traversing the detection volume in buffer solution. Despite the parabolic flow in the channel upstream, a heterogeneous distribution of flow has been detected across the channel intersection. In addition, our current observations also confirmed the aspect of vortex-shaped flow in low-shear design that was developed previously for cell culture. This approach not only overcomes many technical barriers for examining hydrodynamic vortices and movements in miniature structures without physically integrating any probes, but it is also especially useful for the hydrodynamic studies in polymer-glass based micro -reactor and -mixer.     

Hydrodynamics of interaction of particles (including cells) with surfaces

The study of the phenomena related to the motion of particles flowing in the proximity of the wall is pursued for purely cognitive reason as well as for some important practical purposes in various fields of technology, biology and medicine.When small spherical rigid particles move in the direction parallel to the surface their velocity is smaller than that of the fluid and depends on the ratio of the distance from the wall to the particle radius. The velocity of a particle falling down in a vertical cylinder is maximal in an eccentric position. A sphere in contact with the wall remains stationary. Translational velocity of spherical rigid particles the dimension of which are comparable to that of the tube is only slightly dependent of their lateral position. The differences in the flow parameters of deformable particles in comparison with rigid ones depend on the particle and fluid viscosity coefficient. When the particles move perpendicularly toward the wall, their velocity decreases as the particle approaches the surface. The change of particle velocity is inversely proportional to the gap.There are several theories explaining the influence of the channel diameter on the suspension viscosity (sigma phenomenon); a modern approach is based on the analysis of rheological properties of suspensions. The explanations of the Fahraeus effect (i.e. the fact that the concentration of particles flowing in a tube linking two containers are smaller than that in the containers) are based on non-uniform particle distribution in a transverse cross section and on the differences of velocities of particles and medium. The deviation of the velocity profile of a suspension of rigid particles flowing through a tube from the parabolic shape (blunting) does not depend on the flow velocity; as concerns deformable particles, however, this effect is the smaller the greater is the flow velocity.When the Reynolds number for particles is greater than 10^-3, there appears a component of particle velocity perpendicular to the streamline direction.This phenomenon is the cause of the lateral migration of particles. Neutrally buoyant rigid particles migrate to a certain concentrical region situated between the tube axis and the wall (tubular pinch region). Deformable neutrally buoyant particles migrate towards the tube axis, and deformable non-neutrally buoyant particles may move either toward the tube axis or toward the wall.In the research on the influence of the flow delimiting surface on the motion of particles in suspension a considerable progress has recently been made.However, the phenomena in this field are extremely complex. At present, two main types of approach may be distinguished. On a microscopic level direct interactions between particles and surfaces are analyzed. A macroscopic approach consists in treating particle suspension as fluid, and overall influence of the surface on its properties are studied. A comprehensive theory linking these two levels has not yet emerged.     

Diffusioosmotic flow in rectangular microchannels

The diffusioosmosis of an electrolyte solution inside a uniformly charged rectangular channel at steady locally developed conditions is the subject of this study. Utilizing a finite element based numerical procedure, we try to estimate the errors incurred by modeling the actual rectangular geometry of typical microchannels as a slit. We demonstrate that the flow pattern and direction are generally dependent upon the width‐to‐height ratio of the channel. Such a finding, besides showing the ineffectiveness of the slit geometry in representing a rectangular channel of small aspect ratio, informs us of another mechanism of controlling the diffusioosmotic flow. Inspections of the mean velocity reveal that, although it drastically grows by increasing the aspect ratio at smaller values of this parameter, no significant change is observed when the aspect ratio is 5 or higher. The same trend is observed when EDL is shrunk and is considered as a basis for the introduction of a slip‐like velocity, similar to the concept of the Helmholtz–Smoluchowski electroosmotic velocity, which will be of high practical importance when dealing with a micronsized channel. Because of its significance, an expression is presented for this slip velocity utilizing the curve fitting of the results, assuming a typical Peclet number.     

Pressure driven flow of polymer solutions in nanoscale slit pores

Polymer solutions subject to pressure driven flow and in nanoscale slit pores are systematically investigated using the dissipative particle dynamics approach. The authors investigated the effect of molecular weight, polymer concentration, and flow rate on the profiles across the channel of the fluid and polymer velocities, polymer density, and the three components of the polymers radius of gyration. They found that the mean streaming fluid velocity decreases as the polymer molecular weight and/or polymer concentration is increased, and that the deviation of the velocity profile from the parabolic profile is accentuated with increase in polymer molecular weight or concentration. They also found that the distribution of polymers conformation is highly anisotropic and nonuniform across the channel. The polymer density profile is also found to be nonuniform, exhibiting a local minimum in the center plane followed by two symmetric peaks. They found a migration of the polymer chains either from or toward the walls. For relatively long chains, as compared to the thickness of the slit, a migration toward the walls is observed. However, for relatively short chains, a migration away from the walls is observed.     

