scholarly journals Boundary effects of a nonconcentric semipermeable sphere using Happel and Kuwabara cell models

2021 ◽  
Vol 15 (1) ◽  
Author(s):  
Krishna Prasad Madasu
Keyword(s):  
Drag Force ◽  
Spherical Cavity ◽  
Superposition Principle ◽  
Solid Sphere ◽  
Hydrodynamic Drag ◽  
Coordinate Systems ◽  
Spherical Coordinate ◽  
Good Convergence ◽  
Separation Parameter ◽  
Permeability Parameter

The effect of a closed boundary on the hydrodynamic drag of a nonconcentric semipermeable sphere in an incompressible viscous fluid is investigated. Darcy’s law holds in the permeable region and Stokes flow used inside the spherical cavity. Suitable boundary conditions are used on the surface of a semipermeable sphere and spherical cavity. Two spherical coordinate systems are used to solve the problem. By superposition principle, a general solution is constructed from the solutions based on the semipermeable sphere and spherical cavity. Numerical results for the hydrodynamic drag force exerted on the particle is obtained with good convergence for various values of the relative distance between the centers of the inner sphere and spherical cavity, permeability parameter and the separation parameter. The numerical values of the hydrodynamic drag force generalize the results obtained for an eccentric solid sphere.

Translation and rotation of a porous spheroid in a spheroidal container

2010 ◽  
Vol 88 (9) ◽  
pp. 689-700 ◽  
Author(s):  
E. I. Saad
Keyword(s):  
Drag Force ◽  
Volume Fraction ◽  
Particle Volume Fraction ◽  
Spherical Shape ◽  
Solid Sphere ◽  
Brinkman Equation ◽  
Hydrodynamic Drag ◽  
Particle Volume ◽  
Special Cases ◽  
Spheroidal Surface

The flow problem of an incompressible axisymmetrical quasisteady translation and steady rotation of a porous spheroid in a concentric spheroidal container are studied analytically. The same small departure from a sphere is considered for each spheroidal surface. In the limit of small Reynolds number, the Brinkman equation for the flow inside the porous region and the Stokes equation for the outside region in their stream functions formulations and velocity components, which are proportional to the translational and angular velocities, respectively, are used. Explicit expressions are obtained for both inside and outside flow fields to the first order in a small parameter characterizing the deformation of the spheroidal surface from the spherical shape. The hydrodynamic drag force and couple exerted on the porous spheroid are obtained for the special cases of prolate and oblate spheroids in closed forms. The dependence of the normalized wall-corrected translational and rotational mobilities on permeability for a porous spheroid in an unbounded medium and for a solid spheroid in a cell on the particle volume fraction is discussed numerically and graphically for various values of the deformation parameter. In the limiting cases, the analytical solutions describing the drag force and torque or mobilities for a porous spheroid in the spheroidal vessel reduce to those for a solid sphere and for a porous sphere in a spherical cell.

OUTDOOR TESTS OF A TOWED BOAT MODEL WITH FUEL COMBUSTION IN A BOTTOM CAVITY

2020 ◽  
Author(s):  
S. M. FROLOV ◽  
◽  
S. V. Platonov ◽  
K. A. AVDEEV ◽  
V. S. AKSENOV ◽  
...  
Keyword(s):  
Drag Force ◽  
Direct Contact ◽  
Propulsion System ◽  
Hydrodynamic Drag ◽  
Atmospheric Air ◽  
System A ◽  
Bottom Cavity ◽  
Gas Cavity ◽  
System Power ◽  
Gas Supply

To reduce the hydrodynamic drag force to the movement of the boat, an artificial gas cavity is organized under its bottom. Such a cavity partially insulates the bottom from direct contact with water and provides “gas lubrication” by means of forced supply of atmospheric air or exhaust gases from the main propulsion system. A proper longitudinal and transverse shaping of the gas cavity can significantly (by 20%-30%) reduce the hydrodynamic drag of the boat at low (less than 3%) consumption of the propulsion system power for gas supply.

