The accelerated flow method for rapid reactions

A manual syringe drive has been found to fulfil the requirements for a high driving force and a small disturbance to the electro-optical system. A syringe bore has been selected with due regard for the force-speed characteristic of the hand and flow velocities of 25 m./sec. have been obtained in this manner. A direct comparison of a manual and an electric drive has been made and it has been found that the mechanical and electrical effects of the latter upon the photoelectric system greatly reduce the possible range of the electric drive method.     

Electroosmotic flow hysteresis for dissimilar ionic solutions

Electroosmotic flow (EOF) with two or more fluids is commonly encountered in various microfluidics applications. However, no investigation has hitherto been conducted to investigate the hysteretic or flow direction-dependent behavior during the displacement flow of solutions with dissimilar ionic species. In this investigation, electroosmotic displacement flow involving dissimilar ionic solutions was studied experimentally through a current monitoring method and numerically through finite element simulations. The flow hysteresis can be characterized by the turning and displacement times; turning time refers to the abrupt gradient change of current-time curve while displacement time is the time for one solution to completely displace the other solution. Both experimental and simulation results illustrate that the turning and displacement times for a particular solution pair can be directional-dependent, indicating that the flow conditions in the microchannel are not the same in the two different flow directions. The mechanics of EOF hysteresis was elucidated through the theoretical model which includes the ionic mobility of each species, a major governing parameter. Two distinct mechanics have been identified as the causes for the EOF hysteresis involving dissimilar ionic solutions: the widening/sharpening effect of interfacial region between the two solutions and the difference in ion concentration distributions (and thus average zeta potentials) in different flow directions. The outcome of this investigation contributes to the fundamental understanding of flow behavior in microfluidic systems involving solution pair with dissimilar ionic species.     

Extensional flow of blood analog solutions in microfluidic devices

In this study, we show the importance of extensional rheology, in addition to the shear rheology, in the choice of blood analog solutions intended to be used in vitro for mimicking the microcirculatory system. For this purpose, we compare the flow of a Newtonian fluid and two well-established viscoelastic blood analog polymer solutions through microfluidic channels containing both hyperbolic and abrupt contractions∕expansions. The hyperbolic shape was selected in order to impose a nearly constant strain rate at the centerline of the microchannels and achieve a quasihomogeneous and strong extensional flow often found in features of the human microcirculatory system such as stenoses. The two blood analog fluids used are aqueous solutions of a polyacrylamide (125 ppm w∕w) and of a xanthan gum (500 ppm w∕w), which were characterized rheologically in steady-shear flow using a rotational rheometer and in extension using a capillary breakup extensional rheometer (CaBER). Both blood analogs exhibit a shear-thinning behavior similar to that of whole human blood, but their relaxation times, obtained from CaBER experiments, are substantially different (by one order of magnitude). Visualizations of the flow patterns using streak photography, measurements of the velocity field using microparticle image velocimetry, and pressure-drop measurements were carried out experimentally for a wide range of flow rates. The experimental results were also compared with the numerical simulations of the flow of a Newtonian fluid and a generalized Newtonian fluid with shear-thinning behavior. Our results show that the flow patterns of the two blood analog solutions are considerably different, despite their similar shear rheology. Furthermore, we demonstrate that the elastic properties of the fluid have a major impact on the flow characteristics, with the polyacrylamide solution exhibiting a much stronger elastic character. As such, these properties must be taken into account in the choice or development of analog fluids that are adequate to replicate blood behavior at the microscale.     

