Natural convection in shear‐thinning yield stress fluids in a square enclosure

Magnin

2017

Physics of Fluids

International audienceIn this paper, we propose to explore experimentally the origin of the onset of motion in a well-known Carbopol gel, a concentrated suspension of microgels, when submitted to a vertical temperature gradient, namely, the Rayleigh-Bénard Convection (RBC). We consider three possible scenarios: (i) the gel behaves as an elasto-viscoplastic material, (ii) the gel presents a low-stress viscosity µ + below the yield stress τy , and (iii) the gel can be considered as a two phase system , say the microgels and the solvent, i.e., a porous medium. We propose a complete rheological characterization of Carbopol 940. Creep measurements lead to obtain an instantaneous viscosity plateau µ+ ≈ t ^m with m ≈ 1. For the first time, we measure and provide permeability values k in the Carbopol gels. We show that k = O(10^(14)) m^2 and k ∝ τy^(0.2). Our study focuses on the reference case of the RBC with no-slip conditions at walls, and new results are provided. The results lead to the conclusion that the control parameter is the (inverse) of the yield number Y, ratio between the yield stress and the buoyancy stress, and they show that the critical value is 1/Y c ≈ 80 for no-slip conditions. One shows that both scenarios (i) and (ii) lead to recover 1/Y as the control parameter. By considering the Carbopol gels as porous media [scenario (iii)], one finds that the critical porous Rayleigh-Darcy number is Ra p = O(10^4). Published by AIP Publishing. https://doi

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Origin of the onset of Rayleigh-Bénard convection in a concentrated suspension of microgels with a yield stress behavior

Magnin

2017

Physics of Fluids

“…Contrary to the Rayleigh-Bénard convection heated from below which leads to a subcritical bifurcation [19], [20], when the cavity is heated from a side wall for either the Casson…”

Section: 3heat Transfer (Nusselt Number)mentioning

confidence: 98%

Natural convection of Casson fluid in a square enclosure

Aghighi

Masoumi

2020

MMMS

PurposeThe purpose of this paper is to analyze the natural convection of a yield stress fluid in a square enclosure with differentially heated side walls. In particular, the Casson model is considered which is a commonly used model.Design/methodology/approachThe coupled conservation equations of mass, momentum and energy related to the two-dimensional steady-state natural convection within square enclosures are solved numerically by using the Galerkin's weighted residual finite element method with quadrilateral, eight nodes elements.FindingsResults highlight a small degree of the shear-thinning in the Casson fluids. It is shown that the yield stress has a stabilizing effect since the convection can stop for yield stress fluids while this is not the case for Newtonian fluids. The heat transfer rate, velocity and Yc obtained with the Casson model have the smallest values compared to other viscoplastic models. Results highlight a weak dependence of Yc with the Rayleigh number: Yc∼Ra0.07. A supercritical bifurcation at the transition between the convective and the conductive regimes is found.Originality/valueThe originality of the present study concerns the comprehensive and detailed solutions of the natural convection of Casson fluids in square enclosures with differentially heated side walls. It is shown that there exists a major difference between the cases of Casson and Bingham models, and hence using the Bingham model for analyzing the viscoplastic behavior of the fluids which follow the Casson model (such as blood) may not be accurate. Finally, a correlation is proposed for the mean Nusselt number Nu¯.

“…The Rayleigh-Bénard convection in viscoplastic fluids has been studied by several researchers [12,13,14,15,16,17] in the beginning of this century, however theoretical studies never consider elastic yield stress fluids. This is probably because yield stress fluids are usually modeled by inelastic models such as the Bingham and the Herschel-Bulkley ones.…”

Section: Introductionmentioning

confidence: 99%

Oscillatory Rayleigh–Bénard Convection in elasto-viscoplastic gels

Journal of Non-Newtonian Fluid Mechanics

Brochard

Darbouli

et al. 2020

Self Cite

Rayleigh-Bénard convection (RBC) is studied in an elasto-viscoplastic (EVP) gel, the widely used and studied Carbopol gel. The transition from conductive to convective regime is determined by the Schmidt-Milverton principle which leads to a critical value of the inverse of the Yield number 1/Y c . However, an oscillatory motion in the gel is observed below 1/Y c ≈ 60 when smooth and untreated walls are used. Particles within the gel describe periodical loops close to their initial positions for 16.5 < 1/Y < 25. For larger values of 1/Y ≈ 50 < 1/Y c , loops are still obtained but particles move away progressively from their initial position. The oscillations take the form of periodic traveling waves (TW). We demonstrate that elastic effects play the major role in the occurence of oscillations.