Shell balance

About: Shell balance is a research topic. Over the lifetime, 154 publications have been published within this topic receiving 3691 citations.

Peristaltic transport of a Herschel-Bulkley fluid in contact with a Newtonian fluid

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.

Dynamics of a cylindrical shell system coupled by viscous fluid

Abstract: This study was motivated by the need to design the thermal shield in reactor internals and other system components to avoid detrimental flow‐induced vibrations. The system component is modeled as two coaxial shells separated by a viscous fluid. In the analysis, Flugge’s shell equations of motion and linearized Navier–Stokes equation for viscous fluid are employed. First, a traveling‐wave‐type solution is taken for shells and fluid. Then, from the interface conditions between the shells and fluid, the solution for the fluid medium is expressed in terms of shell displacements. Finally, using the shell equations of motion gives the frequency equation, from which the natural frequency, mode shape, and modal damping ratio of coupled modes can be calculated. The analytical results show a fairly good qualitative agreement with the published experimental data. With the presented analysis and results, the frequency and damping characteristics can be analyzed and design parameters can be related to frequency and damping.

Cause of Bimodal Distribution in the Shape of a Terrestrial Gastropod

Abstract: The distribution of a phenotypic state is often discontinuous and dispersed. An example of such a distribution can be found in the shell shapes of terrestrial gastropods, which exhibit a bimodal distribution whereby species possess either a tall shell or a flat shell. Here we propose a simple model to test the hypothesis that the bimodal distribution relates to the optimum shape for shell balance on the substrates. This model calculates the theoretical shell balance by moment and obtains empirical distribution of shell shape by compiling published data and performing a new analysis. The solution of the model supports one part of the hypothesis, showing that a low-spired shell is the best balanced and is better suited for locomotion on horizontal surface. Additionally, the model shows that both high- and low-spired shells are well balanced and suited on vertical surfaces. The shell with a spire index (shell height divided by diameter) of 1.4 is the least well balanced as a whole. Thus, spire index is expected to show a bimodal distribution with a valley at 1.4. This expectation was supported by empirical distribution of a spire index, suggesting that the bimodality of shell shape in terrestrial gastropods is related to shell balance.

Viscous Spreading of Non-Newtonian Gravity Currents on a Plane

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.

3D flow of a generalized Oldroyd-B fluid induced by a constant pressure gradient between two side walls perpendicular to a plate

Abstract: This paper deals with the 3D flow of a generalized Oldroyd-B fluid due to a constant pressure gradient between two side walls perpendicular to a plate. The fractional calculus approach is used to establish the constitutive relationship of the non-Newtonian fluid model. Exact analytic solutions for the velocity and stress fields, in terms of the Fox H-function, are established by means of the finite Fourier sine transform and the Laplace transform. Solutions similar to those for ordinary Oldroyd-B fluid as well as those for Maxwell and second-grade fluids are also obtained as limiting cases of the results presented. Furthermore, 3D figures for velocity and shear stress fields are presented for the first time for certain values of the parameters, and the associated transport characteristics are analyzed and discussed.