Engineering microfluidic papers: effect of fiber source and paper sheet properties on capillary-driven fluid flow

In the present study, we introduce a novel approach to control and modulate fluid transport inside microfluidic papers using lab-engineered paper sheets. Lab-sheets consisting of different fiber sources (eucalyptus sulfate and cotton linters pulp) and varying porosities were designed and further modified with small millimeter-scaled channels using hydrophobic barriers consisting of fiber-attached, hydrophobic polymers. The capillary-driven transport of an aqueous solution was monitored visually, and the influence of parameters such as fiber source, paper grammage, and channel width on the flow rates through the channel was investigated. The experimental results were compared with those obtained with commercially available filter papers. Our findings suggest that accurate control of fluid transport processes with standard filter papers is complex. Additionally, if the channel width is smaller than the mean fiber length, flow rates become dependent on the geometric parameters of the channel because of the formation of dead-end pores at the hydrophobic barriers. Finally, control of the paper sheets porosity, by varying the fiber density of the lab-made paper, affords the fabrication of chemically identical sheets whereby capillary flow is largely influenced and can be modulated accordingly by simple papermaking processes.     

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

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

An electrokinetic mixer driven by oscillatory cross flow

An electrokinetic mixer driven by oscillatory cross flow has been studied numerically as a means for generating chaotic mixing in microfluidic devices for both confined and throughput mixing configurations. The flow is analyzed using numerical simulation of the unsteady Navier–Stokes equations combined with the tracking of single and multi-species passive tracer particles. First, the case of confined flow mixing is studied in which flow in the perpendicular channels of the oscillatory mixing element is driven sinusoidally, and 90° out of phase. The flow is shown to be chaotic by means of positive effective (finite time) Lyapunov exponents, and the stretching and folding of material lines leading to Lagrangian tracer particle dispersion. The transition to chaotic flow in this case depends strongly on the Strouhal number (St), and weakly on the ratio of the cross flow channel length to width (L/W). For L/W = 2, the flow becomes appreciably chaotic as evidenced by visual particle dispersion at approximately St = 0.32, and the transitional value of St increases slightly with increasing aspect ratio. A peak degree of mixing on the order of 85% is obtained for the range of parameter values explored here. In the second phase of the analysis, the effect of combining a fixed throughput flow with the oscillatory cross channel motion for use in a continuous mixing operation is examined in a star cell geometry. Chaotic mixing is again observed, and the characteristics of the downstream dispersion patterns depend mainly on the Strouhal number and the (dimensionless) throughput rate. In the star cell, the flow becomes appreciably chaotic as evidenced by visual particle dispersion at approximately St = 1, slightly higher than for the case of cross cell. The star cell mixing behavior is marked by the convergence of the degree of mixing to a plateau level as the Strouhal number is increased at fixed flow rate. Degree of mixing values from 70 to 80% are obtained indicating that the continuous flow is bounded by the maximum degree of mixing obtained from the confined flow configuration.

Analysis of electroosmotic flow in a microchannel packed with microspheres

The electroosmotic flow in a microchannel packed with microspheres under both direct and alternating electric fields is analyzed. In the case of the steady DC electroosmosis in a packed microchannel, the so-called capillary model is used, in which it is assumed that a porous medium is equivalent to a series of intertwined tubules. The interstitial tubular velocity is obtained by analytically solving the Navier–Stokes equation and the complete Poisson–Boltzmann equation. Then, using the volume-averaging method, the solution for the electroosmotic flow in a single charged cylindrical tubule is applied to estimate the electroosmosis in the overall porous media by introducing the porosity and tortuosity. Assuming uniform porosity, an exact solution accounting for the electrokinetic wall effect is obtained by solving the modified Brinkman momentum equation. For the electroosmotic flow under alternating electric fields in a cylindrical microchannel packed with microspheres of uniform size, two different conditions regarding the openness of the channel ends are considered. Based on the capillary model, the time-periodic oscillating electroosmotic flow in an open-ended microchannel in response to the application of an alternating electric field is obtained using the Greens function approach to the Navier–Stokes equation. When the two ends of the channel are closed, a backpressure is induced to generate a counter flow, resulting in a new zero flow rate. Such induced backpressure associated with the counter flow in a closed-end microchannel is obtained analytically by solving the transient modified Brinkman momentum equation.     

