Simulation of single DNA molecule stretching and immobilization in a de-wetting two-phase flow over micropillar-patterned surface

We investigate single DNA stretching dynamics in a de-wetting flow over micropillars using Brownian dynamics simulation. The Brownian dynamics simulation is coupled with transient flow field computation through a numerical particle tracking algorithm. The droplet formation on the top of the micropillar during the de-wetting process creates a flow pattern that allows DNA to stretch across the micropillars. It is found that DNA nanowire forms if DNA molecules could extend across the stagnation point inside the connecting water filament before its breakup. It also shows that DNA locates closer to the top wall of the micropillar has higher chance to enter the flow pattern of droplet formation and thus has higher chance to be stretched across the micropillars. Our simulation tool has the potential to become a design tool for DNA manipulation in complex biomicrofluidic devices.     

Stretching DNA by electric field and flow field in microfluidic devices: An experimental validation to the devices designed with computer simulations

We examined the performance of three microfluidic devices for stretching DNA. The first device is a microchannel with a contraction, and the remaining two are the modifications to the first. The modified designs were made with the help of computer simulations [C. C. Hsieh and T. H. Lin, Biomicrofluidics 5(4), 044106 (2011) and C. C. Hsieh, T. H. Lin, and C. D. Huang, Biomicrofluidics 6, 044105 (2012)] and they were optimized for operating with electric field. In our experiments, we first used DC electric field to stretch DNA. However, the experimental results were not even in qualitative agreement with our simulations. More detailed investigation revealed that DNA molecules adopt a globular conformation in high DC field and therefore become more difficult to stretch. Owing to the similarity between flow field and electric field, we turned to use flow field to stretch DNA with the same devices. The evolution patterns of DNA conformation in flow field were found qualitatively the same as our prediction based on electric field. We analyzed the maximum values, the evolution and the distributions of DNA extension at different Deborah number in each device. We found that the shear and the hydrodynamic interaction have significant influence on the performance of the devices.     

Electroosmotic flow in vapor deposited silicon dioxide and nitride microchannels

Electroosmotic flow was studied in thin film microchannels with silicon dioxide and silicon nitride sidewalls formed using plasma-enhanced chemical vapor deposition (PECVD). A sacrificial etching process was employed for channel fabrication allowing for cross-sections with heights of 3 μm, ranging from 2 μm to 50 μm in width. Flow rates were measured for single channels and multichannel electroosmotic pump structures for pH levels ranging from 2.6 to 8.3, and zeta potentials were calculated for both silicon dioxide and silicon nitride surfaces. Flow rates as high as 0.086 μL∕min were measured for nitride multichannel pumps at applied electric fields of 300 V∕mm. The surface characteristics of PECVD nitride were analyzed and compared to more well-known oxide surfaces to determine the density of amine sites compared to silanol sites.     

Simulation of conformational preconditioning strategies for electrophoretic stretching of DNA in a microcontraction

We have used Brownian dynamics-finite element method to examine two conformational preconditioning approaches for improving DNA stretching in a microcontraction for the purpose of direct gene analysis. The newly proposed "pre-stretching" strategy is found to significantly improve the degree of DNA extension at the exit of the contraction. On the other hand, applying an oscillating extensional field to DNA yields no preconditioning effect. Detailed analysis of the evolution of DNA extension and conformation reveals that the success of our "pre-stretching" strategy relies on the "non-local" effect that cannot be predicted using simple kinematics analysis. In other words, accurate prediction can only be obtained using detailed simulations. Comparing to the existing preconditioning strategies, our "pre-stretching" method is easy to implement while still providing a very good performance. We hope that the insight gained from this study can be useful for future design of biomicrofluidic devices for DNA manipulation.     

Stagnation point flow toward a stretching/shrinking sheet with a convective surface boundary condition

The steady two-dimensional stagnation point flow toward a stretching/shrinking sheet with the bottom surface of the sheet heated by convection from a hot fluid is considered. The governing partial differential equations are transformed into ordinary differential equations, before being solved numerically. Results for the skin friction coefficient and the local Nusselt number as well as the temperature profiles are presented for different values of the governing parameters. Effects of the governing parameters on the heat transfer characteristics are thoroughly examined. Different from a stretching sheet, it is found that the solutions for a shrinking sheet are non-unique.     

