Laminar Flow Profile Research Articles

Flow-induced deformation of shallow microfluidic channels

We study the elastic deformation of poly(dimethylsiloxane) (PDMS) microchannels under imposed flow rates and the effect of this deformation on the laminar flow profile and pressure distribution within the channels. Deformation is demonstrated to be an important consideration in low aspect ratio (height to width) channels and the effect becomes increasingly pronounced for very shallow channels. Bulging channels are imaged under varying flow conditions by confocal microscopy. The deformation is related to the pressure and is thus non-uniform throughout the channel, with tapering occurring along the stream-wise axis. The measured pressure drop is monitored as a function of the imposed flow rate. For a given pressure drop, the corresponding flow rate in a deforming channel is found to be several times higher than expected in a non-deforming channel. The experimental results are supported by scaling analysis and computational fluid dynamics simulations coupled to materials deformation models.

Continuous flow separation of particles within an asymmetric microfluidic device

A microfluidic based device has been developed for the continuous separation of polymer microspheres, taking advantage of the flow characteristics of systems. The chip consists of an asymmetric cavity with variable channel width which enables continuous amplification of the particle separation for different size particles within the laminar flow profile. The process has been examined by varying the sample inlet position, the sample to media flow rate ratio, and the total flow rate. This technique can be applied for manipulating both microscale biological and colloidal particles within microfluidic systems.

Analytical solution of multimodal acoustic propagation in circular ducts with laminar mean flow profile

In this paper, an analytical solution for the propagation of sound in circular ducts in the presence of Poiseuille mean flow is derived. This solution uses Kummer's functions and it generalizes the results found by Gogate and Munjal. Links between this solution and already-known solutions for more specific cases (no mean flow, uniform flow) are made. Results for calculation of the propagation constant and pressure profiles are presented and compared with the literature. The effect of shear on multimodal acoustic propagation, including modes of higher radial order is discussed.

Considerations for high resolution laser Doppler measurements in very small circular tubes

When performing laser Doppler measurements in channels and tubes of very small dimensions, the velocity gradient across the measurement volume cannot always be neglected in estimating the mean velocity or the variance of the velocity fluctuations. This effect and the corresponding estimator corrections have been previously documented for plane channels and nozzles of diameter much larger than the measurement volume dimensions. However, for very small pipes and microtubes, for instance holes in fuel injection nozzles, additional corrections are required. These corrections are derived for a generalized geometry and their magnitude is computed in dimensionless form for laminar and turbulent flow profiles. One experimental example will be shown. For large tube diameters the solution approaches asymptotically the result for a plane flow geometry.

Transverse Diffusion of Laminar Flow Profiles To Produce Capillary Nanoreactors

We introduce transverse diffusion of laminar flow profiles (TDLFP), the first generic method for mixing two or more reactants inside capillaries. Conceptually, solutions of reactants are injected inside the capillary by pressure as a series of consecutive plugs. Due to the laminar nature of flow inside the capillary, the nondiffused plugs have parabolic profiles with predominantly longitudinal interfaces between them. After injection, the plugs are mixed by transverse diffusion; longitudinal diffusion does not contribute to mixing. To prove the principle, we used TDLFP to mix two reactants-an enzyme and its substrate. After mixing the reactants by TDLFP, we incubated reaction mixtures for different periods of time and measured the reaction kinetics. We found that the reaction proceeded in time- and concentration-dependent fashion, thus confirming that the reactants were mixed by TDLFP. Remarkably, the experimental reaction kinetics were not only in qualitative agreement but also in good quantitative agreement with theoretically predicted ones. TDLFP has a number of enabling features. By facilitating the preparation of reaction mixtures inside the capillary, TDLFP lowers reagent consumption to nanoliters (microliters are required for conventionally mixing reagents in a vial). The reaction products can be then analyzed "on-line" by capillary separation coupled with optical, electrochemical, or mass spectrometric detection. The combination of TDLFP with capillary separation will be an indispensable tool in screening large combinatorial libraries for affinity probes and drug candidates: a few microliters of a target protein will be sufficient to screen thousands of compounds. The new method paves the road to a wide use of capillary nanoreactors in different areas of physical and life sciences.