Hydrodynamic focusing and interdistance control of particle-laden flow for microflow cytometry

Single-file focusing and minimum interdistance of micron-size objects in a sample is a prerequisite for accurate flow cytometry measurements. Here, we report analytical models for predicting the focused width of a sample stream b as a function of channel aspect ratio α, sheath-to-sample flow rate ratio f and viscosity ratio λ in both 2D and 3D focusing. We present another analytical model to predict spacing between an adjacent pair of objects in a focused sample stream as a function of sample concentration C, mobility ? of the objects in the prefocused and postfocused regions and flow rate ratio f in both 2D and 3D flow focusing. Numerical simulations are performed using Ansys Fluent VOF model to predict the width of sample stream in 2D and 3D hydrodynamic focusing for different sample-to-sheath viscosity ratios, aspect ratios and flow rate ratios. Experiments are performed on both planar and three-dimensional devices fabricated in PDMS to demonstrate focusing of sample stream and spacing of polystyrene beads in the unfocused and focused stream at different sample concentrations C. The predictions of the analytical model and simulations are compared with experimental data, and a good match is found (within 12 %). Further, mobility of objects is experimentally studied in 2D and 3D focusing, and the spread of the mobility data is used as tool for the demonstration of particle focusing in flow cytometer applications.     

On the forced convective heat transport in a droplet-laden flow in microchannels

Recently, a great deal of attention has been focused on development of microfabricated devices for manipulating minute amounts of liquids. In particular, an extensive experimental work is devoted to generation, motion and manipulation of drops in microfluidic channels, or digital microfluidics. In the present work the numerical approach based on volume-of-fluid method, combined with the piece-wise linear interface reconstruction scheme, is implemented for modeling of droplet motion and forced heat transport in a droplet-laden laminar flow in a circular microchannel. The simulations show a very good agreement with asymptotic results concerning the motion of spherical and slender drops in confined laminar flows. The effective rates of the forced heat transfer in a droplet-laden flow are found to be superior over that in single-phase Poiseuille flow. The enhancement is anticipated to be a result of the flow disturbance in the carrier fluid due to propagation of a train of translating drops and efficient convective transport within drops due to internal circulation.

Rheometry of non-Newtonian electrokinetic flow in a microchannel T-junction

Two-dimensional finite element simulations of electrokinetic flow in a microchannel T-junction of a fluid with a Carreau-type nonlinear viscosity are presented. The motion of the electrical double layer at the channel walls is approximated by velocity wall slip boundary conditions. The fluid experiences a range of shear rates as it turns the corner, and the flow field is shown to be sensitive to the non-Newtonian characteristics of the Carreau model. A one-to-one mapping between the Carreau parameters and the end wall pressure is demonstrated through statistical analysis of the pressure profile for a broad range of physical and operating parameters. Such a mapping allows the determination of the Carreau parameters of an unknown fluid if the end wall pressure profile is known; thus a highly efficient viscometric device may be constructed. A graphical technique to show that the inverse problem is well posed is shown, and a method for solving the inverse problem is presented. The challenges that must be overcome before a practical device can be constructed are discussed.

Dynamics of capillary flow in an open superoleophilic microchannel and its application to sensing of oil

We report the dynamics of capillary flow of oil in an open superoleophilic channel. The superoleophilic surface is fabricated by spin coating a layer of PDMS?+?n-hexane followed by candle sooting. The occurrence of various flow regimes, including the inertial, visco-inertial, and Lucas–Washburn regimes, are studied using analytical modelling as well as experiments. In case of a superoleophilic channel, much shorter inertial regime is observed as compared to that in an oleophilic channel due to the wicking of oil into the micro-roughness grooves ahead to moving bulk liquid meniscus. The study of the effect of channel aspect ratio \(\varepsilon\) on the mobility parameter \(k~\)showed that the mobility parameter \(k\) is maximum for an aspect ratio of \(\varepsilon =1.6\), which is attributed to the balance between the capillary and viscous forces. Finally, we demonstrate the application of the superoleophilic channel integrated with electrodes for impedance-based sensing of oil from an oil–water emulsion.     