Lubricating motion of a sphere towards a thin porous slab with Saffman slip condition

2019 ◽  
Vol 867 ◽  
pp. 949-968 ◽  
Author(s):  
Sondes Khabthani ◽  
Antoine Sellier ◽  
François Feuillebois
Keyword(s):  
Slip Length ◽  
Solid Sphere ◽  
Slip Condition ◽  
Darcy Law ◽  
Slab Thickness ◽  
Wide Range ◽  
Sphere Radius ◽  
Permeability Parameter ◽  
Interface Slip ◽  
Range Of Values

Near-contact hydrodynamic interactions between a solid sphere and a plane porous slab are investigated in the framework of lubrication theory. The size of pores in the slab is small compared with the slab thickness so that the Darcy law holds there. The slab is thin: that is, its thickness is small compared with the sphere radius. The considered problem involves a sphere translating above the slab together with a permeation flow across the slab and a uniform pressure below. The pressure is continuous across both slab interfaces and the Saffman slip condition applies on its upper interface. An extended Reynolds-like equation is derived for the pressure in the gap between the sphere and the slab. This equation is solved numerically and the drag force on the sphere is calculated therefrom for a wide range of values of the slab interface slip length and of the permeability parameter $\unicode[STIX]{x1D6FD}=24k^{\ast }R/(e\unicode[STIX]{x1D6FF}^{2})$, where $k^{\ast }$ is the permeability, $e$ is the porous slab thickness, $R$ is the sphere radius and $\unicode[STIX]{x1D6FF}$ is the gap. Moreover, asymptotics expansions for the pressure and drag are derived for high and low $\unicode[STIX]{x1D6FD}$. These expansions, which agree with the numerics, are also handy formulae for practical use. All results match with those of other authors in particular cases. The settling trajectory of a sphere towards a porous slab in a fluid at rest is calculated from these results and, as expected, the time for reaching the slab decays for increasing slab permeability and upper interface slip length.

Slip Length Measurement of Water Flow on Graphite Surface Using Atomic Force Microscope

2014 ◽  
Vol 941-944 ◽  
pp. 1581-1584 ◽  
Author(s):  
Da Yong Li ◽  
Da Lei Jing ◽  
Yun Lu Pan ◽  
Khurshid Ahmad ◽  
Xue Zeng Zhao
Keyword(s):  
Atomic Force Microscope ◽  
Water Flow ◽  
Drag Force ◽  
Silicon Surface ◽  
Slip Length ◽  
Graphite Surface ◽  
Length Measurement ◽  
Hydrodynamic Drag ◽  
Experimental Measurements ◽  
Atomic Force

In this paper, we present experimental measurements of slip length of deionized (DI) water flow on a silicon surface and a graphite surface by using atomic force microscope. The results show that the measured hydrodynamic drag force is higher on silicon surface than that on graphite surface, and a measured slip length about 10 nm is obtained on the later surface.

Axisymmetric Thermal Stresses in a Spherical Shell of Arbitrary Thickness

1957 ◽  
Vol 24 (3) ◽  
pp. 376-380
Author(s):  
E. L. McDowell ◽  
E. Sternberg
Keyword(s):  
Steady State ◽  
Spherical Shell ◽  
Spherical Cavity ◽  
Series Solution ◽  
Thermal Stresses ◽  
Solid Sphere ◽  
Theory Of Elasticity ◽  
Infinite Medium ◽  
Series Solutions ◽  
Arbitrary Thickness

Abstract This paper contains an explicit series solution, exact within the classical theory of elasticity, for the steady-state thermal stresses and displacements induced in a spherical shell by an arbitrary axisymmetric distribution of surface temperatures. The corresponding solutions for a solid sphere and for a spherical cavity in an infinite medium are obtained as limiting cases. The convergence of the series solutions obtained is discussed. Numerical results are presented appropriate to a solid sphere if two hemispherical caps of its boundary are maintained at distinct uniform temperatures.

Sign in / Sign up

Export Citation Format

Share Document