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

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.

Section: Discussionmentioning

confidence: 52%

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

Shankar

2015

“…Due to this, it was considered infeasible to practically realise the high Reynolds number instability at a Reynolds number lower than that for transition in a rigid tube/channel. Due to this, the results of Verma & Kumaran (2012) for the flow through a soft tube, and Verma & Kumaran (2013) for a channel flow discussed a little later, were surprising.…”

Section: High Reynolds Numbermentioning

confidence: 98%

“…Experiments on transition in a microchannel have been recently carried out (Verma & Kumaran 2013). The microchannels are made of PDMS gel, in which three walls are made of hard gel with shear modulus 0.5 MPa, while the shear modulus of the fourth wall is decreased by decreasing the concentration of cross-linker while preparing the gel.…”

Section: High Reynolds Numbermentioning

confidence: 99%

Experimental studies on the flow through soft tubes and channels

Kumaran

2015

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.

“…It has been now well established, by a series of theoretical and experimental studies, that such elastohydrodynamic coupling induces new fluid-solid interfacial instabilities both at zero and finite Reynolds number which are qualitatively very different from those present in flow past rigid surfaces (Kumaran 2000;Verma & Kumaran 2013). All these studies illustrated that the presence of deformable fluid-solid interface renders flow unstable at Reynolds number which is much lower than that observed in case of flow past rigid surfaces.…”

Section: Introductionmentioning

confidence: 99%

Manipulation of interfacial instabilities by using a soft, deformable solid layer

Gaurav

Shankar

2015

Multilayer flows are oftensusceptible to interfacial instabilities caused due to jump in viscosity/elasticity across thefluid-fluid interface. It is frequently required to manipulate and control these interfacial instabilities in various applications such as coating processes or polymer coextrusion. We demonstrate here the possibility of using a deformable solid coating to control such interfacial instabilities for various flow configurations and for different fluid rheological behaviors. In particular, we show complete suppression of interfacial flow instabilities by making the walls sufficiently deformable when the configuration was otherwise unstable for the case of flow past a rigid surface. While these interfacial instabilities could be suppressed in certain parameter regimes, it is also possible to enhance the flow instabilities by tuning the shear modulus of the deformable solid coating for other ranges of parameters.