Microfluidic mixing via transverse electrokinetic effects in a planar microchannel

A new micromixer incorporating integrated electrodes deposited on the bottom surface of a glass/PDMS microchannel is used to induce a localized, perpendicular electric field within pressure driven axial flow. The presence of the electric field drives electro-osmotic flow in the transverse direction along the channel walls, creating helical motion that serves to mix the fluid. A numerical model is used to describe the three-dimensional flow field, where characterization is performed via particle tracking of passive tracer particles, and the conditional entropy (S _lc) is utilized to approximate the extent of mixing along cross-sectional planes. The geometrical parameters and operating conditions of the numerical model are used to fabricate an experimental device, and fluorescence microscopy measurements are used to verify mixing of rhodamine B across the width of the microchannel for a wide range of fluid flow rates. The results demonstrate that under certain operating conditions and selective placement of the electrode gaps along the width of the microchannel, efficient mixing can be achieved within 6 mm of the inlet.

-parameter: A local truncation error based adaptive framework for finite volume compressible flow solvers

A residual-based strategy to estimate the local truncation error in a finite volume framework for steady compressible flows is proposed. This estimator, referred to as the -parameter, is derived from the imbalance arising from the use of an exact operator on the numerical solution for conservation laws. The behaviour of the residual estimator for linear and non-linear hyperbolic problems is systematically analysed. The relationship of the residual to the global error is also studied. The -parameter is used to derive a target length scale and consequently devise a suitable criterion for refinement/derefinement. This strategy, devoid of any user-defined parameters, is validated using two standard test cases involving smooth flows. A hybrid adaptive strategy based on both the error indicators and the -parameter, for flows involving shocks is also developed. Numerical studies on several compressible flow cases show that the adaptive algorithm performs excellently well in both two and three dimensions.     

Molecular dynamics simulations of oscillatory flows in microfluidic channels

In this paper we apply the direct non-equilibrium molecular dynamics technique to oscillatory flows of fluids in microscopic channels. Initially, we show that the microscopic simulations resemble the macroscopic predictions based on the Navier–Stokes equation very well for large channel width, high density and low temperature. Further simulations for high temperature and low density show that the non-slip boundary condition traditionally used in the macroscopic equation is greatly compromised when the fluid–wall interactions are the same as the fluid–fluid interactions. Simulations of a system with very narrow channel width confirm earlier findings of Poiseuille flow, namely, that the velocity profiles are modulated. We find that these modulations cannot be explained by the local area density model.

Phase separation of parallel laminar flow for aqueous two phase systems in branched microchannel

Aqueous two phase systems (ATPSs) have good biocompatibility and special selectivity. Their phase equilibrium and applications in biological analysis have received much attention. Herein, parallel laminar flow (PLF) in the microchannel can provide an effective platform to enhance mass transfer and preserve separate phases simultaneously. As fundamentals in feasible and convenient sampling of PLF for ATPS, the phase separation methods and rules in branched microchannel were studied in this work, selecting PEG 4000 + Na₂SO₄ + H₂O as a model system. The exploration of flow pattern showed that a stable PFL was easily to form in the shallow microchannel of 200 μm (depth) × 600 μm (width), as long as the velocity of lower phase was higher than 0.51 mm/s. The phase interface of PLF could be easily controlled by the flow ratio of two phases. Single-phase separation could be reliably achieved in T-junction outlets when the flow rate of outlet ascertains to be smaller or larger than that of inlet on the same side. The trifurcate outlets with an extra middle channel could help realize a simultaneous two-phase separation. The flow rate of the extra channel is the key for the phase separation performance, the range of which available for simultaneous two-phase separation is determined by the resistance balance and the flow rates deviation offsetting as well. It is favor for increasing phase separation efficiency to make the products of flow rate, viscosity, and the length of corresponding outlet channel close with each other for the upper phase and the lower phase. The adjustable lengths of three channels can provide flexible choices to enhance simultaneous two-phase separation of diversified ATPSs at various operating flow ratios. A multiport microchip with T-junction inlets and trifurcate outlets designed for adjusting the lengths of branched channels on-chip is a convenient tool for PLF contact and in situ phase separation of ATPSs in varieties of application.     

Numerical solution of incompressible flow through branched channels

The work deals with numerical solution of 3D turbulent flow in straight channel and branched channels with two outlets. The mathematical model of the flow is based on Reynolds-averaged Navier–Stokes equations for incompressible flow in 3D with explicit algebraic Reynolds stress turbulence model (EARSM). The mathematical model is solved by artificial compressibility method with implicit finite volume discretization. The channels have constant square or circular cross-section, where the hydraulic diameter is same in order to enable comparison between these numerical simulations. First, developed flow in a straight channel of square cross-section is presented in order to show the ability of the used EARSM turbulence model to capture secondary corner vortices, which are not predicted by eddy viscosity models. Next the flow through channels with perpendicular branch is simulated. Methods of setting the flow rate are discussed. The numerical results are presented for two flow rates in the branch.     