Improved analytical solutions to a stagnation-point flow past a porous stretching sheet with heat generation

This paper investigates the steady laminar flow in a porous medium of an incompressible viscous fluid impinging on a permeable stretching surface with heat generation. The resulting system of coupled non-linear ordinary differential equations is solved analytically via homotopy analysis method (HAM). Analytical results are presented for the wall shear stress and the wall heat transfer coefficient as well as the velocity and temperature profiles for some values of governing parameters such as Prandtl number, stretching parameter, porosity parameter and the heat generation/absorption parameter. Appropriate auxiliary parameter, ?, is determined by minimizing Euclidean norm of residual. The convergence of the obtained series solutions is explicitly studied.     

Separation of DNA by length in rotational flow: Lattice-Boltzmann-based simulations

We use a lattice-Boltzmann based Brownian dynamics simulation to investigate the separation of different lengths of DNA through the combination of a trapping force and the microflow created by counter-rotating vortices. We can separate most long DNA molecules from shorter chains that have lengths differing by as little as 30%. The sensitivity of this technique is determined by the flow rate, size of the trapping region, and the trapping strength. We expect that this technique can be used in microfluidic devices to separate long DNA fragments that result from techniques such as restriction enzyme digests of genomic DNA.The development of novel methods for manipulating biopolymers such as DNA is required for the continued advancement of microfluidic devices. Techniques such as restriction enzyme digests for genomic sequencing rely on the detection of DNA that differ in length by sometimes thousands of base pairs.¹ Methods that separate DNA strands with resolutions on the order of kilobase pairs are required to analyze the products of this technique. To gain an insight into possible techniques to separate polymers, it can be helpful to review the methods to separate particles in microfluidic devices. Experimental work has shown how hydrodynamic mechanisms can lead to separation of particles based on size and deformability.² Eddies, microvortices, and hydrodynamic tweezers have been used to trap and sort particles. The mechanism of the trapping and sorting arises from the differences between interactions of the particles with the fluid.^2–8 In particular, counter-rotating vortices have been used to sort particles and manipulate biopolymers. They have been used to deposit DNA precisely across electrodes⁹ and trap DNA.^10,11 Vortex flow may therefore be a good basis for a technique for sorting DNA by length.Streaming flow has been used in experiments to separate colloids of different size.^3,4 Particles are passed through a channel with a flow field driven by oscillating bubbles and pressure. The flow field becomes a combination of closed and open streamlines. The vortex flow is controlled by the accoustic driving of the bubbles while pressure controls the net flow of the fluid. Larger particles are trapped in the closed vortex flow created by the bubbles, while smaller particles can escape the neighborhood of a bubble in the open streamlines. This leads to efficient separation of particles with size differences as small as 1 μm.Previous work on DNA has shown that counter-rotating vortices can be used to trap DNA dynamically. Long strands of DNA have been observed to stretch between the centers of two counter-rotating vortices. The polymer stays trapped in this state for significant amounts of time.¹² In a different experiment, the vortices were used to thermally cycle the polymer and allow replication via the polymerase chain reaction (PCR). The DNA is also trapped against one wall by a thermophoretic force in these experiments.¹⁰ The strength of the trap is controlled by the gradient in temperature created by a focused infrared laser beam.Trapping DNA at one wall by counter-rotating vortices has also been explored in simulation and found to depend on the Peclet number, Pe = u_maxL/D_m, where u_max is the maximum speed of the vortex, L is the box size, and D_m is the diffusion coefficient of one bead in the polymer chain.¹¹ The trapping rate of the DNA was shown to depend on the competition between the flow compressing the DNA into the trap region and the diffusion of the DNA out of the trap. For the work presented here, Pe ≅ 2000, similar to the previous work done with the same simulation.We extend the previous work to investigate if counter-rotating vortices can be used to separate DNA of different lengths. We use the same type of simulation outlined in Refs. ¹¹ and ^13–17, based on the lattice-Boltzmann method. The simulation method has successfully modeled systems as diverse as thermophoresis of DNA,¹⁴ migration of DNA in a microchannel,¹⁶ and translocation of DNA through a micropore.