Velocity Dependence and Tracer Dispersion in Newtonian Fluids Undergoing Creeping Flow

2021 ◽  
Author(s):  
Ibrahim Ayuba ◽  
T. Lateef Akanji ◽  
J. L. Gomes
Keyword(s):  
Fluid Pressure ◽  
Mass Conservation ◽  
Creeping Flow ◽  
Simulation Studies ◽  
Velocity Dependence ◽  
Exact Analytical Solutions ◽  
Varying Thickness ◽  
Tracer Particles ◽  
Tracer Dispersion ◽  
Channel Thickness

Abstract The dynamics of tracer particles in a viscous Newtonian fluid is studied analytically and numerically through channels of varying thickness for fluids undergoing creeping flow. Exact analytical solutions of mass conservation equations of tracer particles including consideration for pressure forces are obtained. Results of the analysis indicates that Stokes velocity is an indispensable parameter and is dependent on parameters such as channel thickness (height), viscosity of the fluid, pressure gradient driven the fluid and Reynolds number corresponding to the channel thickness. The accuracy of the solution obtained is verified by comparing its velocity profiles with those obtained from finite-element-based numerical simulation studies.

scholarly journals Towards an Optimal Pressure Tap Design for Fluid-Flow Characterisation at Microscales

Materials ◽  
2019 ◽  
Vol 12 (7) ◽  
pp. 1086 ◽  
Author(s):  
Tomás Rodrigues ◽  
Francisco Galindo-Rosales ◽  
Laura Campo-Deaño
Keyword(s):  
Pressure Drop ◽  
Soft Lithography ◽  
Rectangular Channel ◽  
Fluid Pressure ◽  
Pressure Sensors ◽  
Optimal Solution ◽  
Channel Length ◽  
Creeping Flow ◽  
Channel Width ◽  
Test Fluid

Measuring fluid pressure in microchannels is difficult and constitutes a challenge to even the most experienced of experimentalists. Currently, to the best of the authors’ knowledge, no optimal solution are being used for the design of pressure taps, nor guidelines concerning their shape and its relation with the accuracy of the readings. In an attempt to address this issue, a parametric study was devised to evaluate the performance of different pressure tap designs, 18 in total. These were obtained by combining three shape parameters: sub-channel width (w) and sub-channel–tap radius (R) or angle (α), while having the sub-channel length kept constant. For each configuration, pressure drop measurements were carried out along several lengths of a straight microfluidic rectangular channel and later compared to an analytical solution. The microchannels were fabricated out of PDMS using standard soft-lithography techniques, pressure drop was measured with differential pressure sensors, the test fluid was DI water and the flow conditions varied from creeping flow up to R e c ∼100. Pressure taps, having smooth contours (characterised by the radius R) and a sub-channel width (w) of 108 μ m , performed the best with results from that of radius R = 50 μ m only falling short of the theory by a mere ∼ 5 % .

Mathematical Model for Condensate Gas Flow in Porous Media with Phase Change

2012 ◽  
Vol 616-618 ◽  
pp. 850-857
Author(s):  
Hua Liu ◽  
Zhi Liang Shi ◽  
Xiang Fang Li ◽  
Yun Cong Gao
Keyword(s):  
Mathematical Model ◽  
Porous Media ◽  
Phase Change ◽  
Gas Flow ◽  
Fluid Pressure ◽  
Mass Conservation ◽  
Dew Point ◽  
Flow In Porous Media ◽  
Set Up ◽  
Energy Equations

The retrograde condensation occurs in the condensate gas reservoir when the formation pressure is under dew point. The condensate appears in the formation with phase change in the process of condensate gas flowing in porous media, which change the temperature field and distribution of fluid pressure and affect flow rules of condensate gas in porous media accordingly. New momentum equations are set up, considering Non-Darcy flow effects, the phase change between condensate gas and condensate, phase velocity and fluid character, based on a simple model of three zones. Surface tension and capillary pressure were introduced into the new model. At the same time energy equations are deduced considering latent heat of vaporization and fluid-solid heat coupling. A mathematical model of multiphase flow in porous media with phase change is set up in this paper combining new momentum equations, new equations of energy with equations of mass conservation.

Longitudinal Dispersion of Tracer Particles in the Blood Flowing in a Pulmonary Alveolar Sheet

1975 ◽  
Vol 42 (3) ◽  
pp. 536-540 ◽  
Author(s):  
Y. C. Fung ◽  
H. T. Tang
Keyword(s):  
Blood Flow ◽  
Cylindrical Tube ◽  
Creeping Flow ◽  
Longitudinal Dispersion ◽  
Porous Layers ◽  
Tracer Particles ◽  
The Mean ◽  
Circular Cylindrical Tube

The analysis of G. I. Taylor on the dispersion of solutes in a circular cylindrical tube is extended to the case of flow in a channel bounded by porous layers. Creeping flow in the channel and the porous layers stimulates the blood flow in the alveolar sheets of the lung. Overall perturbation on the longitudinal dispersion due to the porous layers is evaluated. It is shown that the mean coefficient of apparent diffusivity is smaller in a channel bounded by porous layers than that in a channel with impermeable walls for the case that the channel walls are permeable to solvent but not to tracer. For the case that channel walls are permeable to both solvent and tracer, the mean coefficient of apparent diffusivity is nearly the same as that of a channel with impermeable walls.

