A Model for Steady Laminar Flow through a Deformable Gel-Coated Channel

Yang, Canghu; Grattoni, Carlos A.; Muggeridge, Ann; Zimmerman, Robert W.

doi:10.1006/jcis.2000.6791

Cited by 15 publications

(13 citation statements)

References 13 publications

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“…It was reported that the drag force in a flexible-walled tube is higher than that for a laminar flow for Reynolds numbers as low as 700. However, there has been a subsequent study by Yang et al (2000), using a simulation method developed by Sutterby (1965), which suggested that the higher drag force in Krindel & Silberberg (1979) could be due to a slow convergence of streamlines, rather than a dynamical instability. The low-Reynolds-number instability in the flow past a soft polyacrylamide gel was demonstrated by Kumaran & Muralikrishnan (2000) and Muralikrishnan & Kumaran (2002), and hysteresis and oscillations were also reported by Eggert & Kumar (2004).…”

Section: Introductionmentioning

confidence: 95%

A multifold reduction in the transition Reynolds number, and ultra-fast mixing, in a micro-channel due to a dynamical instability induced by a soft wall

2013

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A dynamical instability is observed in experimental studies on micro-channels of rectangular cross-section with smallest dimension 100 and 160 µm in which one of the walls is made of soft gel. There is a spontaneous transition from an ordered, laminar flow to a chaotic and highly mixed flow state when the Reynolds number increases beyond a critical value. The critical Reynolds number, which decreases as the elasticity modulus of the soft wall is reduced, is as low as 200 for the softest wall used here (in contrast to 1200 for a rigid-walled channel). The instability onset is observed by the breakup of a dye-stream introduced in the centre of the micro-channel, as well as the onset of wall oscillations due to laser scattering from fluorescent beads embedded in the wall of the channel. The mixing time across a channel of width 1.5 mm, measured by dye-stream and outlet conductance experiments, is smaller by a factor of 10 5 than that for a laminar flow. The increased mixing rate comes at very little cost, because the pressure drop (energy requirement to drive the flow) increases continuously and modestly at transition. The deformed shape is reconstructed numerically, and computational fluid dynamics (CFD) simulations are carried out to obtain the pressure gradient and the velocity fields for different flow rates. The pressure difference across the channel predicted by simulations is in agreement with the experiments (within experimental errors) for flow rates where the dye stream is laminar, but the experimental pressure difference is higher than the simulation prediction after dye-stream breakup. A linear stability analysis is carried out using the parallel-flow approximation, in which the wall is modelled as a neo-Hookean elastic solid, and the simulation results for the mean velocity and pressure gradient from the CFD simulations are used as inputs. The stability analysis accurately predicts the Reynolds number (based on flow rate) at which an instability is observed in the dye stream, and it also predicts that the instability first takes place at the downstream converging section of the channel, and not at the upstream diverging section. The stability analysis also indicates that the destabilization is due to the modification of the flow and the local pressure gradient due to the wall deformation; if we assume a parabolic velocity profile with the pressure gradient given by the plane Poiseuille law, the flow is always found to be stable.

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Section: Introductionmentioning

confidence: 95%

A multifold reduction in the transition Reynolds number, and ultra-fast mixing, in a micro-channel due to a dynamical instability induced by a soft wall

2013

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“…They interpreted the parameter (R G |∇p|/2G) as the slope of the gel wall. Though the results were quantitatively reproduced, systematic improvements are possible for the model of Yang et al (2000). Firstly, the authors seem to have considered only normal wall displacements, whereas in reality the gel will experience both tangential and normal displacements due to the shear stress and pressure.…”

Section: High Reynolds Numbermentioning

confidence: 95%

“…A subsequent numerical study (Yang et al 2000) on the flow in a converging tube seems to cast a doubt about the interpretation of the results of Krindel & Silberberg (1979). Yang et al (2000) studied the flow in a converging tube, and found that the flow acceleration due to the convergence of the streamlines could result in a decrease in the ratio (Q/Q 0 ).…”

Section: High Reynolds Numbermentioning

confidence: 95%

“…Yang et al (2000) studied the flow in a converging tube, and found that the flow acceleration due to the convergence of the streamlines could result in a decrease in the ratio (Q/Q 0 ). They also derived a modified expression for the (Q/Q 0 ) which depends on the pressure gradient as well as the shear modulus of the gel.…”

Section: High Reynolds Numbermentioning

confidence: 98%

“…This was interpreted as a decrease in the transition Reynolds number in the flow through a soft tube; the latter being considerably lower than that in the value of 2100 for the flow in a rigid tubes. Subsequently, there have been doubts expressed (Yang et al 2000) whether the decrease in the flow rate is due to an instability of the laminar flow, or whether it could be explained by the convergence of the tube due to the applied pressure gradient. However, there is now a large amount of theoretical and experimental work to establish that the original premise of Lahav et al (1973) and Krindel & Silberberg (1979) is correct, and that the transition in soft tubes and channels could occur at a Reynolds number much lower than that in rigid tubes and channels.…”

Section: Introductionmentioning

confidence: 96%

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Experimental studies on the flow through soft tubes and channels

Kumaran

2015

Sadhana

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Experiments conducted in channels/tubes with height/diameter less than 1 mm with soft walls made of polymer gels show that the transition Reynolds number could be significantly lower than the corresponding value of 1200 for a rigid channel or 2100 for a rigid tube. Experiments conducted with very viscous fluids show that there could be an instability even at zero Reynolds number provided the surface is sufficiently soft. Linear stability studies show that the transition Reynolds number is linearly proportional to the wall shear modulus in the low Reynolds number limit, and it increases as the 1/2 and 3/4 power of the shear modulus for the 'inviscid' and 'wall mode' instabilities at high Reynolds number. While the inviscid instability is similar to that in the flow in a rigid channel, the mechanisms of the viscous and wall mode instabilities are qualitatively different. These involve the transfer of energy from the mean flow to the fluctuations due to the shear work done at the interface. The experimental results for the viscous instability mechanism are in quantitative agreement with theoretical predictions. At high Reynolds number, the instability mechanism has characteristics similar to the wall mode instability. The experimental transition Reynolds number is smaller, by a factor of about 10, than the theoretical prediction for the parabolic flow through rigid tubes and channels. However, if the modification in the tube shape due to the pressure gradient, and the consequent modification in the velocity profile and pressure gradient, are incorporated, there is quantitative agreement between theoretical predictions and experimental results. The transition has important practical consequences, since there is a significant enhancement of mixing after transition.

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