^17,18 Using this method, the fluid is broken into a lattice with size, ΔL, chosen to be 0.5 μm, and is coupled to a worm-like chain model with Brownian dynamics for the polymer.^19,20 The fluid velocity distribution function, n_i(r, t), describes the fraction of fluid particles with a discretized velocity, c_i, at each lattice site.^21–24 A discrete velocity scheme with nineteen different velocities in three dimensions is used. The velocity distributions will evolve according to ni(r+ciΔτ,t+Δτ)=ni(r,t)+Lij[nj(r,t)−njeq(r,t)],(1)where L is a collision operator such that the fluid relaxes to the equilibrium distribution, nieq given by a second-order expansion of the Maxwell-Boltzmann distribution nieq=ρaci[1+(ci·u)/cs2+uu:(cici−cs2I)/(2cs4)],(2)where cs=1/3ΔLΔτ is the speed of sound. Δτ is the time step for the fluid in the simulation, Δτ = 8.8 × 10⁻⁵. The coefficients a^c_i are determined by satisfying a local isotropy condition ∑iaciciαciβciγciδ=cs4(δαβδγδ+δαγδbetaγ+δαδδβγ).(3)To simplify computation, the velocity distributions are transformed into moment space. The density ρ, momentum density j, and momentum flux density Π are some of the hydrodynamic moments of n_i(r, t). The equilibrium conditions for these three moments are given by ρ=∑nieq,(4) j=∑ci·nieq,(5) Π=∑nieq·cici.(6)L has eigenvalues τ0−1,τ1−1,…,τ18−1, which are the characteristic relaxation times of the moments. The Bhatanagar-Gross-Krook model is used to determine L:²⁵ the non-conserved moments have a single relaxation time, τ_s = 1.0. The conserved moments are density and momentum; for these, τ⁻¹= 0. Fluctuations are added to the fluid stress as in the method of Ladd.²⁴ We have also compared simulations with lattice sizes of 1 μm and 0.25 μm and found no significant differences in the results.The DNA used in the simulation is represented by a worm-like chain model parameterized to capture the dynamics of YOYO-stained λ DNA in bulk solution at room temperature.^15,16,26 Long, flexible DNA is modeled since techniques to separate long DNA molecules with kilobase pair resolution are necessary to complete techniques such as genomic level sequencing using restriction enzyme digests.¹ In addition, such DNA is often used in experiment. Its properties are similar to unstained DNA or DNA stained by other methods.²⁷ Each molecule is represented by N_b beads and N_b − 1 springs. A chain composed of N_b − 1 springs will have a contour length of (N_b − 1) × 2.1 μm. The forces acting on each monomer include: an excluded volume force, a non-linear spring force, the viscous drag force, a random force that produces Brownian motion, a repulsive force from the container walls, and an attractive trapping force only at one wall as shown in Fig. ​Fig.11.¹³ The excluded volume interaction between beads i and j located at r_i and r_j is modeled using the following potential: Uijev=12kBTνNks2(34πSs2)exp(−3|ri−rj|24Ss2),(7)where ν=σk3 is the excluded volume parameter with σ_k = 0.105 μm, the length of one Kuhn segment, N_ks = 19.8 is the number of Kuhn segments per spring, and Ss2=Nks/6)σk2 is the characteristic size of the bead. This excluded volume potential reproduces self avoiding walk statistics. The non-linear spring force is based on force-extension curves from experiments and is given by fijS=kBT2σk[(1−|rj−ri|Nksσk)−2+4|rj−ri|nKσk−1]rj−ri|rj−ri|,(8)which applies when N_ks ≫ 1.Open in a separate windowFIG. 1.Simulation set-up. Arrows indicate direction of fluid flow. The region where the trapping force is active is shaded, and its width (X_stick) is shown. The region used to determine the trapping rate is indicated by the area labeled trap region. Figure is not to scale, the trap region and X_stick are smaller than shown.The beads are modeled as freely draining but subject to a drag force given by F_f = ?6πηa(u_p ? u_f).(9)The beads are also subjected to a random forcing term that is drawn from a Gaussian distribution with zero mean and a variance σ_v = 2k_BTζΔt.(10)The random force reproduces Brownian motion. To conserve total momentum, the momentum change imparted to the beads through their interactions with the fluid is balanced by a momentum change in the fluid. The momentum change is distributed to the three closest fluid lattice sites using a linear interpolation scheme based on the proximity of the lattice site to the polymer beads. Through this momentum transfer, hydrodynamic interactions between the beads occur.The beads are repelled from the walls with a force of magnitude Fwall=250kBTσk3(xbead−xwall)2, xbead>(xwall−1),(11)where the repulsion range is 1ΔL. Each monomer will also be attracted to the top wall by a force with magnitude Fstick=KstickkBTσk3(xbead−xwall+10)2, xbead>(xwall−Xstick)(12)and range X_stick (see Fig. ​Fig.1).1). The sticking force is turned off every one out of one hundred time steps of the polymer (1% of the simulation time steps). We vary both X_stick and K_stick to achieve separation of the polymers.In previous experiments, DNA has been trapped against one wall by using thermophoresis,¹⁰ dielectrophoresis,²⁸ and nanoplasmonic tweezers.