Clouds of bubbles in a viscoplastic fluid

2021 ◽  
Vol 927 ◽  
Author(s):  
Emad Chaparian ◽  
Ian A. Frigaard
Keyword(s):  
Yield Stress ◽  
Volume Fraction ◽  
Viscoplastic Fluid ◽  
Algebraic Expression ◽  
Bubble Cloud ◽  
Yield Stress Fluid ◽  
Expression Model ◽  
Critical Yield ◽  
Shed Light ◽  
Key Parameter

Viscoplastic fluids can hold bubbles/particles stationary by balancing the buoyancy stress with the yield stress – the key parameter here is the yield number $Y$ , the ratio of the yield stress to the buoyancy stress. In the present study, we investigate a suspension of bubbles in a yield-stress fluid. More precisely, we compute how much is the gas fraction $\phi$ that could be held trapped in a yield-stress fluid without motion. Here the goal is to shed light on how the bubbles feel their neighbours through the stress field and to compute the critical yield number for a bubble cloud beyond which the flow is suppressed. We perform two-dimensional computations in a full periodic box with randomized positions of the monosized circular bubbles. A large number of configurations are investigated to obtain statistically converged results. We intuitively expect that for higher volume fractions, the critical yield number is larger. Not only here do we establish that this is the case, but also we show that short-range interactions of bubbles increase the critical yield number even more dramatically for bubble clouds. The results show that the critical yield number is a linear function of volume fraction in the dilute regime. An algebraic expression model is given to approximate the critical yield number (semi-empirically) based on the numerical experiment in the studied range of $0\le \phi \le 0.31$ , together with lower and upper estimates.

Yield limit analysis of particle motion in a yield-stress fluid

2017 ◽  
Vol 819 ◽  
pp. 311-351 ◽  
Author(s):  
Emad Chaparian ◽  
Ian A. Frigaard
Keyword(s):  
Yield Stress ◽  
Numerical Study ◽  
Creeping Flow ◽  
Viscoplastic Fluid ◽  
Yield Limit ◽  
Yield Stress Fluid ◽  
Rigid Particles ◽  
Aspect Ratios ◽  
Wide Range ◽  
Critical Yield

A theoretical and numerical study of yield-stress fluid creeping flow about a particle is presented. Yield-stress fluids can hold rigid particles statically buoyant if the yield stress is large enough. In addressing sedimentation of rigid particles in viscoplastic fluids, we should know this critical ‘yield number’ beyond which there is no motion. As we get close to this limit, the role of viscosity becomes negligible in comparison to the plastic contribution in the leading order, since we are approaching the zero-shear-rate limit. Admissible stress fields in this limit can be found by using the characteristics of the governing equations of perfect plasticity (i.e. the sliplines). This approach yields a lower bound of the critical plastic drag force or equivalently the critical yield number. Admissible velocity fields also can be postulated to calculate the upper bound. This analysis methodology is examined for three families of particle shapes (ellipse, rectangle and diamond) over a wide range of aspect ratios. Numerical experiments of either resistance or mobility problems in a viscoplastic fluid validate the predictions of slipline theory and reveal interesting aspects of the flow in the yield limit (e.g. viscoplastic boundary layers). We also investigate in detail the cases of high and low aspect ratio of the particles.

Locomotion over a viscoplastic film

2013 ◽  
Vol 727 ◽  
pp. 1-29 ◽  
Author(s):  
Samuel S. Pegler ◽  
Neil J. Balmforth
Keyword(s):  
Yield Stress ◽  
Travelling Wave ◽  
Constitutive Law ◽  
Viscoplastic Fluid ◽  
Viscous Drag ◽  
Continuum Approximation ◽  
Muscle Fibres ◽  
Main Body ◽  
Terrestrial Gastropods ◽  
Critical Yield

AbstractWe present a modelling study of locomotion over a layer of viscoplastic fluid motivated by the self-propulsion of marine and terrestrial gastropods. Our model comprises a layer of viscoplastic mucus lying beneath a fluid-filled foot that is laced internally by muscular fibres under tension and overlain by the main body of the locomotor, which is assumed to be rigid. The mucus is described using lubrication theory and the Bingham constitutive law, and the foot using a continuum approximation for the action of the muscle fibres. The model is first used to study the retrograde strategy of locomotion employed by marine gastropods, wherein the muscle fibres create a backwards-travelling wave of predominantly normal displacements along the surface of the foot. Once such a retrograde forcing pattern is switched on, the system is shown to converge towards a steady state of locomotion in a frame moving with the wave. The steady speed of locomotion decreases with the yield stress, until it vanishes altogether above a critical yield stress. Despite the absence of locomotion above this threshold, waves still propagate along the foot, peristaltically pumping mucus in the direction of the wave. The model is next used to study the prograde strategy employed by terrestrial gastropods, wherein the muscle fibres create a forwards-travelling wave of predominantly tangential displacements of the foot surface. In this case, a finite yield stress is shown to be necessary for locomotion, with the speed of locomotion initially increasing with the yield stress. Beyond a critical yield stress, localized rigid plugs form across the depth of the mucus layer, adhering parts of the foot to the base. These stop any transport of mucus, but foot motions elsewhere still drive locomotion. As the yield stress is increased further, the rigid plugs widen horizontally, increasing the viscous drag and eventually reducing the speed of locomotion, which is therefore maximized for an intermediate value of the yield stress.

scholarly journals Experimental demonstration of negative refraction with 3D locally resonant acoustic metafluids

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Benoit Tallon ◽  
Artem Kovalenko ◽  
Olivier Poncelet ◽  
Christophe Aristégui ◽  
Olivier Mondain-Monval ◽  
...  
Keyword(s):  
Experimental Data ◽  
Yield Stress ◽  
Multiple Scattering ◽  
Silicone Rubber ◽  
Acoustic Waves ◽  
Scattering Theory ◽  
Negative Refraction ◽  
Volume Fraction ◽  
Experimental Demonstration ◽  
Acoustic Beam

AbstractNegative refraction of acoustic waves is demonstrated through underwater experiments conducted at ultrasonic frequencies on a 3D locally resonant acoustic metafluid made of soft porous silicone-rubber micro-beads suspended in a yield-stress fluid. By measuring the refracted angle of the acoustic beam transmitted through this metafluid shaped as a prism, we determine the acoustic index to water according to Snell’s law. These experimental data are then compared with an excellent agreement to calculations performed in the framework of Multiple Scattering Theory showing that the emergence of negative refraction depends on the volume fraction $$\Phi$$ Φ of the resonant micro-beads. For diluted metafluid ($$\Phi =3\%$$ Φ = 3 % ), only positive refraction occurs whereas negative refraction is demonstrated over a broad frequency band with concentrated metafluid ($$\Phi =17\%$$ Φ = 17 % ).

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