Radial lift on a suspended finite-sized sphere due to fluid inertia for low-Reynolds-number flow through a cylinder

2013 ◽  
Vol 722 ◽  
pp. 159-186 ◽  
Author(s):  
Sukalyan Bhattacharya ◽  
Dil K. Gurung ◽  
Shahin Navardi
Keyword(s):  
Reynolds Number ◽  
Particle Diameter ◽  
Axial Direction ◽  
Perturbation Scheme ◽  
Fluid Inertia ◽  
Regular Perturbation ◽  
Cross Sectional ◽  
First Order ◽  
Reynolds Number Flow ◽  
Freely Suspended

AbstractThis article describes the radial drift of a suspended sphere in a cylinder-bound Poiseuille flow where the Reynolds number is small but finite. Unlike past studies, it considers a circular narrow conduit whose cross-sectional diameter is only $1. 5$–$6$ times the particle diameter. Thus, the analysis quantifies the effect of fluid inertia on the radial motion of the particle in the channel when the flow field is significantly influenced by the presence of the suspended body. To this end, the hydrodynamic fields are expanded as a series in Reynolds number, and a set of hierarchical equations for different orders of the expansion is derived. Accordingly, the zeroth-order fields in Reynolds number satisfy the Stokes equation, which is accurately solved in the presence of the spherical particle and the cylindrical conduit. Then, recognizing that in narrow vessels Stokesian scattered fields from the sphere decrease exponentially in the axial direction, a simpler regular perturbation scheme is used to quantify the first-order inertial correction to hydrodynamic quantities. Consequently, it is possible to obtain two results. First, the sphere is assumed to follow the axial motion of a freely suspended sphere in a Stokesian condition, and the radial lift force on it due to the presence of fluid inertia is evaluated. Then, the approximate motion is determined for a freely suspended body on which net hydrodynamic force including first-order inertial lift is zero. The results agree well with the available experimental results. Thus, this study along with the measured data would precisely describe particle dynamics inside narrow tubes.

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.

scholarly journals Low Reynolds number flow in a heated tube of varying section

1983 ◽  
Vol 25 (2) ◽  
pp. 244-260 ◽  
Author(s):  
A. R. Bestman
Keyword(s):  
Reynolds Number ◽  
Free Convection ◽  
Asymptotic Series ◽  
Convection Heat Transfer ◽  
Axial Direction ◽  
Reynolds Number Flow ◽  
Free Convection Heat ◽  
Number Flow ◽  
Convection Parameter ◽  
Constricted Tube

AbstractIn this paper we study the effect of forced and free convection heat transfer on flow in an axisymmctric tube whose radius varies slowly in the axial direction. Asymptotic series expansions in terms of a small parameter ∈, which is a measure of the radius variation, are obtained for the velocity components, pressure and temperature on the assumption that the Reynolds number (R) is of order one. The effect of the free convection parameter or Grashof number (G) on the axial velocity, temperature distribution, shear stress and heat flux at the wall are discussed quantitatively for a locally constricted tube.

scholarly journals Asymptotic solution of the low Reynolds-number flow between two co-axial cones of common apex

1984 ◽  
Vol 7 (4) ◽  
pp. 765-784 ◽  
Author(s):  
M. A. Serag-Eldin ◽  
Y. K. Gayed
Keyword(s):  
Reynolds Number ◽  
Stokes Equations ◽  
Asymptotic Series ◽  
Creeping Flow ◽  
Navier Stokes ◽  
Cross Sectional ◽  
Navier Stokes Equations ◽  
Spherical Coordinate ◽  
Flow Solution ◽  
Reynolds Number Flow

The paper is concerned with the axi-symmetrlc, incompressible, steady, laminar and Newtonian flow between two, stationary, conical-boundaries, which exhibit a common apex but may include arbitrary angles. The flow pattern and pressure field are obtained by solving the pertinent Navier-Stokes' equations in the spherical coordinate system. The solution is presented in the form of an asymptotic series, which converges towards the creeping flow solution as a cross-sectional Reynolds-number tends to zero. The first term in the series, namely the creeping flow solution, is given in closed form; whereas, higher order terms contain functions which generally could only be expressed in infinite series form, or else evaluated numerically. Some of the results obtained for converging and diverging flows are displayed and they are demonstrated to be plausible and informative.