156 ENHANCED BOVINE EMBRYONIC DEVELOPMENT AFTER MICROFLUIDIC CUMULUS CELL REMOVAL POST-FERTILIZATION

Microfluidic technologies are increasingly being used in cell biology and embryology research. In order to manipulate an embryonic environment microfluidics take advantage of miniscule media amounts. With the use of pressure heads and laminar flow profiles, a presumptive zygote can be gently manipulated in a microfluidic device for removal of the supporting cumulus cells post-fertilization. Presumptive embryos were assigned at random to three cumulus removal treatments at 48 h post-fertilization: vortexing (3 min), handstripping (with 135-μm-ID stripping pipette), and microfluidics. Blastocyst rates were determined through Day 8 post-fertilization. Rates were analyzed by the GENMOD procedure in SAS (SAS Institute, Inc., Cary, NC, USA), accounting for replicates and treatment. Kinetics of development were also impacted as larger proportions of embryos in the microfluidic group reached the blastocyst stage before embryos of the vortex or hand-stripping treatments. These data suggest that cumulus cell removal in a gentle fashion is associated with enhanced embryonic development in the bovine. Table 1. Comparison of cumulus cell removal techniques on bovine blastocyst rates

Continuous particle separation in a microchannel having asymmetrically arranged multiple branches

A new method for continuous size separation and collection of particles in microfabricated devices, asymmetric pinched flow fractionation (AsPFF), has been proposed and demonstrated. This method improves the separation scheme of pinched flow fractionation (PFF), which utilizes a laminar flow profile inside a microchannel. In this study, multiple branch channels with different channel dimensions were arranged at the end of the pinched segment, so that the flow rate distributions to each branch channel were varied, and a large part of the liquid was forced to go through one branch channel (drain channel). In the proposed channel system, the flow profile inside the microchannel was asymmetrically amplified, enabling the separation of one-order smaller particles compared with PFF. After introducing the method, we examined the effect of the asymmetric amplification by controlling the outlet of the drain channel. Also, a mixture of 1.0 approximately 5.0 microm particles was separated, and erythrocytes were successfully separated from blood. The results indicate that the AsPFF method could be applied to the separation of much smaller-size particles, since more precise separation can be achieved simply by changing the geometries of branch channels.

Pinched flow fractionation: continuous size separation of particles utilizing a laminar flow profile in a pinched microchannel.

A concept of "pinched flow fractionation" for the continuous size separation and analysis of particles in microfabricated devices has been proposed and demonstrated. In this method, particles suspended in liquid were continuously introduced into a microchannel having a pinched segment and were aligned to one sidewall in the pinched segment by another liquid flow without particles. The particles were then separated perpendicularly to the flow direction according to their sizes by the spreading flow profile inside the microchannel. Polymer microbeads were successfully separated, and the effects of the flow rate and channel shapes on the separation performance were examined. Also, separated particles were collected independently by making branches at the end of the pinched segment. Since this method utilizes only the laminar flow profile inside a microchannel, complicated outer field control could be eliminated, which is usually required for other kinds of particle separation methods such as field flow fractionation. Also, this method can be applied both for particle size analysis and for preparation of monodispersed particles, since separation can be rapidly and continuously performed.

