scholarly journals The lift on a small sphere in a slow shear flow

1965 ◽  
Vol 22 (2) ◽  
pp. 385-400 ◽  
Author(s):  
P. G. Saffman
Keyword(s):  
Shear Flow ◽  
Velocity Profile ◽  
Kinematic Viscosity ◽  
Lift Force ◽  
Flow Direction ◽  
Functional Dependence ◽  
Small Sphere ◽  
Translation Velocity ◽  
Parabolic Velocity Profile ◽  
Direction Opposite

It is shown that a sphere moving through a very viscous liquid with velocity V relative to a uniform simple shear, the translation velocity being parallel to the streamlines and measured relative to the streamline through the centre, experiences a lift force 81·2μVa2k½/v½ + smaller terms perpendicular to the flow direction, which acts to deflect the particle towards the streamlines moving in the direction opposite to V. Here, a denotes the radius of the sphere, κ the magnitude of the velocity gradient, and μ and v the viscosity and kinematic viscosity, respectively. The relevance of the result to the observations by Segrée & Silberberg (1962) of small spheres in Poiseuille flow is discussed briefly. Comments are also made about the problem of a sphere in a parabolic velocity profile and the functional dependence of the lift upon the parameters is obtained.

The lift on a small sphere in wall-bounded linear shear flows

1993 ◽  
Vol 246 ◽  
pp. 249-265 ◽  
Author(s):  
John B. McLaughlin
Keyword(s):  
Shear Flow ◽  
Closed Form ◽  
Lift Force ◽  
Closed Form Solution ◽  
Analytical Form ◽  
Form Solution ◽  
Rigid Sphere ◽  
Small Sphere ◽  
Bounded Linear ◽  
Linear Shear

This paper presents a closed-form solution for the inertial lift force acting on a small rigid sphere that translates parallel to a flat wall in a linear shear flow. The results provide connections between results derived by other workers for various limiting cases. An analytical form for the lift force is derived in the limit of large separations. Some new results are presented for the disturbance flow created by a small rigid sphere translating through an unbounded linear shear flow.

scholarly journals Simulation of Flexible Fibre Particle Interaction with a Single Cylinder

Processes ◽  
2021 ◽  
Vol 9 (2) ◽  
pp. 191
Author(s):  
Naser Hamedi ◽  
Lars-Göran Westerberg
Keyword(s):  
Reynolds Number ◽  
Shear Flow ◽  
Fibre Orientation ◽  
Flow Direction ◽  
Particle Interaction ◽  
Orientation Angle ◽  
Factors Affecting ◽  
Single Cylinder ◽  
Flow Past ◽  
Fibre Suspension

In the present study, the flow of a fibre suspension in a channel containing a cylinder was numerically studied for a very low Reynolds number. Further, the model was validated against previous studies by observing the flexible fibres in the shear flow. The model was employed to simulate the rigid, semi-flexible, and fully flexible fibre particle in the flow past a single cylinder. Two different fibre lengths with various flexibilities were applied in the simulations, while the initial orientation angle to the flow direction was changed between 45° ≤ θ ≤ 75°. It was shown that the influence of the fibre orientation was more significant for the larger orientation angle. The results highlighted the influence of several factors affecting the fibre particle in the flow past the cylinder.

scholarly journals Combined electrokinetic and shear flows control colloidal particle distribution across microchannel cross-sections

Soft Matter ◽  
2021 ◽  
Author(s):  
Varun Lochab ◽  
Shaurya Prakash
Keyword(s):  
Shear Flow ◽  
Cross Sections ◽  
Lift Force ◽  
Shear Flows ◽  
Colloidal Particle ◽  
Particle Distribution ◽  
Particle Migration ◽  
Flow Parameters

We quantify and investigate the effects of flow parameters on the extent of colloidal particle migration and the corresponding electrophoresis-induced lift force under combined electrokinetic and shear flow.

