Thermal instability of viscoelastic fluids in porous media

Kim, Min Chan; Lee, Sang Baek; Kim, Sin; Chung, Bum-Jin

doi:10.1016/s0017-9310(03)00363-6

Cited by 143 publications

(108 citation statements)

References 8 publications

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“…Recently, a modified Darcy's law was employed to study the stability of a viscoelastic fluid in a horizontal porous layer using linear and nonlinear stability theory [1][2][3][4][5][6][7][8][9]. Kim et al [1] and Yoon et al [2] performed a linear stability analysis and showed that in viscoelastic fluids, such as polymeric liquids, a Hopf bifurcation, as well as a stationary bifurcation may occur depending on the magnitude of the viscoelastic parameter. From the nonlinear point of view, Kim et al [1] carried out a nonlinear stability analysis by assuming a densely-packed porous layer and found that both stationary and Hopf bifurcations are supercritical relative to the critical heating rate.…”

Section: Introductionmentioning

confidence: 99%

“…Kim et al [1] and Yoon et al [2] performed a linear stability analysis and showed that in viscoelastic fluids, such as polymeric liquids, a Hopf bifurcation, as well as a stationary bifurcation may occur depending on the magnitude of the viscoelastic parameter. From the nonlinear point of view, Kim et al [1] carried out a nonlinear stability analysis by assuming a densely-packed porous layer and found that both stationary and Hopf bifurcations are supercritical relative to the critical heating rate. The question of whether standing or traveling waves are preferred at onset has been fully addressed by Hirata et al [4].…”

Section: Introductionmentioning

confidence: 99%

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Onset of Primary and Secondary Instabilities of Viscoelastic Fluids Saturating a Porous Layer Heated from below by a Constant Flux

Gueye

Ouarzazi

Hirata

et al. 2017

Fluids

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Abstract:We analyze the thermal convection thresholds and linear characteristics of the primary and secondary instabilities for viscoelastic fluids saturating a porous horizontal layer heated from below by a constant flux. The Galerkin method is used to solve the eigenvalue problem by taking into account the elasticity of the fluid, the ratio between the viscosity of the solvent and the total viscosity of the fluid and the lateral confinement of the medium. For the primary instability, we found out that depending on the rheological parameters, two types of convective structures may appear when the basic conductive solution loses its stability: stationary long wavelength instability as for Newtonian fluids and oscillatory convection. The effect of the lateral confinement of the porous medium by adiabatic walls is to stabilize the oblique and longitudinal rolls and therefore selects transverse rolls at the onset of convection. In the range of the rheological parameters where stationary long wave instability develops first, we use a parallel flow approximation to determine analytically the velocity and temperature fields associated with the monocellular convective flow. The linear stability analysis of the monocellular flow is performed, and the critical conditions above which the flow becomes unstable are determined. The combined influence of the viscoelastic parameters and the lateral confinement on the characteristics of the secondary instability is quantified. The major new findings concerning the secondary instabilities may be summarized as follows: (i) For concentrated viscoelastic fluids, computations showed that the most amplified mode of convection corresponds to oscillatory transverse rolls, which appears via a Hopf bifurcation. This pattern selection is independent of both the fluid elasticity and the lateral confinement of the porous medium; (ii) For diluted viscoelastic fluids, the preferred mode of convection is found to be oscillatory transverse rolls for a very laterally-confined medium. Otherwise, stationary or oscillatory longitudinal rolls may develop depending on the fluid elasticity. Results also showed the destabilizing effect of the relaxation fluid elasticity and the stabilizing effect of the viscosity ratio for the onset of both primary and secondary instabilities.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Onset of Primary and Secondary Instabilities of Viscoelastic Fluids Saturating a Porous Layer Heated from below by a Constant Flux