²⁹ In the case of thermophoresis, the trap strength (K_stick) can be controlled by tuning the intensity of the temperature gradient and the trap extension (X_stick) can be controlled through the area over which the gradient extends. Both of these are set through focusing of the laser used to produce local heating. Similarly, the trap parameters can be controlled when using plasmonic tweezers by controlling the laser beam exciting the nanoplasmonic structures. In dielectrophoresis, the DNA is trapped by an AC electric field and can be controlled by tuning the frequency and amplitude of the field.In this work, the number of polymers, N_p, is 10 unless otherwise noted, and the container size is 25 ΔL × 50 ΔL × 2 ΔL. The time step for the fluid is Δτ = 8.8 × 10⁻⁵ s, and for the polymer is Δt = 3.7 × 10⁻⁶ s. The total simulation time is over 100 chain relaxation times, allowing sufficient independent samples to perform statistical analysis.Two counter-rotating vortices, shown in 1, are produced by introducing external forces to the fluid bound by walls in the x-direction and periodic in the y and z. Two forces of equal magnitude push on the fluid in the upper x region (12ΔL < x < 25ΔL): one in the +y-direction along y = 10ΔL, and one in the –y-direction along y = 40ΔL. Such counter-rotating vortices can be produced in microfluidic channels using acoustically driven bubbles,^3,4,30 local heating,¹⁰ or plasmonic nanostructures.⁵ The flow speed is controlled by very different external mechanisms in each case. We therefore choose a simple model to produce fluid flow that is not specific to one mechanism.The simulations are started using random initial conditions, and therefore, both lengths of polymer are dispersed throughout the channel. Within a few minutes, the steady state configurations pictured in Figs. ​Figs.22 and ​and33 are reached. We define the steady state as when the number of polymer chains in the trap changes by less than one chain (10 beads) per 1000 polymer time steps. Intermittently, some polymers may still escape and re-enter the trap even in the steady state. Three final configurations are possible: Both the lengths of DNA have become trapped, both lengths continue to rotate freely, or the shorter strand has become trapped while the longer rotates freely. Two of these states leave the polymers mixed; in the third, the strands have separated by size.Open in a separate windowFIG. 2.Snapshots at t = 0Δt (left) and t = 2500Δt (right) showing the separation of 15-bead strands (grey) from 10-bead strands (black) of DNA. For these simulations, K_stick = 55 and Y_stick = 0.7ΔL.Open in a separate windowFIG. 3.Snapshots at t = 0Δt and t = 2500Δt showing the separation of 13-bead strands (grey) from 10-bead strands (black) of DNA. For these simulations, K_stick = 55 and Y_stick = 0.7ΔL as in Fig. ​Fig.2.2. Note that one long polymer is trapped, as well as all of the shorter polymers.By tuning the attractive wall force parameters and fluid flow, the separated steady state can be realized. We first set the flow parameters that allow the larger chains to rotate freely at the center of the vortices while the shorter chains rotate closer to the wall. The trap strength, K_stick, and extension, X_stick, are changed until the shorter polymers do not leave the trap. The same parameters were used to separate 10-bead chains from 15-bead and 13-bead chains.As shown in Fig. ​Fig.2,2, we have been able to separate shorter 10-bead chains from longer 15-bead chains. In the steady state, 97% of the rotating polymers were long polymers averaged over twenty simulations initialized with different random starting conditions. For three simulations, one small polymer would intermittently leave the trap region. In two of these simulations, one long polymer became stably trapped in the steady state. In another simulation, one 15-bead chain was intermittently trapped. On average, the trapped polymers were 5% 15-bead chains and 95% 10-bead chains. Again, 97% of the rotating polymers were 15-bead chains.Simulations conducted with 10-bead and 13-bead chains also showed significant separation of the two sizes as can be seen in Fig. ​Fig.3.3. In the steady state, 30% of the trapped polymers are 13-bead chains and 70% are 10-bead chains, averaged over twenty different random initial starting conditions and 1000 polymer time steps. Only 14.8% of the shorter polymers were not trapped, leading to 85.2% of the freely rotating chains being 13-bead chains. This is therefore a viable test to detect the presence of these longer chains.We have also separated 20-bead chains from 10-bead chains with all of the shorter chains trapped and all of the longer chains freely rotating in the steady-state. These results do not change for twenty different random initial starting conditions