A note on the instabilities of a horizontal shear flow with a free surface

2000 ◽  
Vol 406 ◽  
pp. 337-346 ◽  
Author(s):  
L. ENGEVIK
Keyword(s):  
Surface Tension ◽  
Free Surface ◽  
Shear Flow ◽  
Velocity Profile ◽  
Froude Number ◽  
The Other ◽  
Algebraic Equations ◽  
Horizontal Shear ◽  
Analytical Treatment ◽  
Unstable Region

The instabilities of a free surface shear flow are considered, with special emphasis on the shear flow with the velocity profile U* = U*0sech2 (by*). This velocity profile, which is found to model very well the shear flow in the wake of a hydrofoil, has been focused on in previous studies, for instance by Dimas & Triantyfallou who made a purely numerical investigation of this problem, and by Longuet-Higgins who simplified the problem by approximating the velocity profile with a piecewise-linear profile to make it amenable to an analytical treatment. However, none has so far recognized that this problem in fact has a very simple solution which can be found analytically; that is, the stability boundaries, i.e. the boundaries between the stable and the unstable regions in the wavenumber (k)–Froude number (F)-plane, are given by simple algebraic equations in k and F. This applies also when surface tension is included. With no surface tension present there exist two distinct regimes of unstable waves for all values of the Froude number F > 0. If 0 < F [Lt ] 1, then one of the regimes is given by 0 < k < (1 − F2/6), the other by F−2 < k < 9F−2, which is a very extended region on the k-axis. When F [Gt ] 1 there is one small unstable region close to k = 0, i.e. 0 < k < 9/(4F2), the other unstable region being (3/2)1/2F−1 < k < 2 + 27/(8F2). When surface tension is included there may be one, two or even three distinct regimes of unstable modes depending on the value of the Froude number. For small F there is only one instability region, for intermediate values of F there are two regimes of unstable modes, and when F is large enough there are three distinct instability regions.

The heat/mass transfer to a finite strip at small Péclet numbers

1978 ◽  
Vol 86 (1) ◽  
pp. 49-65 ◽  
Author(s):  
R. C. Ackerberg ◽  
R. D. Patel ◽  
S. K. Gupta
Keyword(s):  
Heat Transfer ◽  
Mass Transfer ◽  
Shear Flow ◽  
Sodium Hydroxide Solution ◽  
Flow Direction ◽  
Mathematical Problem ◽  
Limiting Current ◽  
Transfer Rates ◽  
Uniform Shear ◽  
Uniform Shear Flow

The problem of heat transfer (or mass transfer at low transfer rates) to a strip of finite length in a uniform shear flow is considered. For small values of the Péclet number (based on wall shear rate and strip length), diffusion in the flow direction cannot be neglected as in the classical Leveque solution. The mathematical problem is solved by the method of matched asymptotic expansions and expressions for the local and overall dimensionless heat-transfer rate from the strip are found. Experimental data on wall mass-transfer rates in a tube at small Péclet numbers have been obtained by the well-known limiting-current method using potassium ferrocyanide and potassium ferricyanide in sodium hydroxide solution. The Schmidt number is large, so that a uniform shear flow can be assumed near the wall. Experimental results are compared with our theoretical predictions and the work of others, and the agreement is found to be excellent.

Drag Reduction for Blunt Body With Cross Flow by Extremum-Seeking Control

2008 ◽  
Author(s):  
Nobuhiko Kamagata ◽  
Susumu Horio ◽  
Koichi Hishida
Keyword(s):  
Control System ◽  
Drag Reduction ◽  
Shear Layer ◽  
Flow Velocity ◽  
Drag Force ◽  
Lift Force ◽  
Flow Direction ◽  
Extremum Seeking ◽  
Extremum Seeking Control ◽  
Separated Shear Layer

The active flow control, which can adapt to variation of flow velocity and/or direction, is an effective technique to achieve drag reduction. The present study has investigated a separated shear layer and established two control systems; the system reduces drag force and lift force by controlling the separated shear layer to reattachment for variation of flow velocity and /or direction. The adaptive control system to the variation of flow velocity was constructed by using a hot wire anemometer as a sensor to detect flow separation. The system to flow direction was constructed by using pressure transducers as a sensor to estimate drag force and lift force. The extremum-seeking control was introduced as a controller of the both systems. It is indicated from the experimental results that adaptive drag/lift control system to various flow velocity ranging from 3 to 7 m/s and various flow direction ranging from 0 to 30 deg. was established.

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