Showing papers on "Shell balance published in 2006"
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TL;DR: In this article, the authors derived the relationship between the ensemble average stress in a dilute suspension of spheres and the imposed rate of strain and rotation for a general linear flow of a suspension in a second-order fluid.
Abstract: The relationship between the ensemble average stress in a dilute suspension of spheres and the imposed rate of strain and rotation is derived for a general linear flow of a suspension in a second-order fluid. In a Newtonian fluid, the particulate phase only contributes to the stress via the shear viscosity; the contribution takes the form of a stresslet, the symmetric first moment of the force distribution on the surface of a suspended particle. In a second-order fluid, the interactions of the particles and polymers contribute to the stress in three ways: (1) the particle-induced fluid velocity disturbance alters the polymer stress in the fluid; (2) the polymer stresses exerted on the particle contribute to the particle’s stresslet; (3) the non-Newtonian nature of the fluid changes the pressure and velocity field, thereby modifying the Newtonian contributions to the particle stresslet. The particle contributions Ψ 1 P and Ψ 2 P to the first and second normal stress differences are related to the corresponding stress differences ( Ψ 1 0 and Ψ 2 0 ) for the suspending fluid by Ψ 1 P = ( 5 / 2 ) ϕ Ψ 1 0 and Ψ 2 P = ( 75 / 28 ) ϕ Ψ 2 0 − ( 5 / 28 ) ϕ Ψ 1 0 , where ϕ is the particle volume fraction.
56 citations
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TL;DR: The Herschel-Bulkley fluid model considered here reduces to the power law model in the absence of yield stress and the results obtained for the flow characteristics reveal many interesting behaviors that warrant further study of the peristaltic transport models with two immiscible physiological fluids.
Abstract: Peristaltic transport of Herschel-Bulkley fluid in contact with a Newtonian fluid in a channel is investigated for its various applications to flows with physiological fluids (blood, chyme, intrauterine fluid, etc.). The primary application is when blood flows through small vessels; blood has a peripheral layer of plasma and a core region of suspension of all the erythrocytes. That is, in the modeling of blood flow, one needs to consider the core region consisting of a yield stress fluid and the peripheral region consisting of a Newtonian fluid. Peristaltic pumping of a yield stress fluid in contact with a Newtonian fluid has not previously been studied in detail. Our goal is to initiate such a study. The Herschel-Bulkley fluid model considered here reduces to the power law model in the absence of yield stress. The stream function, the velocity field, and the equation of the interface are obtained and discussed. When the yield stress TO → 0 and when the index n = 1, our results agree with those of Brasseur et al. (J. Fluid Mech. 174 (1987), 495) for peristaltic transport of the Newtonian fluid. It is observed that for a given flux Q the pressure rise Ap increases with an increase in the amplitude ratio Φ. Furthermore, the results obtained for the flow characteristics reveal many interesting behaviors that warrant further study of the peristaltic transport models with two immiscible physiological fluids.
26 citations
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TL;DR: In this paper, a gravity current originated by a power-law viscous fluid propagating on a horizontal rigid plane below a fluid of lower density is examined, and the set of equations governing the flow is presented, under the assumption of buoyancy-viscous balance and negligible inertial forces.
Abstract: A gravity current originated by a power-law viscous fluid propagating on a horizontal rigid plane below a fluid of lower density is examined. The intruding fluid is considered to have a pure Ostwald power-law constitutive equation. The set of equations governing the flow is presented, under the assumption of buoyancy-viscous balance and negligible inertial forces. The conditions under which the above assumptions are valid are examined and a self-similar solution in terms of a nonlinear ordinary differential equation is derived. For the release of a time-variable volume of fluid, the shape of the gravity current is determined numerically using an approximate analytical solution derived close to the current front as a starting condition. A closed-form analytical expression is derived for the special case of the release of a fixed volume of fluid. The space-time development of the gravity current is discussed for different flow behavior indexes.
24 citations
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TL;DR: In this paper, the dependence of the shear strength of a fluid on the fluid pressure and the bulk fluid temperature, respectively, was studied for given bulk fluid temperatures and fluid pressures in the whole ranges of fluid pressure.
Abstract: Purpose – Seeks to study the dependence of the shear strength of a fluid on the fluid pressure and the bulk fluid temperature, respectively, theoretically for given bulk fluid temperatures and fluid pressures in the whole ranges of fluid pressure and bulk fluid temperature.Design/methodology/approach – The analyses are, respectively, carried out with emphasis on the dependence of the shear strength of a fluid in liquid state, i.e. at low pressures on the fluid pressure and the bulk fluid temperature for given bulk fluid temperatures and fluid pressures based on the theory of the compression of the fluid by the pressurization of the fluid.Findings – The fluid shear strength versus fluid pressure curve in the whole range of fluid pressure and the fluid shear strength versus bulk fluid temperature curve in the whole range of bulk fluid temperature, respectively, for a given bulk fluid temperature and a given fluid pressure are obtained. It is shown by this fluid shear strength versus fluid pressure curve tha...
4 citations
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TL;DR: In this article, the optimum shape of the fluid flow boundaries, which would ensure minimum undesirable phenomena, like "dead water" zones, unsteady fluid flow, etc., is one of the crucial hydraulic engineering's task.
Abstract: Fluid flow in curved channels with various cross-sections, as a common problem in theoretical and applied fluid mechanics, is a very complex and quite undiscovered phenomenon. Defining the optimum shape of the fluid flow boundaries, which would ensure minimum undesirable phenomena, like "dead water" zones, unsteady fluid flow, etc., is one of the crucial hydraulic engineering’s task. Method of kinetic balance is described and used for this purpose, what is illustrated with few examples. .
1 citations