Transition From Planar Stratified Flow in Converging Microchannels

2018 ◽  
Author(s):  
Zachary Lamberty ◽  
Minseo Park ◽  
Nelson Macken ◽  
Adam T. Melvin
Keyword(s):  
Reynolds Number ◽  
Soft Lithography ◽  
Annular Flow ◽  
Stratified Flow ◽  
Reynolds Numbers ◽  
Fluid Interface ◽  
Total Flow ◽  
Mixing Processes ◽  
Cross Sectional ◽  
Reynolds Number Flow

Microfluidic applications may involve the control of flows through a series of junctions. For example, flow branching is typically used to deliver specific quantities of fluid to various locations and converging flows are associated with mixing processes. The shape of the fluid interface of the converging flows at and downstream of the flow junction is the focus of this study. In particular, we investigate the transition from planar stratified flow to annular flow. We report results for microchannel configurations which have a main channel and an intersecting (at 90 or 45 degrees) daughter channel. Two 90 degree channels are investigated, one with cross sectional dimensions 129 × 100 um and the other 200 × 100 um. The 45 degree channel dimensions are 161 × 100 um. We compare flows of water over various Reynolds numbers (based on total flow) of 5–400. Flow visualization is achieved using confocal fluorescence microscopy. Flow modules are fabricated using soft lithography techniques and are enclosed by bonding plasma cleaned glass slides to the PDMS module. At lower Reynolds numbers, e.g., < 20, stratified flow is achieved with some curvature at the interface. As the Reynolds number increases, the flow transitions to have large degrees of curvature and eventually into annular flow. This transition is influenced by Reynolds number, flow ratio (daughter/total flow), channel geometry (cross section) and configuration (45 vs. 90 degrees). Flow regime plots are produced for all microchannel configurations. This study should provide insight into intersecting microfluidic flows when the Reynolds number is high enough to produce a non-planar fluid interface at the junction.

The Rayleigh Problem for the Interior of a Torus

1993 ◽  
Vol 115 (4) ◽  
pp. 603-607
Author(s):  
W. J. Rae ◽  
C. J. Ollila
Keyword(s):  
Reynolds Number ◽  
Low Reynolds Number ◽  
Secondary Flows ◽  
Dean Number ◽  
Primary Flow ◽  
Cross Sectional ◽  
Reynolds Number Flow ◽  
Moving Wall ◽  
The Cross ◽  
Low Reynolds

This paper contains a description of the low Reynolds number flow inside a torus which has been set impulsively in motion about its central axis. The moving wall drags with it a primary flow confined to a sheath that grows steadily toward the center of the torus cross section. The primary flow in turn produces centrifugal and Coriolis accelerations which lead to secondary flows in the cross-sectional plane. At very long time the secondary flows subside, and the primary flow approaches a condition of solid-body rotation. The present analysis treats this problem in the thin-torus limit, where the cross-sectional radius is small compared to the toroidal radius, and is restricted to wall velocities small enough to support a low Reynolds-number assumption. At this level of approximation, the flow is characterized by a single dimensionless parameter, analogous to the Dean number.

Long-wavelength peristaltic pumping at low Reynolds number

1975 ◽  
Vol 68 (3) ◽  
pp. 467-476 ◽  
Author(s):  
M. J. Manton
Keyword(s):  
Reynolds Number ◽  
Pressure Gradient ◽  
Low Reynolds Number ◽  
Separated Flow ◽  
Axial Direction ◽  
Reynolds Number Flow ◽  
Peristaltic Pumping ◽  
Mean Pressure ◽  
The Mean ◽  
Low Reynolds

An asymptotic expansion is found for the low Reynolds number flow induced in an axisymmetric tube by long peristaltic waves of arbitrary shape. Expressions are determined for the relationship between the mean pressure gradient and the volume flux, for the mean rate of working by the wall of the tube and for the shear stress a t the wall. A necessary and sufficient condition for the occurrence of trapping (that is, regions of separated flow near the axis of the tube in a reference frame moving at the wave speed) is obtained. It is shown that reflux (that is, a mean flux in the negative axial direction in a layer of fluid adjacent to the wall when the net mean flux is positive) occurs whenever there is an adverse mean pressure gradient, independently of the shape of the wave. A n estimate of the amount of reflux is derived.