Three-phase slug flow in microchips can provide beneficial reaction conditions for enzyme liquid-liquid reactions

Here, we introduce a solution to low stability of a two-phase slug flow with a chemical reaction occurring at the phase interface in a microfluidic reactor where substantial merging of individual reacting slugs results in the loss of uniformity of the flow. We create a three-phase slug flow by introducing a third fluid phase into the originally two-phase liquid-liquid slug flow, which generates small two-phase liquid slugs separated by gas phase. Introduction of the third phase into our system efficiently prevents merging of slugs and provides beneficial reaction conditions, such as uniform flow pattern along the whole reaction capillary, interfacial area with good reproducibility, and intensive water-oil interface renewal. We tested the three-phase flow on an enzyme hydrolysis of soybean oil and compared the reaction conversion with those from unstable two-phase slug flows. We experimentally confirmed that the three-phase slug flow arrangement provides conversions and pressure drops comparable or even better with two-phase liquid-liquid arrangements.     

A tapered channel microfluidic device for comprehensive cell adhesion analysis, using measurements of detachment kinetics and shear stress-dependent motion

We have developed a method for studying cellular adhesion by using a custom-designed microfluidic device with parallel non-connected tapered channels. The design enables investigation of cellular responses to a large range of shear stress (ratio of 25) with a single input flow-rate. For each shear stress, a large number of cells are analyzed (500–1500 cells), providing statistically relevant data within a single experiment. Besides adhesion strength measurements, the microsystem presented in this paper enables in-depth analysis of cell detachment kinetics by real-time videomicroscopy. It offers the possibility to analyze adhesion-associated processes, such as migration or cell shape change, within the same experiment. To show the versatility of our device, we examined quantitatively cell adhesion by analyzing kinetics, adhesive strength and migration behaviour or cell shape modifications of the unicellular model cell organism Dictyostelium discoideum at 21 °C and of the human breast cancer cell line MDA-MB-231 at 37 °C. For both cell types, we found that the threshold stresses, which are necessary to detach the cells, follow lognormal distributions, and that the detachment process follows first order kinetics. In addition, for particular conditions’ cells are found to exhibit similar adhesion threshold stresses, but very different detachment kinetics, revealing the importance of dynamics analysis to fully describe cell adhesion. With its rapid implementation and potential for parallel sample processing, such microsystem offers a highly controllable platform for exploring cell adhesion characteristics in a large set of environmental conditions and cell types, and could have wide applications across cell biology, tissue engineering, and cell screening.     

Extensional flow of hyaluronic acid solutions in an optimized microfluidic cross-slot device

We utilize a recently developed microfluidic device, the Optimized Shape Cross-slot Extensional Rheometer (OSCER), to study the elongational flow behavior and rheological properties of hyaluronic acid (HA) solutions representative of the synovial fluid (SF) found in the knee joint. The OSCER geometry is a stagnation point device that imposes a planar extensional flow with a homogenous extension rate over a significant length of the inlet and outlet channel axes. Due to the compressive nature of the flow generated along the inlet channels, and the planar elongational flow along the outlet channels, the flow field in the OSCER device can also be considered as representative of the flow field that arises between compressing articular cartilage layers of the knee joints during running or jumping movements. Full-field birefringence microscopy measurements demonstrate a high degree of localized macromolecular orientation along streamlines passing close to the stagnation point of the OSCER device, while micro-particle image velocimetry is used to quantify the flow kinematics. The stress-optical rule is used to assess the local extensional viscosity in the elongating fluid elements as a function of the measured deformation rate. The large limiting values of the dimensionless Trouton ratio, Tr ∼ O(50), demonstrate that these fluids are highly extensional-thickening, providing a clear mechanism for the load-dampening properties of SF. The results also indicate the potential for utilizing the OSCER in screening of physiological SF samples, which will lead to improved understanding of, and therapies for, disease progression in arthritis sufferers.     

