Galerkin representations and fundamental solutions for an axisymmetric microstretch fluid flow

2009 ◽  
Vol 619 ◽  
pp. 277-293 ◽  
Author(s):  
H. H. SHERIEF ◽  
M. S. FALTAS ◽  
E. A. ASHMAWY
Keyword(s):  
Fluid Flow ◽  
Rigid Body ◽  
Fundamental Solutions ◽  
Reciprocal Theorem ◽  
Rigid Sphere ◽  
Microstretch Fluid ◽  
Point Body

The method of associated matrices is used to obtain Galerkin type representations. Fundamental solutions are then obtained for the cases of a point body couple and a point microstretch force. A formula for calculating the total couple acting on a rigid body rotating axi-symmetrically in a microstretch fluid is deduced. A generalized reciprocal theorem is deduced. An application for a rigid sphere rotating in a microstretch fluid is discussed. The results of the application are represented graphically.

Fundamental solutions for axi-symmetric translational motion of a microstretch fluid

2012 ◽  
Vol 28 (3) ◽  
pp. 605-611 ◽  
Author(s):  
H. H. Sherief ◽  
M. S. Faltas ◽  
E. A. Ashmawy
Keyword(s):  
Translational Motion ◽  
Fundamental Solutions ◽  
Microstretch Fluid

Characteristics of Fluid Flow Between Single Rigid Body and Wall of Small-Diameter Tube

2007 ◽  
Author(s):  
Daichi Ishii ◽  
Kohei Aratake ◽  
Tatsuya Otsuka ◽  
Masatsugu Yoshizawa
Keyword(s):  
Boundary Layer ◽  
Fluid Flow ◽  
Rigid Body ◽  
Constant Velocity ◽  
Multibody System ◽  
Small Diameter ◽  
Flow Characteristics ◽  
The Body ◽  
Narrow Tube ◽  
Drive Effect

A multibody system that moves with fluid inside a small-diameter tube is applied to some parts of industry such as a PIG and it is also expected to be developed for future engineering applications. As a first step to considering a multibody system, this study focused on elucidating the flow characteristics around a single rigid body and understanding the effect of a bypass hole. The model considered has been a single rigid body moving at a constant velocity in a narrow tube. Assuming that the flow is steady axisymmetric laminar flow, the fluid flow around the body has been experimentally observed and numerically analyzed. A Rankine’s combined vortex was observed around the body and it was also observed that a layer of fluid near the top wall has characteristics of the boundary layer. Furthermore, a minimum allowable thickness of a bypass hole to cause the successful front-drive effect was obtained.

scholarly journals On the Necessary Conditions for Non-Equivalent Solutions of the Rotlet-Induced Stokes Flow in a Sphere: Towards a Minimal Model for Fluid Flow in the Kupffer’s Vesicle

Mathematics ◽  
2019 ◽  
Vol 8 (1) ◽  
pp. 1
Author(s):  
Yunay Hernández-Pereira ◽  
Adán O. Guerrero ◽  
Juan Manuel Rendón-Mancha ◽  
Idan Tuval
Keyword(s):  
Fluid Flow ◽  
Symmetry Breaking ◽  
Stokes Problem ◽  
Superposition Principle ◽  
Vortical Flow ◽  
Biophysical Model ◽  
Rigid Sphere ◽  
Kupffer’S Vesicle ◽  
Kupffer's Vesicle ◽  
General Conditions

The emergence of left–right (LR) asymmetry in vertebrates is a prime example of a highly conserved fundamental process in developmental biology. Details of how symmetry breaking is established in different organisms are, however, still not fully understood. In the zebrafish (Danio rerio), it is known that a cilia-mediated vortical flow exists within its LR organizer, the so-called Kupffer’s vesicle (KV), and that it is directly involved in early LR determination. However, the flow exhibits spatio-temporal complexity; moreover, its conversion to asymmetric development has proved difficult to resolve despite a number of recent experimental advances and numerical efforts. In this paper, we provide further theoretical insight into the essence of flow generation by putting together a minimal biophysical model which reduces to a set of singular solutions satisfying the imposed boundary conditions; one that is informed by our current understanding of the fluid flow in the KV, that satisfies the requirements for left–right symmetry breaking, but which is also amenable to extensive parametric analysis. Our work is a step forward in this direction. By finding the general conditions for the solution to the fluid mechanics of a singular rotlet within a rigid sphere, we have enlarged the set of available solutions in a way that can be easily extended to more complex configurations. These general conditions define a suitable set for which to apply the superposition principle to the linear Stokes problem and, hence, by which to construct a continuous set of solutions that correspond to spherically constrained vortical flows generated by arbitrarily displaced infinitesimal rotations around any three-dimensional axis.

A numerical study on unsteady natural/mixed convection in a cavity with fixed and moving rigid bodies using the ISPH method

2018 ◽  
Vol 28 (3) ◽  
pp. 684-703 ◽  
Author(s):  
Minh Tuan Nguyen ◽  
Abdelraheem M. Aly ◽  
Sang-Wook Lee
Keyword(s):  
Heat Transfer ◽  
Fluid Flow ◽  
Circular Cylinder ◽  
Boundary Conditions ◽  
Mixed Convection ◽  
Rigid Body ◽  
Transfer Rate ◽  
Rigid Bodies ◽  
Content Type ◽  
Free Falling