Steady symmetric low-Reynolds-number flow past a film-coated cylinder

2012 ◽  
Vol 24 (1) ◽  
pp. 1-24 ◽  
Author(s):  
L. R. BAND ◽  
J. M. OLIVER ◽  
S. L. WATERS ◽  
D. S. RILEY
Keyword(s):  
Reynolds Number ◽  
Film Thickness ◽  
Bulk Flow ◽  
Immiscible Fluid ◽  
Viscous Stress ◽  
First Order ◽  
Reynolds Number Flow ◽  
Flow Past ◽  
Number Flow ◽  
Coated Cylinder

In this study, we examine a steady two-dimensional slow flow past a rigid cylinder coated with a thin layer of immiscible fluid. The Reynolds number for the external bulk flow is assumed small and flow within the film is driven by the action of the bulk fluid’s tangential viscous stress acting at the interface. Using double asymptotic expansions based on the bulk fluid’s Reynolds number and the aspect ratio of the film thickness to the cylinder’s radius, we derive the leading- and first-order equations governing the steady-state film dynamics, and obtain analytical solutions, in terms of the film thickness, for the bulk flow. We solve the governing film equations, finding that solutions feature a drained region. We briefly discuss the influence of the Capillary number and fluid viscosities, and conclude by showing how the presence of the film affects the drag on the film-coated cylinder.

Low Reynolds number flow around and heat transfer from a heated circular cylinder

2010 ◽  
Vol 1 (1-2) ◽  
pp. 15-20 ◽  
Author(s):  
B. Bolló
Keyword(s):  
Reynolds Number ◽  
Circular Cylinder ◽  
Lift Coefficient ◽  
Reynolds Numbers ◽  
Low Reynolds Numbers ◽  
Reynolds Number Flow ◽  
Two Dimensional Flow ◽  
Number Flow ◽  
Low Reynolds ◽  
Increasing Temperature

Abstract The two-dimensional flow around a stationary heated circular cylinder at low Reynolds numbers of 50 < Re < 210 is investigated numerically using the FLUENT commercial software package. The dimensionless vortex shedding frequency (St) reduces with increasing temperature at a given Reynolds number. The effective temperature concept was used and St-Re data were successfully transformed to the St-Reeff curve. Comparisons include root-mean-square values of the lift coefficient and Nusselt number. The results agree well with available data in the literature.

scholarly journals Examination of Construct Validity and Criterion-Related Validity of the German Motor Test in Egyptian Schoolchildren

2021 ◽  
Vol 18 (16) ◽  
pp. 8341
Author(s):  
Osama Abdelkarim ◽  
Julian Fritsch ◽  
Darko Jekauc ◽  
Klaus Bös
Keyword(s):  
Construct Validity ◽  
Physical Fitness ◽  
Large Scale ◽  
Body Height ◽  
Cross Sectional Study ◽  
Latent Factors ◽  
Cross Sectional ◽  
First Order ◽  
Motor Test ◽  
Health Related

Physical fitness is an indicator for children’s public health status. Therefore, the aim of this study was to examine the construct validity and the criterion-related validity of the German motor test (GMT) in Egyptian schoolchildren. A cross-sectional study was conducted with a total of 931 children aged 6 to 11 years (age: 9.1 ± 1.7 years) with 484 (52%) males and 447 (48%) females in grades one to five in Assiut city. The children’s physical fitness data were collected using GMT. GMT is designed to measure five health-related physical fitness components including speed, strength, coordination, endurance, and flexibility of children aged 6 to 18 years. The anthropometric data were collected based on three indicators: body height, body weight, and BMI. A confirmatory factor analysis was conducted with IBM SPSS AMOS 26.0 using full-information maximum likelihood. The results indicated an adequate fit (χ2 = 112.3, df = 20; p < 0.01; CFI = 0.956; RMSEA = 0.07). The χ2-statistic showed significant results, and the values for CFI and RMSEA showed a good fit. All loadings of the manifest variables on the first-order latent factors as well as loadings of the first-order latent factors on the second-order superordinate factor were significant. The results also showed strong construct validity in the components of conditioning abilities and moderate construct validity in the components of coordinative abilities. GMT proved to be a valid method and could be widely used on large-scale studies for health-related fitness monitoring in the Egyptian population.

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