STATIC MIXER TO IMPROVE BOUND SOLUTE DIALYSIS (BSD) PERFORMANCE WITH STANDARD DIALYSIS EQUIPMENT

Bound solute dialysis (BSD), as practiced by the Molecular Adsorbents Recycling System (MARS), has shown clinical promise in detoxification of liver failure patients. MARS uses 10% albumin solution in recycle mode (to conserve albumin) with specially designed equipment to effect BSD. Theoretical and experimental analysis has shown that BSD can be effective at 0.1 % albumin, opening the possibility of practicing BSD with standard hospital equipment in single pass mode by metering readily available 25% albumin into the dialysate flow. Since optimal dialysis performance requires well-mixed dialysate, two factors mitigate against direct metering: laminar flow profile in the dialysate and density segregation between the albumin concentrate and the dialysate. We have designed a simple static mixer that can be inserted into the dialysate flow path just prior to the dialyzer. The static mixer accomplishes several goals: (1) it provides a well-mixed dialysate/albumin mix for optimal dialyzer performance; (2) it provides a port for metering albumin into the dialysate; (3) it has minimal pressure drop so that it can be used with standard hospital equipment to provide BSD capability. Photography is used to highlight flow patterns as a function of the number of static mixer elements in both the dialysate stream and dialysate cartridge. Experimental results that quantitate the enhancement in BSD performance as a function of number of static mixer elements will be presented.

Using laminar-flow velocity profiles to locate the wall behind roughness elements

Boundary-layer experiments that use hotwire anemometry often perform least-squares fits of the boundary-layer velocity profile to estimate the position of the wall in the hotwire’s coordinate frame. This approach fails in the wake of roughness elements where the profile is nonlinear at the wall. A modified approach makes least-squares fits only at selected locations outside roughness wakes and estimates the wall location across entire lines using a function generated from these estimates. Comparing these two approaches shows that the first produces incorrect results just behind roughness elements but that the techniques produce identical results farther downstream.

Separation of lipids from blood utilizing ultrasonic standing waves in microfluidic channels.

A method to continuously separate different particle types in a suspension is reported. Acoustic forces in a standing wave field were utilized to discriminate lipid particles from erythrocytes in whole blood. The presented technology proposes a new method of cleaning, i.e. removing lipid emboli from, shed blood recovered during cardiac surgery. Blood contaminated with lipid particles enter a laminar flow micro channel. Erythrocytes and lipid particles suspended in blood plasma are exposed to a half wavelength standing wave field orthogonal to the direction of flow as they pass through the channel. Because of differences in compressibility and density the two particle types move in different directions, the erythrocytes towards the centre of the channel and the lipid particles towards the side walls. The end of the channel is split into three outlet channels conducting the erythrocytes to the centre outlet and the lipid particles to the side outlets due to the laminar flow profile. The separation channel was evaluated in vitro using polyamide spheres suspended in water, showing separation efficiencies approaching 100%. The system was also evaluated on whole blood using tritium labelled lipid particles added to bovine blood. More than 80% of the lipid particles could be removed while approximately 70% of the erythrocytes were collected in one third of the original fluid volume. The study showed that the further reduced micro channel dimensions provided improved performance with respect to; (i) separation efficiency, (ii) actuation voltage, and (iii) volumetric throughput as compared to earlier work.

Precision test apparatus for evaluating the heating pattern of radiofrequency ablation devices

Radiofrequency has established itself as a useful technique for managing cardiac arrhythmias and treating soft tissue tumors. However, despite its pervasive use, many of the biophysical principals needed to fully understand and optimize the radiofrequency ablation technique have not been explored. We have designed a test rig that is useful for studying the heat transfer mechanisms that affect the outcome of radiofrequency ablation devices. Using both solid and liquid phantom materials, which simulate body tissues and blood, the test rig is designed for systematic testing of the effects of predictable flow patterns on the temperature profiles generated within the solid phantom. The test rig consists of a custom built thermistor array, a linear test chamber, and a radiofrequency generator. We calibrate the flow of a liquid phantom material to demonstrate that predictable laminar flow profiles are generated. To demonstrate the performance of the ablation system, we present preliminary data attained using a commercially available cardiac ablation catheter. The advantages of this test system are its flexibility, its reproducibility, its precision, and its low cost. Thus, it is ideally suited for studying a variety of complex ablation problems involving multiple tissues types and complex blood flow geometries.