CFD simulation and analysis of emulsion droplet formation from straight-through microchannels

We recently proposed a technique for preparing monodisperse emulsions with a coefficient of variation below 5% from a silicon array of micrometer-sized channels perpendicular to the plate surface, named a straight-through microchannel (MC). This study involved three-dimensional computational fluid dynamics (CFD) simulations to calculate the formation of an oil-in-water (O/W) emulsion droplet from straight-through MCs with circular and elliptic cross sections. The CFD results demonstrated that the oil phase that passed through the elliptic MCs exceeding a threshold aspect ratio between 3 and 3.5 was cut off spontaneously into a small droplet with a diameter of approximately 40 microm. Sufficient space for water at the channel exit had to be maintained for successful droplet formation. The formation and shrinkage of a neck inside the channel caused an increased pressure difference inside the channel and an increased velocity value near the neck. The pressure and velocity values at the neck drastically changed, and the neck was cut off instantaneously just before the completion of droplet formation. This process was triggered by a gradually increased pressure difference between the circular neck and inflating oil phase. The findings obtained in this paper provide useful numerical and visual information about the droplet formation phenomena from the straight-through MCs. The CFD results were verified by the experimental results, showing that the CFD approach can help design a suitable channel structure.     

Optimisation of a microfluidic analysis chamber for the placement of microelectrodes

The behaviour of droplets entering a microfluidic chamber designed to house microelectrode detectors for real time analysis of clinical microdialysate is described. We have designed an analysis chamber to collect the droplets produced by multiphase flows of oil and artificial cerebral spinal fluid. The coalescence chamber creates a constant aqueous environment ideal for the placement of microelectrodes avoiding the contamination of the microelectrode surface by oil. A stream of alternating light and dark coloured droplets were filmed as they passed through the chamber using a high speed camera. Image analysis of these videos shows the colour change evolution at each point along the chamber length. The flow in the chamber was simulated using the general solution for Poiseuille flow in a rectangular chamber. It is shown that on the centre line the velocity profile is very close to parabolic, and an expression is presented for the ratio between this centre line velocity and the mean flow velocity as a function of channel aspect ratio. If this aspect ratio of width/height is 2, the ratio of flow velocities closely matches that of Poiseuille flow in a circular tube, with implications for connections between microfluidic channels and connection tubing. The droplets are well mixed as the surface tension at the interface with the oil dominates the viscous forces. However once the droplet coalesces with the solution held in the chamber, the no-slip condition at the walls allows Poiseuille flow to take over. The meniscus at the back of the droplet continues to mix the droplet and acts as a piston until the meniscus stops moving. We have found that the no-slip conditions at the walls of the chamber, create a banding effect which records the history of previous drops. The optimal position for sensors is to be placed at the plane of droplet coalescence ideally at the centre of the channel, where there is an abrupt concentration change leading to a response time ?16 ms, the compressed frame rate of the video. Further away from this point the response time and sensitivity decrease due to convective dispersion.     

Effects of overlapping electric double layer on mass transport of a macro‐solute across porous wall of a micro/nanochannel for power law fluid

Effects of overlapping electric double layer and high wall potential on transport of a macrosolute for flow of a power law fluid through a microchannel with porous walls are studied in this work. The electric potential distribution is obtained by coupling the Poisson's equation without considering the Debye–Huckel approximation. The numerical solution shows that the center line potential can be 16% of wall potential at pH 8.5, at wall potential −73 mV and scaled Debye length 0.5. Transport phenomena involving mass transport of a neutral macrosolute is formulated by species advective equation. An analytical solution of Sherwood number is obtained for power law fluid. Effects of fluid rheology are studied in detail. Average Sherwood number is more for a pseudoplastic fluid compared to dilatant upto the ratio of Poiseuille to electroosmotic velocity of 5. Beyond that, the Sherwood number is independent of fluid rheology. Effects of fluid rheology and solute size on permeation flux and concentration of neutral solute are also quantified. More solute permeation occurs as the fluid changes from pseudoplastic to dilatant.     

CFD Simulation of Droplet Formation in a Wide-Type Microfluidic T-Junction

Droplet formation in a wide-type microfluidic T-junction was studied using the computational fluid dynamics (CFD) method. Two distinct regimes of droplet formation were confirmed: dripping and jetting; and, at both regimes, droplet size decreases with an increase in capillary number. CFD simulation demonstrated that droplet formation in the T-junction can be divided into three steps: droplet emergence and growing up; separation with the disperse phase; and detachment from the channel wall. The wettability of the channel wall significantly affects the process of droplet detachment from the channel wall; also, the simulation clearly showed that droplets can be formed only when the continuous phase fluid preferentially wets the channel wall, that is, its contact angle on the wall is smaller than 90°. Finally, the CFD study verified that the disperse phase flow rate can significantly affect the droplet size as well as the mechanism of droplet formation.