Experimental study of the instability of the viscous flow past a flexible surface

Muralikrishnan, R.; Kumaran, V.

doi:10.1063/1.1427923

Cited by 53 publications

(61 citation statements)

References 21 publications

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“…In the experiments of Kumaran & Muralikrishnan (2000); Muralikrishnan & Kumaran (2002), it was found that as the stress is increased, the viscosity was a constant until a critical stress where the viscosity showed a sudden and dramatic increase. Since the rheometer was operated in the stress-controlled mode, the increase in viscosity was accompanied by a decrease in the strain rate.…”

Section: Low Reynolds Numbermentioning

confidence: 96%

“…Later studies by Chokshi & Kumaran (2008) found that when the neo-Hookean model is used for the solid wall, the transition Reynolds number increases in comparison to that for a linear model. The details of the wall model were not important for the experiments conducted in a rheometer (Kumaran & Muralikrishnan 2000;Muralikrishnan & Kumaran 2002;Eggert & Kumar 2004) because the ratio of gel and fluid thickness was relatively large in those cases (greater than about 4), and the wall constitutive relations do not significantly affect the transition Reynolds number when the wall thickness is much larger than the fluid thickness. Further experiments are required for the case where wall and fluid thicknesses are comparable, in order to examine the effect of wall constitutive relations on the stability.…”

Section: Low Reynolds Numbermentioning

confidence: 98%

“…There do not seem to be experiments which have examined the viscous flow (Re 1) in conduits whose walls are made of a soft material. However, there have been a series of experiments carried out by Kumaran & Muralikrishnan (2000); Muralikrishnan & Kumaran (2002) and Eggert & Kumar (2004) in a commercial rheometer which is used for measuring fluid viscosity. Though this is an open flow, where the fluid is sheared between two parallel plates, the experiments were motivated by theoretical predictions of an instability in channel and tube flows at low Reynolds number (Kumaran et al 1994;Kumaran 1995).…”

Section: Low Reynolds Numbermentioning

confidence: 99%

“…In the experiments of Kumaran & Muralikrishnan (2000); Muralikrishnan & Kumaran (2002) and Eggert & Kumar (2004), the bottom plate was replaced by a soft poly-acrylamide gel. The gel is very nearly incompressible, and the shear modulus of the gel can be made as low as 1000 Pa by adjusting the concentration of the cross-linker during the gelation process.…”

Section: Low Reynolds Numbermentioning

confidence: 99%

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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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Section: Low Reynolds Numbermentioning

confidence: 96%

Section: Low Reynolds Numbermentioning

confidence: 98%

Section: Low Reynolds Numbermentioning

confidence: 99%

Section: Low Reynolds Numbermentioning

confidence: 99%

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Experimental studies on the flow through soft tubes and channels

Kumaran

2015

Sadhana

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“…To simplify the stability analysis, we assume a frequency-independent viscosity to describe dissipative effects in the solid medium. The neutral stability curves obtained from this assumption can be extended to a solid with frequency-dependent viscosity by following an iterative procedure described in Muralikrishnan & Kumaran (2002). A simple single-mode Maxwellian model for the viscoelastic response of the solid has been used in Chokshi & Kumaran (2008).…”

Section: Continuum Models For Solid Deformationmentioning

confidence: 99%

Stability of fluid flow through deformable tubes and channels: An overview

Shankar

2015

Sadhana

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The aim of this paper is to provide a systematic overview of the study of instabilities in flow past deformable solid surfaces, with particular emphasis on internal flows through tubes and channels. The subject is certainly more than five decades old, and arguably began with Kramer's pioneering experiments on drag reduction by compliant surfaces. This was immediately followed by the theoretical studies of Benjamin and Landhal in the early 1960s. Most earlier theoretical studies were focused on stability of external flows such as boundary layers, and used relatively simple wall models composed of spring-backed plates. There has been a resurgence in the field since the mid-1980s, and more attention was focused on internal flows through deformable tubes and channels. The wall deformation was described by both phenomenological spring-backed plate models and continuum linear viscoelastic solid models. All these studies predict several types of instabilities in flow past deformable surfaces. This paper will attempt to place the various theoretical results in perspective, and to classify the instabilities predicted by various studies. Recent studies have also emphasized the importance of using a frame-invariant constitutive model, such as the neo-Hookean model, for the solid deformation. Until recently, however, the field has been dominated by theoretical and numerical studies, with very little experimental observations to corroborate the theoretical predictions. Recent experiments in flow through deformable tubes and channels indeed show instability at Reynolds number much lower than their rigid counterparts, and the experimental observations are in qualitative agreement with some of the theoretical predictions. There have also been a few studies on the non-linear aspects of the instability using the weakly non-linear formulation to determine the nature of the bifurcation at the linear instability. A brief discussion on weakly nonlinear analyses is also provided in this paper.

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Hydrodynamic Stability of Flow Through Compliant Channels and Tubes

Kumaran

2003

Flow Past Highly Compliant Boundaries and in Collapsible Tubes

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Experimental study of the instability of the viscous flow past a flexible surface

Cited by 53 publications

References 21 publications

Experimental studies on the flow through soft tubes and channels

Experimental studies on the flow through soft tubes and channels

Stability of fluid flow through deformable tubes and channels: An overview

Hydrodynamic Stability of Flow Through Compliant Channels and Tubes

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