Numerical Simulation of the Conditioning of Volatile Particles in Laminar Flow Tube Reactors

The conditioning of aerosol particles to a predefined composition and size can be considered as a standard problem in aerosol technology. Quite often aerosols generated by dispersing diluted solutions are conditioned in a subsequent flow reactor.To make the design of such reactors easier, a computer model was developed to simulate the behavior of particles with a volatile component during their passage through the reactor. The model is based on the assumption that part of the surface of the reactor is covered with a layer of the requested activity of the volatile component whose fraction has to be adjusted. The diffusion to or from this surface and the corresponding change of the particle size and composition is calculated for each streamline of the flow on the basis of a laminar flow profile. At the moment data for the system H 2 O/H 2 SO 4 are implemented in the model, but an extension to other systems can easily be done. Circular as well as annular flow cross sections can be taken into account.

Taylor dispersion monitored by electrospray mass spectrometry: a novel approach for studying diffusion in solution

This work describes a novel approach for monitoring analyte diffusion in solution that is based on electrospray ionization mass spectrometry (ESI-MS). A mass spectrometer at the end of a laminar flow tube is used to measure the Taylor dispersion of an initially sharp boundary between two solutions of different analyte concentration. This boundary is dispersed by the laminar flow profile in the tube. However, this effect is diminished by analyte diffusion that continuously changes the radial position, and hence the flow velocity of individual analyte molecules. The steepness of the resulting dispersion profile therefore increases with increasing diffusion coefficient of the analyte. A theoretical framework is developed to adapt the equations governing the dispersion process to the case of mass spectrometric detection. This novel technique is applied to determine the diffusion coefficients of choline and cytochrome c. The measured diffusion coefficients, (11.9 +/- 1.0) x 10(-10) m(2) s(-1) and (1.35 +/- 0.08) x 10(-10) m(2) s(-1), respectively, are in agreement with the results of control experiments where the Taylor dispersion of these two analytes was monitored optically. Due to the inherent selectivity and sensitivity of ESI-MS, it appears that the approach described in this work could become a valuable alternative to existing methods for studying diffusion processes, especially for experiments on multicomponent systems.

Quantification of myocardial blood flow and blood flow reserve in the presence of arterial dispersion: a simulation study.

Myocardial blood flow (MBF) can be quantified using dynamic T1-weighted MRI of diffusible tracers and a mathematical model of underlying vasculature. Quantification of MBF by means of T1- weighted MRI requires knowledge of the arterial input function (AIF). The AIF can be estimated from the left ventricular (LV) cavity. However, dispersion may occur between the LV and the tissue of interest because of the laminar blood flow profiles, branching of venules, and because of stenosis. To evaluate the influence of dispersion on the results of MBF quantification, a simulation study was performed. The dispersion was described as a convolution of the AIF with an exponential residue function. Synthetic tissue and AIF curves were analyzed and the derived parameters fit to the simulated parameters. The results show that an unaccounted dispersion may result in a systematic underestimation of MBF up to approximately 50%. Underestimation increases with increasing dispersion and with increasing MBF. Assuming equal dispersion at rest and during hyperemia, myocardial perfusion reserve (MPR) estimates are also susceptible to underestimation of approximately 20%. An unaccounted dispersion therefore can lead to systematic underestimation of both blood flow and perfusion reserve.

Temperature gradients and flow-meter performance

A quantitative treatment of the influence of radial temperature gradients on flow-meter performance is described for the first time. It is shown that large flow-meter errors can be induced due to temperature gradients in the case of fundamental mode propagation (several percentage error values are possible using typical parameter values for water as medium at low flow values corresponding to laminar parabolic flow profiles). It is also found that decreasing the cylinder radius or ultrasound frequency are effective ways to diminish the influence of temperature gradients on flow-meter performance besides the obvious choice of reducing temperature gradients by thermal insulation of the flow-meter tubes and connecting tubes.

Mechanism of temporal gradients in shear-induced ERK1/2 activation and proliferation in endothelial cells.