and 1000 polymer time steps. None of the longer polymers intermittently enter the trap region nor do any of the shorter polymers intermittently escape.The separation is achieved by tuning the trapping force and flow rate. Strong flows will push all the DNA molecules into the trap. The final state is mixed, with both short and long strands trapped. For flows that are too weak, the short molecules are not sufficiently compressed by the flow and therefore do not enter the trap region. The end state is mixed, with all polymers freely rotating. Separation is achieved when the flow rate is tuned so that the short strands are compressed against the channel wall while the long polymers rotate near the center of the vortices. The trap strength must then be set sufficiently high enough to prevent the short strands from being pulled by the hydrodynamic drag force out of the trap.The mechanism of the separation depends on the differences in the steady state configurations of the polymers and chances of a polymer escaping the trap. As shown in Fig. ​Fig.4,4, both longer and shorter chains are pulled into the trap region by the flow. However, the longer chains have a larger chance of a bead escaping into a region of the flow where the fluid velocity is sufficient to pull the entire strand out of the trap. As shown in Ref. ¹¹, the trapping rate depends on diffusion in a polymer depleted region near the trap, in agreement with classical theory which neglects bead-wall interactions. In addition, the theory depends on the single bead diffusion rate and does not take into account the elastic force holding the beads together. Diffusion becomes as significant as convection in the polymer depleted region leading to dependence on the Peclet number. Since longer polymers have more beads; they have more chances of a single bead diffusing through this layer into the region where convection is again more important. Thus, they are pulled out of the trap at a faster rate than the shorter chains.Open in a separate windowFIG. 4.N, number of beads in the trap region, versus time for 15-bead DNA strands (solid line) and 10-bead DNA strands (dashed line). Here, ΔT = 10000Δt. The simulation parameters are the same as in Fig. ​Fig.22.In addition, longer chains have a second trap resulting from the microflow. As shown in Ref. ¹², DNA in counter-rotating vortices can tumble at the center of one vortex or be stretched between the centers of the two vortices. We have observed both these conformations for the longer polymer strand. They are a stable trajectory for the longer polymer that remains outside of the trapping region. As seen in Fig. ​Fig.4,4, few monomers of the longer chains enter the trap region once the steady state has been reached. However, the shorter polymer rotates at a larger radius than the longer polymer as seen in Fig. ​Fig.5.5. The shorter polymers therefore are pushed back into the trap while the longer strands rotate stably outside the trapping region.Open in a separate windowFIG. 5.Trajectories of 15-bead DNA (grey) and 10-bead DNA (black). The position of each monomer is plotted for 100 consecutive time steps. Note that the longer polymers rotate in the center of the channel while the shorter polymers rotate at the edges. Simulation parameters are the same as in Fig. ​Fig.22.This mechanism is similar to the one proposed for the separation of colloids by size in Refs. ³ and ⁴. In that experimental work, the smaller colloidal particles rotated at larger radii. This allowed the smaller beads to be pushed out of the vicinity of the vortices by the streaming flow, while the larger beads continued to circle. However, in our simulations, we have the additional mechanism of separation based on the increased chance of a longer polymer escaping the trap region. This mechanism is important for maintaining the separation. Long polymers initially in the trap region or which diffuse into the trap would not be able to escape without it.We expect that this technique could be used to detect the sizes of DNA fragments on the order of thousands of base pairs. It relies on the flexibility of the molecule and its interaction with the flow. Common lab procedures such as restriction enzyme digests for DNA fingerprinting can produce these long fragments. Current techniques such as gel electrophoresis require significant time to separate the long strands that move more slowly through the matrix. This effect could therefore be a good candidate for developing a microfluidic analysis that is significantly faster than traditional procedures. Our separation occurs in minutes rather than in hours as for gel electrophoresis.As pointed out in Ref. ², hydrodynamic effects have been shown to be important for microfluidic devices for separation. We have demonstrated, in simulation, a novel hydrodynamic mechanism for separating polymers by length. We hope that these promising calculations will inspire experiments to verify these results.     

