Viscous flows: The practical use of theory

White, Frank M.

doi:10.1016/0142-727x(89)90031-3

Cited by 43 publications

(61 citation statements)

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“…The corresponding maximum fluid velocities in the flow and the cell chamber are 8.6 mm min −1 and 1 µm min −1 respectively, for a 8500-fold reduction in maximum fluid velocity. The shear reduction provided by the membrane can be calculated with

τ_{wall} = \frac{6 μ Q}{w h^{2}}

where µ is the fluid viscosity, Q is the volumetric flow rate, and w and h are the channel width and height, respectively [41]. At 1 µL min −1 input flow, the maximum shear stress at the flow chamber side of the membrane is 16.3 ×10 −3 dyn cm −2 (16.3 ×10 −4 Pa), while the maximum shear at the cell chamber floor is 6.7 ×10 −8 dyn cm −2 , yielding a 240,000 fold reduction.…”

Section: Resultsmentioning

confidence: 99%

Highly permeable silicon membranes for shear free chemotaxis and rapid cell labeling

et al. 2014

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Microfluidic systems are powerful tools for cell biology studies because they enable the precise addition and removal of solutes in small volumes. However, the fluid forces inherent in the use of microfluidics for cell cultures are sometimes undesirable. An important example is chemotaxis systems where fluid flow creates well-defined and steady chemotactic gradients but also pushes cells downstream. Here we demonstrate a chemotaxis system in which two chambers are separated by a molecularly thin (15 nm), transparent, and nanoporous silicon membrane. One chamber is a microfluidic channel that carries a flow-generated gradient while the other chamber is a shear-free environment for cell observation. The molecularly thin membranes provide effectively no resistance to molecular diffusion between the two chambers, making them ideal elements for creating flow-free chambers in microfluidic systems. Analytical and computational flow models that account for membrane and chamber geometry, predict shear reduction of more than five orders of magnitude. This prediction is confirmed by observing the pure diffusion of nanoparticles in the cell-hosting chamber despite high input flow (Q = 10 µL min−1; vavg ~45 mm min−1) in the flow chamber only 15 nm away. Using total internal reflection fluorescence (TIRF) microscopy, we show that a flow-generated molecular gradient will pass through the membrane into the quiescent cell chamber. Finally we demonstrate that our device allows us to expose migrating neutrophils to a chemotactic gradient or fluorescent label without any influence from flow.

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τ_{wall} = \frac{6 μ Q}{w h^{2}}

Section: Resultsmentioning

confidence: 99%

Highly permeable silicon membranes for shear free chemotaxis and rapid cell labeling

et al. 2014

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“…13,14 Diffusion lengths can be reduced greatly with turbulent fluid motion, but this requires high flow rates to achieve high Reynolds numbers. 15 The fastest commercially available stop-flow mixing devices use turbulent flow and have dead times of ~0.25 ms (e.g., see BioLogic, Claix, France). Custom-designed turbulent mixers have been used to study protein folding with circular dichroism 16 and small-angle X-ray scattering (SAXS) 17 with dead times on the order of a few hundreds of microseconds and sample mass consumption as high as 8 mg/s.…”

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confidence: 99%

Femtomole Mixer for Microsecond Kinetic Studies of Protein Folding

et al. 2004

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We have developed a microfluidic mixer for studying protein folding and other reactions with a mixing time of 8 μs and sample consumption of femtomoles. This device enables us to access conformational changes under conditions far from equilibrium and at previously inaccessible time scales. In this paper, we discuss the design and optimization of the mixer using modeling of convective diffusion phenomena and a characterization of the mixer performance using microparticle image velocimetry, dye quenching, and Förster resonance energy-transfer (FRET) measurements of single-stranded DNA. We also demonstrate the feasibility of measuring fast protein folding kinetics using FRET with acyl-CoA binding protein.In protein folding, important structural events occur on a microsecond time scale. 1 To study their kinetics, folding reactions must be initiated at even shorter time scales. Photochemical initiation 2 and changes in temperature, 3 pressure, 4,5 or chemical potential, as in salt or chemical denaturant concentration changes, 6-9 all provide the perturbation of protein conformational equilibria necessary to initiate folding. Laser temperature-jump relaxation provides the best temporal resolution with dead times in the nanosecond range, 3 but only a small number of proteins denature reversibly at elevated temperature. Temperature-jump techniques are also limited to conditions near the equilibrium unfolding transition where marginally stable folding intermediates are less likely to accumulate. Pressure relaxation initiates the folding process by exploiting a change in the volume between the folded and unfolded conformers. Pressure changes up to 20 MPa in under 100 μs have been created with piezoelectric devices to monitor rate-limiting barrier crossing in the cold shock protein with Förster resonance energy transfer (FRET). 10 However, in pressure-jump experiments, the folding equilibrium is shifted only marginally at low denaturant concentrations where collapse occurs, and chain collapse is therefore not easily measured via FRET as refolding amplitudes are small. 10-12In comparison to temperature-and pressure-jump relaxation techniques, folding experiments based on changes in chemical potential, via rapid mixing of protein solutions in to and out of chaotrope solvents, are more versatile. The technique is applicable to a wide range of proteins as most unfold reversibly in the presence of chemical denaturants such as urea 7 and guanidine hydrochloride (GdCl). 6 Further, mixer-based experiments are not limited to proteins near the folding transition state. Until recently, the main limitation of mixer-based experiments was

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“…This effect can be explained by the boundary-layer theory of laminar flows, whose stability is related to the shape of the velocity profile, originating the so-called Rayleigh's instability. 34 …”

Section: Kelvin-helmholtz's Criterion (K-h)mentioning

confidence: 97%

Stability analysis of core‐annular flow and neutral stability wave number

Rodriguez

Bannwart

2007

AIChE Journal

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in Wiley InterScience (www.interscience.wiley.com).A general transition criterion is proposed in order to locate the core-annular flow pattern in horizontal and vertical oil-water flows. It is based on a rigorous one-dimensional two-fluid model of liquid-liquid two-phase flow and considers the existence of critical interfacial wave numbers related to a non-negligible interfacial tension term to which the linear stability theory still applies. The viscous laminar-laminar flow problem is fully resolved and turbulence effects on the stability are analyzed through experimentally obtained shape factors. The proposed general transition criterion includes in its formulation the inviscid Kelvin-Helmholtz's discriminator. If a theoretical maximum wavelength is considered as a necessary condition for stability, a stability criterion in terms of the Eo¨tvo¨s number is achieved. Effects of interfacial tension, viscosity ratio, density difference, and shape factors on the stability of core-annular flow are analyzed in detail. The more complete modeling allowed for the analysis of the neutral-stability wave number and the results strongly suggest that the interfacial tension term plays an indispensable role in the correct prediction of the stable region of core-annular flow pattern. The incorporation of a theoretical minimum wavelength into the transition model produced significantly better results. The criterion predictions were compared with recent data from the literature and the agreement is encouraging.

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Viscous flows: The practical use of theory

Cited by 43 publications

References 0 publications

Highly permeable silicon membranes for shear free chemotaxis and rapid cell labeling

Highly permeable silicon membranes for shear free chemotaxis and rapid cell labeling

Femtomole Mixer for Microsecond Kinetic Studies of Protein Folding

Stability analysis of core‐annular flow and neutral stability wave number

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