The aim of the current study was to investigate the intracellular signaling cascade that leads to temporal gradients in shear (TGS)-induced endothelial cell proliferation, with a focus on the involvement of extracellular signal-regulated kinases 1 and 2 (ERK1/2). With the use of well-defined pulsatile, impulse, step, and ramp laminar flow profiles, we found that TGS (impulse flow and pulsatile flow) induced an enhanced and sustained (>30 min) phosphorylation of ERK1/2 relative to step flow (which contains a step increase in shear followed by steady shear), whereas steady shear (ramp flow) alone downregulated activated ERK1/2. Nitric oxide (NO) was found to mediate both the stimulatory effect of TGS and the inhibitory effect of steady shear on endothelial ERK1/2 phosphorylation. Reactive oxygen species (ROS) were also demonstrated to be associated with TGS-induced ERK1/2 phosphorylation. Both G(q/11) and G(i3) were necessary for the activation of ERK1/2 by TGS. Finally, the TGS-induced endothelial proliferative response was abolished by ERK1/2 inhibition. Our study demonstrated the essential role of G proteins, NO, and ROS in TGS-dependent ERK1/2 activation and proliferative response in vascular endothelial cells.

Force field particle filter, combining ultrasound standing waves and laminar flow

A continuous flow microparticle filter that combines megahertz frequency ultrasonic standing waves and laminar flow is described. The filter has a 0.25 mm, single half wavelength, acoustic pathlength at right angles to the flow. Standing wave radiation pressure on suspended particles drives them towards the centre of the acoustic pathlength. Clarified suspending phase from the region closest to the filter wall is drawn away through a downstream outlet. Experimental tests achieved >1000-fold clearance of 5 μm yeast cells, at a sample flow rate of 6 ml min −1, from which the clarified aliquot is 1 ml min −1. At this flow rate the average residence time in the sound field was <1 s. Latex particles of 25, 9, 5.7, 2.8 and 1.5 μm diameter were also tested. The temperature increase during an operating period >1 h was less than 1 K. The design criteria considered in the fabrication of this high performance device are discussed. A theoretical model of the filter’s efficiency, which considers the action of primary radiation force and the particle distribution across a laminar flow profile is presented here. The model predicts that totally clarified filtrate (i.e. zero suspended particles) may be drawn from the downstream outlet. The system described offers a generic approach to automated filtration in some applications. It is continuous flow thereby solving many of the problems of automation presented by batch filter methods and centrifuges. It could be developed for both larger scale and microfluidic applications.

Taylor dispersion of a solute in a microfluidic channel

The dispersion of a solute, traveling in a laminar-flow microfluidic channel, along the major axis of the channel is described by Taylor dispersion. It is shown that although diffusion of solute along the major axis is often neglected in constructing a governing transport equation, axial dispersion due to the laminar flow profile influences the distribution of solute in the channel. An expression for the effective Taylor dispersion coefficient due to the laminar velocity profile is derived and verified by comparing the predicted dispersion to results from a three-dimensional finite-element representation of the fluid dynamics and solute transport. Since the dispersion coefficient can be several orders of magnitude greater than the molecular diffusion coefficient, axial dispersion in microfluidic channels should not be casually neglected.

Perturbation theory applied to sound propagation in flowing media confined by a cylindrical waveguide.

First-order perturbation theory is employed to examine sound propagation in flowing media confined by a cylindrical waveguide. The use of perturbation theory allows examination of mode phase-speed changes due to any radially dependent flow w(r) as long as the flow magnitude is sufficiently small. The condition to be fulfilled is satisfied in the flow range: 0-0.3 m/s for the specific values of cylinder radius, ultrasound frequency, and sound speed analyzed in the present work [in the general case, however, the condition in Eq. (1) of the present work must be fulfilled]. This freedom of choice, i.e., the possibility to handle any radial flow profile, is used to analyze two flow profile cases: (1) where w(r) is a linear combination of a laminar flow profile and a flat profile corresponding to turbulent flow, and (2) where w(r) is a linear combination of a laminar flow profile and a more realistic logarithmic-dependent turbulent flow profile. In both cases, it is shown that large errors may result in ultrasound flow measurements if several modes are excited by the transmitting transducer, and that a logarithmic flow profile in the turbulent regime leads to somewhat larger measurement errors at high flow values as compared to assuming a simple flat profile in the turbulent regime.