Study of flow behaviors on single-cell manipulation and shear stress reduction in microfluidic chips using computational fluid dynamics simulations

Various single-cell retention structures (SCRSs) were reported for analysis of single cells within microfluidic devices. Undesirable flow behaviors within micro-environments not only influence single-cell manipulation and retention significantly but also lead to cell damage, biochemical heterogeneity among different individual cells (e.g., different cell signaling pathways induced by shear stress). However, the fundamentals in flow behaviors for single-cell manipulation and shear stress reduction, especially comparison of these behaviors in different microstructures, were not fully investigated in previous reports. Herein, flow distribution and induced shear stress in two different single-cell retention structures (SCRS I and SCRS II) were investigated in detail to study their effects on single-cell trapping using computational fluid dynamics (CFD) methods. The results were successfully verified by experimental results. Comparison between these two SCRS shows that the wasp-waisted configuration of SCRS II has a better performance in trapping and manipulating long cylinder-shaped cardiac myocytes and provides a safer “harbor” for fragile cells to prevent cell damage due to the shear stress induced from strong flows. The simulation results have not only explained flow phenomena observed in experiments but also predict new flow phenomena, providing guidelines for new chip design and optimization, and a better understanding of the cell micro-environment and fundamentals of microfluidic flows in single-cell manipulation and analysis.     

Transport and shear in a microfluidic membrane bilayer device for cell culture

Microfluidic devices have been established as useful platforms for cell culture for a broad range of applications, but challenges associated with controlling gradients of oxygen and other soluble factors and hemodynamic shear forces in small, confined channels have emerged. For instance, simple microfluidic constructs comprising a single cell culture compartment in a dynamic flow condition must handle tradeoffs between sustaining oxygen delivery and limiting hemodynamic shear forces imparted to the cells. These tradeoffs present significant difficulties in the culture of mesenchymal stem cells (MSCs), where shear is known to regulate signaling, proliferation, and expression. Several approaches designed to shield cells in microfluidic devices from excessive shear while maintaining sufficient oxygen concentrations and transport have been reported. Here we present the relationship between oxygen transport and shear in a "membrane bilayer" microfluidic device, in which soluble factors are delivered to a cell population by means of flow through a proximate channel separated from the culture channel by a membrane. We present an analytical model that describes the characteristics of this device and its ability to independently modulate oxygen delivery and hemodynamic shear imparted to the cultured cells. This bilayer configuration provides a more uniform oxygen concentration profile that is possible in a single-channel system, and it enables independent tuning of oxygen transport and shear parameters to meet requirements for MSCs and other cells known to be sensitive to hemodynamic shear stresses.     

Exploring solutions for mobile companionship: A design research approach to context-aware management

The mobile phone is not just another device; it is with you day and night, and you rely on its capabilities in work and in private. In short, the mobile phone is your companion. As your companion, it should understand your situational and informational needs. How do we increase the friendliness of your mobile phone, in order to fulfil this promise? In this paper, we explore how context awareness can be used for managing the user mobile experience. To this end, we employed a design research approach to integrate context-aware and cloud based services in an Android application. Through a user evaluation and proof-of-concept implementation we show how new technologies can increase the friendliness of your mobile phone. In so doing, we provide evidence that adaptive applications based on user context offer a fertile ground for taking mobile companionship to the next level.     

冶炼粗锡奥斯麦特炉冷调试发现问题及解决方案

对奥斯麦特炉冷调试过程发现的问题作分析说明,并提出相应的解决方法。     

Review Article: Recent advancements in optofluidic flow cytometer

There is an increasing need to develop optofluidic flow cytometers. Optofluidics, where optics and microfluidics work together to create novel functionalities on a small chip, holds great promise for lab-on-a-chip flow cytometry. The development of a low-cost, compact, handheld flow cytometer and microfluorescence-activated cell sorter system could have a significant impact on the field of point-of-care diagnostics, improving health care in, for example, underserved areas of Africa and Asia, that struggle with epidemics such as HIV∕AIDS. In this paper, we review recent advancements in microfluidics, on-chip optics, novel detection architectures, and integrated sorting mechanisms.     