Simulation guided design of a microfluidic device for electrophoretic stretching of DNA

We have used Brownian dynamics-finite element method (BD-FEM) to guide the optimization of a microfluidic device designed to stretch DNA for gene mapping. The original design was proposed in our previous study [C. C. Hsieh and T. H. Lin, Biomicrofluidics 5(4), 044106 (2011)] for demonstrating a new pre-conditioning strategy to facilitate DNA stretching through a microcontraction using electrophoresis. In this study, we examine the efficiency of the original device for stretching DNA with different sizes ranging from 48.5 kbp (λ-DNA) to 166 kbp (T4-DNA). The efficiency of the device is found to deteriorate with increasing DNA molecular weight. The cause of the efficiency loss is determined by BD-FEM, and a modified design is proposed by drawing an analogy between an electric field and a potential flow. The modified device does not only regain the efficiency for stretching large DNA but also outperforms the original device for stretching small DNA.     

Regulation of DNA conformations and dynamics in flows with hybrid field microfluidics

Visualizing single DNA dynamics in flow provides a wealth of physical insights in biophysics and complex flow study. However, large signal fluctuations, generated from diversified conformations, deformation history dependent dynamics and flow induced stochastic tumbling, often frustrate its wide adoption in single molecule and polymer flow study. We use a hybrid field microfluidic (HFM) approach, in which an electric field is imposed at desired locations and appropriate moments to balance the flow stress on charged molecules, to effectively regulate the initial conformations and the deformation dynamics of macromolecules in flow. With λ-DNA and a steady laminar shear flow as the model system, we herein studied the performance of HFM on regulating DNA trapping, relaxation, coil-stretch transition, and accumulation. DNA molecules were found to get captured in the focused planes when motions caused by flow, and the electric field were balanced. The trapped macromolecules relaxed in two different routes while eventually became more uniform in size and globule conformations. When removing the electric field, the sudden stretching dynamics of DNA molecules exhibited a more pronounced extension overshoot in their transient response under a true step function of flow stress while similar behaviors to what other pioneering work in steady shear flow. Such regulation strategies could be useful to control the conformations of other important macromolecules (e.g., proteins) and help better reveal their molecular dynamics.     

Curvature-induced dielectrophoresis for continuous separation of particles by charge in spiral microchannels

The separation of particles from a heterogeneous mixture is critical in chemical and biological analyses. Many methods have been developed to separate particles in microfluidic devices. However, the majority of these separations have been limited to be size based and binary. We demonstrate herein a continuous dc electric field driven separation of carboxyl-coated and noncoated 10 μm polystyrene beads by charge in a double-spiral microchannel. This method exploits the inherent electric field gradients formed within the channel turns to manipulate particles by dielectrophoresis and is thus termed curvature-induced dielectrophoresis. The spiral microchannel is also demonstrated to continuously sort noncoated 5 μm beads, noncoated 10 μm beads, and carboxyl-coated 10 μm beads into different collecting wells by charge and size simultaneously. The observed particle separation processes in different situations are all predicted with reasonable agreements by a numerical model. This curvature-induced dielectrophoresis technique eliminates the in-channel microelectrodes and obstacles that are required in traditional electrode- and insulator-based dielectrophoresis devices. It may potentially be used to separate multiple particle targets by intrinsic properties for lab-on-a-chip applications.     

Simulation of electrophoretic stretching of DNA in a microcontraction using an obstacle array for conformational preconditioning

Recently our group has reported experiments using an obstacle array to precondition the conformations of DNA molecules to facilitate their stretch in a microcontraction. Based upon previous successes simulating electrophoretic stretching in microcontractions without obstacles, we use our simulation model to study the deformation of DNA chains in a microcontraction preceded by an array of cylindrical obstacles. We compare our data to the experimental results and find good qualitative, and even quantitative, agreement concerning the behavior of the chains in the array; however, the simulations overpredict the mean stretch of the chains as they leave the contraction. We examine the amount of stretch gained between leaving the array and reaching the end of the contraction and speculate that the differences seen are caused by nonlinear electrokinetic effects that become important in the contraction due to a combination of field gradients and high field strengths.     