Gueye

Ouarzazi

Hirata

et al. 2017

Fluids

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“…The thermal convective instability in a viscoelastic fluid-saturated porous layer has been studied by several authors in the recent past. Kim et al (2003) has dealt with the thermal instability driven by buoyancy forces in a horizontal porous layer saturated by a viscoelastic fluid. Yoon et al (2004) have followed the formulation of Akhatov and Chembarisova (1993) and sought analytically the onset of thermal convection in an isothermally heated porous layer saturated with viscoelastic fluid.…”

Section: Introductionmentioning

confidence: 99%

Effect of Thermal Modulation on the Onset of Convection in Walters B Viscoelastic Fluid-Saturated Porous Medium

et al. 2010

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The linear stability of Walters B viscoelastic fluid-saturated horizontal porous layer is examined theoretically when the walls of the porous layer are subjected to time-periodic temperature modulation. Three types of boundary temperature modulations are considered namely, symmetric, asymmetric, and only the lower wall temperature is modulated while the upper wall is held at constant temperature. A regular perturbation method based on small amplitude of applied temperature field is used to compute the critical values of Rayleigh number and the corresponding wave number. The shift in critical Rayleigh number is calculated as a function of modulation frequency, viscoelastic parameter, and Prandtl number. The effect of all three types of modulations is found to be destabilizing as compared to the unmodulated system. This result is in contrast to the system with other types of fluids. Besides, the influence of physical parameters on the control of convective instability of the system is discussed.

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“…They question the viability of equation (2.8) to model the filtration of Oldroyd-B fluids, since the predictions of their macroscopic law depart strongly from those of the phenomenological model (2.8). Nevertheless, equation (2.8) continues to be used to model viscoelastic convection phenomena in porous media, with the convective onset properties now well understood (Kim et al 2003). More recent developments include the use of fractional derivative forms of equation (2.8) to model transient stress relationships in generalized Burgers' fluids (Khan & Hayat 2008;Xue et al 2008), and the potential for convective instability in doubly diffusive systems exposed to constant fluid throughflow (Shivakumara & Sureshkumar 2008).…”

Section: Generalized Constitutive Equationmentioning

confidence: 99%

On oscillating flows in randomly heterogeneous porous media

Trefry

McLaughlin

Metcalfe

et al. 2010

Phil. Trans. R. Soc. A.

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The emergence of structure in reactive geofluid systems is of current interest. In geofluid systems, the fluids are supported by a porous medium whose physical and chemical properties may vary in space and time, sometimes sharply, and which may also evolve in reaction with the local fluids. Geofluids may also experience pressure and temperature conditions within the porous medium that drive their momentum relations beyond the normal Darcy regime. Furthermore, natural geofluid systems may experience forcings that are periodic in nature, or at least episodic. The combination of transient forcing, nearcritical fluid dynamics and heterogeneous porous media yields a rich array of emergent geofluid phenomena that are only now beginning to be understood. One of the barriers to forward analysis in these geofluid systems is the problem of data scarcity. It is most often the case that fluid properties are reasonably well known, but that data on porous medium properties are measured with much less precision and spatial density. It is common to seek to perform an estimation of the porous medium properties by an inverse approach, that is, by expressing porous medium properties in terms of observed fluid characteristics. In this paper, we move toward such an inversion for the case of a generalized geofluid momentum equation in the context of time-periodic boundary conditions. We show that the generalized momentum equation results in frequency-domain responses that are governed by a second-order equation which is amenable to numerical solution. A stochastic perturbation approach demonstrates that frequency-domain responses of the fluids migrating in heterogeneous domains have spatial spectral densities that can be expressed in terms of the spectral densities of porous media properties.

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Thermal instability of viscoelastic fluids in porous media

Cited by 143 publications

References 8 publications

Onset of Primary and Secondary Instabilities of Viscoelastic Fluids Saturating a Porous Layer Heated from below by a Constant Flux

Onset of Primary and Secondary Instabilities of Viscoelastic Fluids Saturating a Porous Layer Heated from below by a Constant Flux

Effect of Thermal Modulation on the Onset of Convection in Walters B Viscoelastic Fluid-Saturated Porous Medium

On oscillating flows in randomly heterogeneous porous media

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