A polymeric micro-optical interface for flow monitoring in biomicrofluidics

We describe design and miniaturization of a polymeric optical interface for flow monitoring in biomicrofluidics applications based on polydimethylsiloxane technology, providing optical transparency and compatibility with biological tissues. Design and ray tracing simulation are presented as well as device realization and optical analysis of flow dynamics in microscopic blood vessels. Optics characterization of this polymeric microinterface in dynamic experimental conditions provides a proof of concept for the application of the device to two-phase flow monitoring in both in vitro experiments and in vivo microcirculation investigations. This technology supports the study of in vitro and in vivo microfluidic systems. It yields simultaneous optical measurements, allowing for continuous monitoring of flow. This development, integrating a well-known and widely used optical flow monitoring systems, provides a disposable interface between live mammalian tissues and microfluidic devices making them accessible to detection∕processing technology, in support or replacing standard intravital microscopy.     

Modelling information flow for organisations: A review of approaches and future challenges

Modelling is a classic approach to understanding complex problems that can be achieved diagrammatically to visualise concepts, and mathematically to analyse attributes of concepts. An organisation as a communicating entity is a made up of constructs in which people can have access to information and speak to each other. Modelling information flow for organisations is a challenging task that enables analysts and managers to better understand how to: organise and coordinate processes, eliminate redundant information flows and processes, minimise the duplication of information and manage the sharing of intra- and inter-organisational information.     

我国西南喀斯特生态修复的十大问题与对策

西南喀斯特地区是美丽中国建设的重点和难点区域之一,其中包括土壤侵蚀、坡耕地比例、水资源污染、岩溶干旱、生态修复、协同碳汇、城市化生态效应、石漠化治理指标、生物多样性及可持续性评估等方面的问题。文章将喀斯特地区生态修复实践过程中积累的知识综合成土壤侵蚀、坡耕地比例、水资源污染、岩溶干旱、生态修复、协同碳汇、城市化生态效应、石漠化治理指标、生物多样性及可持续性评估等10个方面的问题和解决措施。它们有助于解释在喀斯特生态修复方面实现可持续性所面临的挑战,进而文章也指出了解决办法。它们构成了一套核心原则,可以指导科学家、政策制定者和实践者应对喀斯特生态修复工程中的可持续性挑战。     

Slow,frictionless ring forming: further exact solutions for a wide class of ductile materials

The plastic flow of material in a slowly deforming ring under frictionless conditions is analyzed. Exact solutions are obtained without necessarily making explicit the choice of the yield criterion. The results are valid for rigid-perfectly plastic materials with a linear relation between the deviator of the stress tensor and the rate-of-strain tensor. The graphical presentation of the results is for the particular cases of materials obeying the maximum shear stress yield criterion, the constant energy of distortion yield criterion and two other yield criteria. The general behavior is the same for all the materials studied here, but significant numerical differences are observed for process parameters.     

Life under flow: A novel microfluidic device for the assessment of anti-biofilm technologies

In the current study, we have developed and fabricated a novel lab-on-a-chip device for the investigation of biofilm responses, such as attachment kinetics and initial biofilm formation, to different hydrodynamic conditions. The microfluidic flow channels are designed using computational fluid dynamic simulations so as to have a pre-defined, homogeneous wall shear stress in the channels, ranging from 0.03 to 4.30 Pa, which are relevant to in-service conditions on a ship hull, as well as other man-made marine platforms. Temporal variations of biofilm formation in the microfluidic device were assessed using time-lapse microscopy, nucleic acid staining, and confocal laser scanning microscopy (CLSM). Differences in attachment kinetics were observed with increasing shear stress, i.e., with increasing shear stress there appeared to be a delay in bacterial attachment, i.e., at 55, 120, 150, and 155 min for 0.03, 0.60, 2.15, and 4.30 Pa, respectively. CLSM confirmed marked variations in colony architecture, i.e.,: (i) lower shear stresses resulted in biofilms with distinctive morphologies mainly characterised by mushroom-like structures, interstitial channels, and internal voids, and (ii) for the higher shear stresses compact clusters with large interspaces between them were formed. The key advantage of the developed microfluidic device is the combination of three architectural features in one device, i.e., an open-system design, channel replication, and multiple fully developed shear stresses.     

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.