scholarly journals Swimming at small Reynolds number of a planar assembly of spheres in an incompressible viscous fluid with inertia

2017 ◽  
Vol 29 (9) ◽  
pp. 091901 ◽  
Author(s):  
B. U. Felderhof
Keyword(s):  
Reynolds Number ◽  
Viscous Fluid ◽  
Incompressible Viscous Fluid ◽  
Small Reynolds Number

On Kelvin–Stuart vortices in a viscous fluid

2008 ◽  
Vol 366 (1876) ◽  
pp. 2717-2728 ◽  
Author(s):  
L.E Fraenkel
Keyword(s):  
Reynolds Number ◽  
Viscous Fluid ◽  
Small Time ◽  
Navier Stokes ◽  
Initial Condition ◽  
Small Reynolds Number ◽  
The One ◽  
Stuart Vortices ◽  
Reversed Time

When one contemplates the one-parameter family of steady inviscid shear flows discovered by J. T. Stuart in 1967, an obvious thought is that these flows resemble a row of vortices diffusing in a viscous fluid, with the parameter playing the role of a reversed time. In this paper, we ask how close this resemblance is. Accordingly, the paper begins to explore Navier–Stokes solutions having as initial condition the classical, irrotational flow due to a row of point vortices. However, since we seek explicit answers, such exploration seems possible only in two relatively easy cases: that of small time and arbitrary Reynolds number and that of small Reynolds number and arbitrary time.

On the flow past a sphere at low Reynolds number

1969 ◽  
Vol 37 (4) ◽  
pp. 751-760 ◽  
Author(s):  
W. Chester ◽  
D. R. Breach ◽  
Ian Proudman
Keyword(s):  
Reynolds Number ◽  
Viscous Fluid ◽  
Low Reynolds Number ◽  
Incompressible Viscous Fluid ◽  
Euler’S Constant ◽  
Stokes Drag ◽  
Flow Past ◽  
Low Reynolds ◽  
Euler's Constant ◽  
Flow Past A Sphere

The flow of an incompressible, viscous fluid past a sphere is considered for small values of the Reynolds number. In particular the drag is found to be given by \[ D = D_s\{1+{\textstyle\frac{3}{8}}R+{\textstyle\frac{9}{40}}R^2(\log R+\gamma + {\textstyle\frac{5}{3}}\log 2 - {\textstyle\frac{323}{360}})+{\textstyle\frac{27}{80}}R^3\log R+O(R^3)\}, \] where Ds is the Stokes drag, R is the Reynolds number and γ is Euler's constant.

Some Comments on Reynolds Number

1964 ◽  
Vol 86 (3) ◽  
pp. 225-226 ◽  
Author(s):  
L. H. Smith
Keyword(s):  
Reynolds Number ◽  
Viscous Fluid ◽  
Dimensional Analysis ◽  
Flow Parameter ◽  
Incompressible Viscous Fluid ◽  
Physical Variables ◽  
Real Fluids ◽  
Physical Laws ◽  
Real Test

The physical laws that govern fluid motions are examined to gain justification for the grouping of physical variables that we call Reynolds number. First, a perfect incompressible viscous fluid is considered, and it is shown that Reynolds number is the only flow parameter of its kind upon which the performance of a turbomachine can depend. The extent to which Reynolds number loses this uniqueness when real fluids are employed in real test situations is then discussed. The necessity of the use of educated engineering judgment, not furnished by dimensional analysis, is pointed out.

The stability of a viscous fluid between rotating cylinders with an axial flow

1960 ◽  
Vol 9 (4) ◽  
pp. 621-631 ◽  
Author(s):  
R. C. Diprima
Keyword(s):  
Reynolds Number ◽  
Viscous Fluid ◽  
Axial Flow ◽  
Taylor Number ◽  
Small Reynolds Number ◽  
Rotating Cylinders ◽  
The Stability

The stability of a viscous fluid between two concentric rotating cylinders with an axial flow is investigated. It is assumed that the cylinders are rotating in the same direction and that the spacing between the cylinders is small. The critical Taylor number is computed for small Reynolds number associated with the axial flow. It is found that the critical Taylor number increases with increasing Reynolds number.

Creeping flow around a deforming sphere

1972 ◽  
Vol 56 (1) ◽  
pp. 61-71 ◽  
Author(s):  
S. P. Lin ◽  
A. K. Gautesen
Keyword(s):  
Reynolds Number ◽  
Viscous Fluid ◽  
Strouhal Number ◽  
Creeping Flow ◽  
Incompressible Viscous Fluid

The flow of an incompressible viscous fluid past a deforming sphere is studied for small values of the Reynolds number. The deformation is assumed to be radial but is otherwise quite general. The case of S = O(l), where S is the Strouhal number, is investigated in detail. In particular, the drag is obtained up to O(R2 In R), where R is the Reynolds number.

scholarly journals Angular velocity of a sphere in a simple shear at small Reynolds number

2016 ◽  
Vol 1 (8) ◽  
Author(s):  
J. Meibohm ◽  
F. Candelier ◽  
T. Rosén ◽  
J. Einarsson ◽  
F. Lundell ◽  
...  
Keyword(s):  
Reynolds Number ◽  
Angular Velocity ◽  
Simple Shear ◽  
Small Reynolds Number

Small Reynolds Number Electro-Hydrodynamic Flow Around Drops and the Resulting Deformation

1979 ◽  
Vol 46 (3) ◽  
pp. 510-512 ◽  
Author(s):  
M. B. Stewart ◽  
F. A. Morrison
Keyword(s):  
Reynolds Number ◽  
Flow Field ◽  
Order Approximation ◽  
Creeping Flow ◽  
Small Reynolds Number ◽  
Zeroth Order ◽  
Regular Perturbation ◽  
Low Reynolds Number Flow ◽  
Reynolds Number Flow ◽  
Number Flow

Low Reynolds number flow in and about a droplet is generated by an electric field. Because the creeping flow solution is a uniformly valid zeroth-order approximation, a regular perturbation in Reynolds number is used to account for the effects of convective acceleration. The flow field and resulting deformation are predicted.

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