Resolving dynamics of inertial migration in straight and curved microchannels by direct cross-sectional imaging

The explosive development of inertial microfluidic systems for label-free sorting and isolation of cells demands improved understanding of the underlying physics that dictate the intriguing phenomenon of size-dependent migration in microchannels. Despite recent advances in the physics underlying inertial migration, migration dynamics in 3D is not fully understood. These investigations are hampered by the lack of easy access to the channel cross section. In this work, we report on a simple method of direct imaging of the channel cross section that is orthogonal to the flow direction using a common inverted microscope, providing vital information on the 3D cross-sectional migration dynamics. We use this approach to revisit particle migration in both straight and curved microchannels. In the rectangular channel, the high-resolution cross-sectional images unambiguously confirm the two-stage migration model proposed earlier. In the curved channel, we found two vertical equilibrium positions and elucidate the size-dependent vertical and horizontal migration dynamics. Based on these results, we propose a critical ratio of blockage ratio (β) to Dean number (De) where no net lateral migration occurs (β/De ∼ 0.01). This dimensionless number (β/De) predicts the direction of lateral migration (inward or outward) in curved and spiral channels, and thus serves as a guideline in design of such channels for particle and cell separation applications. Ultimately, the new approach to direct imaging of the channel cross section enables a wealth of previously unavailable information on the dynamics of inertial migration, which serves to improve our understanding of the underlying physics.     

Electrotaxis of oral squamous cell carcinoma cells in a multiple-electric-field chip with uniform flow field

We report a new design of microfluidic chip (Multiple electric Field with Uniform Flow chip, MFUF chip) to create multiple electric field strengths (EFSs) while providing a uniform flow field simultaneously. MFUF chip was fabricated from poly-methyl methacrylates (PMMA) substrates by using CO₂ laser micromachining. A microfluidic network with interconnecting segments was utilized to de-couple the flow field and the electric field (EF). Using our special design, different EFSs were obtained in channel segments that had an identical cross-section and therefore a uniform flow field. Four electric fields with EFS ratio of 7.9:2.8:1:0 were obtained with flow velocity variation of only 7.8% CV (coefficient of variation). Possible biological effect of shear force can therefore be avoided. Cell behavior under three EFSs and the control condition, where there is no EF, was observed in a single experiment. We validated MFUF chip performance using lung adenocarcinoma cell lines and then used the chip to study the electrotaxis of HSC-3, an oral squamous cell carcinoma cell line. The MFUF chip has high throughput capability for studying the EF-induced cell behavior under various EFSs, including the control condition (EFS = 0).     

Modeling of dielectrophoretic transport of myoglobin molecules in microchannels

Myoglobin is one of the premature identifying cardiac markers, whose concentration increases from 90 pg∕ml or less to over 250 ng∕ml in the blood serum of human beings after minor heart attack. Separation, detection, and quantification of myoglobin play a vital role in revealing the cardiac arrest in advance, which is the challenging part of ongoing research. In the present work, one of the electrokinetic approaches, i.e., dielectrophoresis (DEP), is chosen to separate the myoglobin. A mathematical model is developed for simulating dielectrophoretic behavior of a myoglobin molecule in a microchannel to provide a theoretical basis for the above application. This model is based on the introduction of a dielectrophoretic force and a dielectric myoglobin model. A dielectric myoglobin model is developed by approximating the shape of the myoglobin molecule as sphere, oblate, and prolate spheroids. A generalized theoretical expression for the dielectrophoretic force acting on respective shapes of the molecule is derived. The microchannel considered for analysis has an array of parallel rectangular electrodes at the bottom surface. The potential and electric field distributions are calculated using Green’s theorem method and finite element method. These results also compared to the Fourier series method, closed form solutions by Morgan et al. [J. Phys. D: Appl. Phys. 34, 1553 (2001)] and Chang et al. [J. Phys. D: Appl. Phys. 36, 3073 (2003)]. It is observed that both Green’s theorem based analytical solution and finite element based numerical solution for proposed model are closely matched for electric field and square electric field gradients. The crossover frequency is obtained as 40 MHz for given properties of myoglobin and for all approximated shapes of myoglobin molecule. The effect of conductivity of medium and myoglobin on the crossover frequency is also demonstrated. Further, the effect of hydration layer on the crossover frequency of myoglobin molecules is also presented. Both positive and negative DEP effects on myoglobin molecules are obtained by switching the frequency of applied electric field. The effect of different shapes of myoglobin on DEP force is studied and no significant effect on DEP force is observed. Finally, repulsion of myoglobin molecules from the electrode plane at 1 KHz frequency and 10 V applied voltage is observed. These results provide the ability of applying DEP force for manipulating nanosized biomolecules such as myoglobin.     

dc electrokinetic transport of cylindrical cells in straight microchannels

Electrokinetic transport of cylindrical cells under dc electric fields in a straight microfluidic channel is experimentally and numerically investigated with emphasis on the dielectrophoretic (DEP) effect on their orientation variations. A two-dimensional multiphysics model, composed of the Navier–Stokes equations for the fluid flow and the Laplace equation for the electric potential defined in an arbitrary Lagrangian–Eulerian framework, is employed to capture the transient electrokinetic motion of cylindrical cells. The numerical predictions of the particle transport are in quantitative agreement with the obtained experimental results, suggesting that the DEP effect should be taken into account to study the electrokinetic transport of cylindrical particles even in a straight microchannel with uniform cross-sectional area. A comprehensive parametric study indicates that cylindrical particles would experience an oscillatory motion under low electric fields. However, they are aligned with their longest axis parallel to the imposed electric field under high electric fields due to the induced DEP effect.     