Fabrication and integration of microscale permanent magnets for particle separation in microfluidics

Microfluidic magnetophoresis is an effective technique to separate magnetically labeled bioconjugates in lab-on-a-chip applications. However, it is challenging and expensive to fabricate and integrate microscale permanent magnets into microfluidic devices with conventional methods that use thin-film deposition and lithography. Here, we propose and demonstrate a simple and low-cost technique to fabricate microscale permanent magnetic microstructures and integrate them into microfluidic devices. In this method, microstructure channels were fabricated next to a microfluidic channel and were injected with a liquid mixture of neodymium (NdFeB) powders and polydimethylsiloxane (PDMS). After the mixture was cured, the resulted solid NdFeB–PDMS microstructure was permanently magnetized to form microscale magnets. The microscale magnets generate strong magnetic forces capable of separating magnetic particles in microfluidic channels. Systematic experiments and numerical simulations were conducted to study the geometric effects of the microscale magnets. It was found that rectangular microscale magnets generate larger \(({\mathbf {H}}\cdot \nabla ) {\mathbf {H}}\) which is proportional to magnetic force and have a wider range of influence than the semicircle or triangle magnets. For multiple connected rectangular microscale magnet, additional geometric parameters, including separation distance, height and width of the individual elements, further influence the particle separation and were characterized experimentally. With an optimal size combination, complete separation of yeast cells and magnetic microparticles of similar sizes (\(4\;\upmu \hbox {m}\)) was demonstrated with the multi-rectangular magnet microfluidic device.     

Noise generated by turbulent flow over forward facing steps

In this study, aeroacoustical characteristics of forward facing steps (FFSs) subject to turbulent freestream are assessed by means of linearized Euler equations (LEE). The investigated parameters are the velocity scaling of SPL and the different construction of sharp edge of FFSs. In addition to numerical simulation, an analytical vortex injection method and flow measurement are also utilized for validation purposes. It is found that the sound signal obtained from the simulation and from the theoretical approach at prescribed positions are of same phases and have comparable amplitudes. Moreover, it is reported that sound intensity scales with 5.8th power of freestream velocity. This result agrees well with the theoretical result of Curle et al. Sound radiation pattern is found to have dipole character lying horizontally. Finally, it is shown that one gains reduction in SPL by replacing sharp edged FFS with the half round edged one. Furthermore, round edged FFS, i.e. r=h, is more silent than half round edged FFS at the same frequency level.     

UpdateSearch: A New Dynamic Channel Allocation Scheme for Mobile Networks That Can Adjust to System Loads

Distributed dynamic channel allocation techniques are an integral part of distributed mobile computing systems where nodes communicate among themselves via wireless radio channels. The channel allocation schemes can be broadly categorized as search based or update based. Search based techniques have low messaging complexity and are suited for high system load and low request rates. On the other hand update based schemes have higher messaging complexity but are more suitable for low system load and high request rates. This paper presents a combined scheme, called UpdateSearch, which provides the advantages of both types of schemes. UpdateSearch is parameterized by the number of channel classes k, 1kn, where n is the total number of channels in the system. The parameter k can be adjusted to control the number of concurrent searches and degree of contention between cells competing for channels in the system. For k=1 and k=n the scheme respectively behaves as basic search and basic update scheme [2]. A simple analytical model is used to compare the performance of UpdateSearch for various values of k with the basic update and search techniques in terms of channel allocation time and number of simultaneous channel selections allowed in the system under different system loading conditions.     

A preliminary study of a diagonal channel-routing model

The layout of two-terminal nets in a VLSI channel is realized in a new diagonal channel-routing model (DCRM), where the tracks are segments respectively displayed at +45 ° and –45 ° on the two layers of the channel. A new definition of channel density is introduced, and a lower bound to the channel width is derived by the application of an algorithm, whose complexity is evaluated as a function of the channel density, and other parameters of the problem.A simple linear-time algorithm is proposed, which produces an optimal layout (i.e., it requires a channel of minimum width) if the length of the longest net equals the lower bound for the channel width. In any case, the number of vias is at most one for each net. Some particular solutions are proposed for problems with long nets.Specific problems are much easier in DCRM than in the classical Manhattan model. For example, any shift-by-i can be realized in DCRM in a channel of widthi.This work has been supported by Consiglio Nazionale delle Ricerche of Italy under a research grant.