Purpose This paper aims to conduct numerical simulations of unsteady natural/mixed convection in a cavity with fixed and moving rigid bodies and different boundary conditions using the incompressible smoothed particle hydrodynamics (ISPH) method. Design/methodology/approach In the ISPH method, the pressure evaluation is stabilized by including both of divergence of velocity and density invariance in solving pressure Poisson equation. The authors prevented the particles anisotropic distributions by using the shifting technique. Findings The proposed ISPH method exhibited good performance in natural/mixed convection in a cavity with fixed, moving and free-falling rigid body. In natural convection, the authors investigated the effects of an inner sloshing baffle as well as fixed and moving circular cylinders on the heat transfer and fluid flow. The heated baffle has higher effects on the heat transfer rate compared to a cooled baffle. In the mixed convection, a free-falling circular cylinder over a free surface cavity and heat transfer in the presence of a circular cylinder in a lid-driven cavity are simulated. Fixed or moving rigid body in a cavity results in considerable effects on the heat transfer rate and fluid flow. Originality/value The authors conducted numerical simulations of unsteady natural/mixed convection in a cavity with fixed and moving rigid bodies and different boundary conditions using the ISPH method.

scholarly journals Elastohydrodynamics of wet bristles, carpets and brushes

2011 ◽  
Vol 467 (2130) ◽  
pp. 1665-1685 ◽  
Author(s):  
A. Gopinath ◽  
L. Mahadevan
Keyword(s):  
Field Theory ◽  
Fluid Flow ◽  
Effective Field Theory ◽  
Effective Field ◽  
Squeeze Flow ◽  
Rigid Sphere ◽  
Bed Deformation ◽  
Elastic Filaments ◽  
Natural Settings ◽  
Shearing Motion

Surfaces covered by bristles, hairs, polymers and other filamentous structures arise in a variety of natural settings in science such as the active lining of many biological organs, e.g. lungs, reproductive tracts, etc., and have increasingly begun to be used in technological applications. We derive an effective field theory for the elastohydrodynamics of ordered brushes and disordered carpets that are made of a large number of elastic filaments grafted on to a substrate and interspersed in a fluid. Our formulation for the elastohydrodynamic response of these materials leads naturally to a set of constitutive equations coupling bed deformation to fluid flow, accounts for the anisotropic properties of the medium, and generalizes the theory of poroelasticity to these systems. We use the effective medium equations to study three canonical problems—the normal settling of a rigid sphere onto a carpet, the squeeze flow in a carpet and the tangential shearing motion of a rigid sphere over the carpet, all problems of relevance in mechanosensation in biology with implications for biomimetic devices.

Integral Equations for a Three-Dimensional Crack in an Infinite, Fluid-Filled, Poroelastic Solid With Zero Permeability in One Direction

1996 ◽  
Vol 63 (1) ◽  
pp. 62-68 ◽  
Author(s):  
Michio Kurashige ◽  
R. J. Clifton
Keyword(s):  
Integral Equations ◽  
Oil Recovery ◽  
Crack Opening ◽  
Fluid Pressure ◽  
Three Dimensional ◽  
Fundamental Solutions ◽  
Injection Rate ◽  
Water Flooding ◽  
Reciprocal Theorem ◽  
Hydraulic Fractures

Fundamental solutions for an instantaneous point force and an instantaneous fluid point source are derived for an infinite, fluid-saturated, poroelastic solid with zero permeability in one direction. Applying these solutions and Cleary’s reciprocal theorem to the three-dimensional problem of a pressurized plane crack yields two integral equations, which relate normal tractions and fluid pressure on the crack faces to crack opening and fluid injection rate per unit fracture area. An important application of these equations is the prediction of hydraulic fractures induced during water-flooding of reservoirs to enhance gas and oil recovery. Zero permeability in one direction may be a good approximation for the case in which the reservoir is sandwiched between two impermeable rock layers.

On Fundamental Solutions and Green’s Functions in the Theory of Elastic Plates

1966 ◽  
Vol 33 (1) ◽  
pp. 31-38 ◽  
Author(s):  
A. Kalnins
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Bessel Functions ◽  
Arbitrary Point ◽  
Fundamental Solutions ◽  
Addition Theorem ◽  
Reciprocal Theorem ◽  
Elastic Plates ◽  
Concentrated Load ◽  
The Reciprocal Theorem

This paper is concerned with fundamental solutions of static and dynamic linear inextensional theories of thin elastic plates. It is shown that the appropriate conditions which a fundamental singularity must satisfy at the pole follow from the requirement that the reciprocal theorem is satisfied everywhere in the region occupied by the plate. Furthermore, dynamic Green’s function for a plate bounded by two concentric circular boundaries is derived by means of the addition theorem of Bessel functions. The derived Green’s function represents the response of the plate to a harmonically oscillating normal concentrated load situated at an arbitrary point on the plate.

scholarly journals Soft-lubrication interactions between a rigid sphere and an elastic wall

2021 ◽  
Vol 933 ◽  
Author(s):  
Vincent Bertin ◽  
Yacine Amarouchene ◽  
Elie Raphaël ◽  
Thomas Salez
Keyword(s):  
Stress Field ◽  
Viscous Fluid ◽  
Thin Layers ◽  
Reciprocal Theorem ◽  
Rigid Sphere ◽  
Hydrodynamic Stress ◽  
Soft Surface ◽  
Elastic Wall ◽  
Elastic Substrates ◽  
Small Deformations

The motion of an object within a viscous fluid and in the vicinity of a soft surface induces a hydrodynamic stress field that deforms the latter, thus modifying the boundary conditions of the flow. This results in elastohydrodynamic interactions experienced by the particle. Here, we derive a soft-lubrication model, in order to compute all the forces and torque applied on a rigid sphere that is free to translate and rotate near an elastic wall. We focus on the limit of small deformations of the surface with respect to the fluid-gap thickness, and perform a perturbation analysis in dimensionless compliance. The response is computed in the framework of linear elasticity, for planar elastic substrates in the limiting cases of thick and thin layers. The EHD forces are also obtained analytically using the Lorentz reciprocal theorem.

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