scholarly journals Tracer dispersion in bedload transport

2013 ◽  
Vol 37 ◽  
pp. 1-6 ◽  
Author(s):  
E. Lajeunesse ◽  
O. Devauchelle ◽  
M. Houssais ◽  
G. Seizilles
Keyword(s):  
Steady State ◽  
Initial Conditions ◽  
Bedload Transport ◽  
Square Root ◽  
Transitional Regime ◽  
Advection Diffusion ◽  
Tracer Particles ◽  
Tracer Dispersion ◽  
Particle Exchange ◽  
Average Position

Abstract. Bedload particles entrained by rivers tends to disperse as they move downstream. In this paper, we use the erosion-deposition model of Charru et al. (2004) to describe the velocity and the spreading of a plume of tracer particles. We restrict our analysis to steady-state transport above a flat bed of uniform sediment. The transport of tracer particles is then controlled by downstream advection and particle exchange with the immobile bed. After a transitional regime dominated by initial conditions, the evolution of a plume of markers tends asymptotically towards classical advection-diffusion: its average position grows linearly with time, whereas it spreads like the square root of time.

scholarly journals Tracer Dispersion in the Turbulent Convective Layer

2013 ◽  
Vol 70 (12) ◽  
pp. 4112-4121 ◽  
Author(s):  
Alex Skvortsov ◽  
Milan Jamriska ◽  
Timothy C. DuBois
Keyword(s):  
Surface Layer ◽  
Exit Time ◽  
Scaling Law ◽  
Surface Layers ◽  
Obukhov Length ◽  
Tracer Particles ◽  
Tracer Dispersion ◽  
Relative Separation ◽  
Atmospheric Observations ◽  
Convective Layer

Abstract Experimental results for passive tracer dispersion in the turbulent surface layer under convective conditions are presented. In this case, the dispersion of tracer particles is determined by the interplay of two mechanisms: buoyancy and advection. In the atmospheric surface layer under unstable stratification the buoyancy mechanism dominates when the distance from the ground is greater than the Monin–Obukhov length, resulting in a different exponent in the scaling law for relative separation of Lagrangian particles (a deviation from the celebrated Richardson's law). This conclusion is supported by atmospheric observations. Exit-time statistics and a probability density function of concentration increments derived from a previously published experimental dataset demonstrate a noticeable difference between tracer dispersion in the convective and neutrally stratified surface layers.

Lubrication Model of an Artificial Hip Joint: Pressure Profile Versus Inclination Angle of the Acetabular Cup

1999 ◽  
Vol 121 (3) ◽  
pp. 492-498 ◽  
Author(s):  
Donna M. Meyer ◽  
John A. Tichy
Keyword(s):  
Inclination Angle ◽  
Hip Joint ◽  
Hip Prosthesis ◽  
Fluid Pressure ◽  
Vertical Direction ◽  
Mass Conservation ◽  
Acetabular Cup ◽  
Film Rupture ◽  
Artificial Hip Joint ◽  
Artificial Hip

Formulation of a three-dimensional, quasi-static lubrication model of an artificial hip joint is proposed which includes the inclination angle of the acetabular cup. This is performed by deriving a transformed Reynolds equation accounting for this cup tilt angle. The numerical simulation also addresses mass conservation at the location of film rupture. A 3-D spherical representation of the articulating surfaces of the hip prosthesis is mapped onto a cartesian coordinate system of the entire geometry of the “ball and socket” joint. Results include the lubricating fluid pressure distributions for various inclination angles of the acetabular cup demonstrating that the greatest pressures occur for large eccentricities in the upward vertical direction.

Benefits from Computerized Adaptive Testing as Seen in Simulation Studies

1999 ◽  
Vol 15 (2) ◽  
pp. 91-98 ◽  
Author(s):  
Lutz F. Hornke
Keyword(s):  
Measurement Error ◽  
Computerized Adaptive Testing ◽  
Test Procedure ◽  
Adaptive Testing ◽  
Parameter Estimates ◽  
Simulation Studies ◽  
Computerized Adaptive Test ◽  
Item Banks ◽  
Item Parameters ◽  
General Reliability

Summary: Item parameters for several hundreds of items were estimated based on empirical data from several thousands of subjects. The logistic one-parameter (1PL) and two-parameter (2PL) model estimates were evaluated. However, model fit showed that only a subset of items complied sufficiently, so that the remaining ones were assembled in well-fitting item banks. In several simulation studies 5000 simulated responses were generated in accordance with a computerized adaptive test procedure along with person parameters. A general reliability of .80 or a standard error of measurement of .44 was used as a stopping rule to end CAT testing. We also recorded how often each item was used by all simulees. Person-parameter estimates based on CAT correlated higher than .90 with true values simulated. For all 1PL fitting item banks most simulees used more than 20 items but less than 30 items to reach the pre-set level of measurement error. However, testing based on item banks that complied to the 2PL revealed that, on average, only 10 items were sufficient to end testing at the same measurement error level. Both clearly demonstrate the precision and economy of computerized adaptive testing. Empirical evaluations from everyday uses will show whether these trends will hold up in practice. If so, CAT will become possible and reasonable with some 150 well-calibrated 2PL items.

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