Observation of hydrophobic-like behavior in geometrically patterned hydrophilic microchannels

We present our observation of meta-hydrophobicity, where geometrically patterned surfaces make hydrophilic microchannels exhibit hydrophobic-like behaviors. We analyze the wetting-induced energy decrease that results from the surface geometries and experimentally demonstrate how those geometries can modulate the dynamics of capillary-driven wetting and evaporation-driven drying of microfluidic systems. Our results also show that the modulated wetting dynamics can be employed to generate regulated patterns of microbubbles.     

Focused ion beam milling of microchannels in lithium niobate

We present experimental and simulation results for focused ion beam (FIB) milling of microchannels in lithium niobate in this paper. We investigate two different cuts of lithium niobate, Y- and Z-cuts, and observe that the experimental material removal rate in the FIB for both Y-cut and Z-cut samples was 0.3 μm³/nC, roughly two times greater than the material removal rate previously reported in the literature but in good agreement with the value we obtain from stopping and range of ions in matter (SRIM) simulations. Further, we investigate the FIB milling rate and resultant cross-sectional profile of microchannels at various ion beam currents and find that the milling rate decreases as a function of ion dose and correspondingly, the cross-sectional profiles change from rectangular to V-shaped. This indicates that material redeposition plays an important role at high ion dose or equivalently, high aspect ratio. We find that the experimental material removal rate decreases as a function of aspect ratio of the milled structures, in good agreement with our simulation results at low aspect ratio and in good agreement with the material removal rates previously reported in the literature at high aspect ratios. Our results show that it is indeed easier than previously assumed to fabricate nanochannels with low aspect ratio directly on lithium niobate using the FIB milling technique.     

湿式脱硫除尘装置内非等温流场的数值研究

SHG-Ⅱ-Z型组合式湿式脱硫除尘器是新一代湿式除尘脱硫一体化设备。在假设粉尘、SO2分别与水发生吸收反应而被去除的条件下,使用FLUENT软件,选择容积反应模型,数值模拟设备内脱硫除尘过程和气液固三维三相非等温流场;数值研究了不同烟气温度对脱硫除尘效率的影响。结果表明,温度在塔板截面中心最低,与入口温度相差90℃左右,脱硫率随烟气温度的增大而升高,而除尘率随温度的升高略有上升但变化不明显,数值模拟结果对设备的优化设计和实际运行有一定的指导意义。     

Band-broadening suppressed effect in long turned geometry channel and high-sensitive analysis of DNA sample by using floating electrokinetic supercharging on a microchip

A featured microchip owning three big reservoirs and long turned geometry channel was designed to improve the detection limit of DNA fragments by using floating electrokinetic supercharging (FEKS) method. The novel design matches the FEKS preconcentration needs of a large sample volume introduction with electrokinetic injection (EKI), as well as long duration of isotachophoresis (ITP) process to enrich low concentration sample. In the curved channel [∼45.6 mm long between port 1 (P1) and the intersection point of two channels], EKI and ITP were performed while the side port 3 (P3) was electrically floated. The turn-induced band broadening with or without ITP process was investigated by a computer simulation (using CFD-ACE+ software) when the analytes traveling through the U-shaped geometry. It was found that the channel curvature determined the extent of band broadening, however, which could be effectively eliminated by the way of ITP. After the ITP-stacked zones passed the intersection point from P1, they were rapidly destacked for separation and detection from ITP to zone electrophoresis by using leading ions from P3. The FEKS carried on the novel chip successfully contributed to higher sensitivities of DNA fragments in comparison with our previous results realized on either a single channel or a cross microchip. The analysis of low concentration 50 bp DNA step ladders (0.23 μg∕ml after 1500-fold diluted) was achieved with normal UV detection at 260 nm. The obtained limit of detections (LODs) were on average 100 times better than using conventional pinched injection, down to several ng∕ml for individual DNA fragment.