On the advection of spherical and non-spherical particles in a non-uniform flow

1990 ◽  
Vol 333 (1631) ◽  
pp. 289-307 ◽  
Keyword(s):  
Settling Velocity ◽  
Fluid Velocity ◽  
Added Mass ◽  
Laminar Flows ◽  
Chaotic Advection ◽  
Spherical Particles ◽  
Inertial Effects ◽  
Gravitational Settling ◽  
Regular Motion ◽  
Velocity Gradients

Small spherical particles when introduced into a non-uniform or unsteady flow are usually subject to inertial effects, either of the particle mass or of the fluid added-mass, and the gravitational settling. Small non-spherical particles, even when inertial effects are negligible, turn in response to the local fluid velocity gradients and the settling velocity of a particle varies with its orientation. These features are distinct from the response of lagrangian elements which simply move with the local fluid velocity. In this paper these different responses for small, stokesian particles are considered for some example non-uniform laminar flows. It is noted that this added feature may lead to chaotic particle motion where the motion of lagrangian elements is regular, and conversely regular motion where there is chaotic advection of lagrangian elements.

scholarly journals Numerical Analysis of Liquid Mixing in a T-Micromixer with Taylor Dispersion Obstructions

2019 ◽  
Vol 5 (1) ◽  
pp. 147-160
Author(s):  
T. Manoj Dundi ◽  
S. Chandrasekhar ◽  
Shasidar Rampalli ◽  
V. R. K. Raju ◽  
V. P. Chandramohan
Keyword(s):  
Biomedical Engineering ◽  
Flow Direction ◽  
Taylor Dispersion ◽  
Chaotic Advection ◽  
Mixing Enhancement ◽  
Chemical Processing ◽  
Inertial Effects ◽  
Mixing Performance ◽  
Velocity Gradients

Passive micromixers are of great importance in biomedical engineering (lab-on-chips) and chemical processing (microreactors) fields. Various hydrodynamic principles such as lamination, flow separation, and chaotic advection were employed previously to improve mixing in passive mixers. However, mixing enhancement due to velocity gradients in the flow, which is known as the Taylor dispersion effect, has been seldom studied. In the present study, thin rectangular slabs oriented in the flow direction are placed in the mixing channel of a T-micromixer. The thin rectangular slabs are referred to as Taylor Dispersion Obstructions (TDOs) as they are designed to create velocity gradients in the flow. The mixing performance of T-micromixer with and without TDOs is estimated in the Re range of 0 to 350. It is observed that there is no effect on mixing in the presence of TDOs in the low Re (0 < Re < 100), as the velocity gradients created in the flow are considerably small. The vortex formed in the flow for Re of 100 to 220 damped the gradients of velocity created in the flow (due to the presence of TDOs) which resulted in negligible improvement in the quality of mixing. However, considerable enhancement in mixing performance is obtained at high Re (250 to 350) with the presence of TDOs in the mixer. The increase in inertial effects at higher Recreated larger gradients of velocity near the walls of TDOs and mixing channel walls and thereby a significant enhancement in mixing performance is obtained due to Taylor dispersion.

scholarly journals Slurry flow, gravitational settling and a proppant transport model for hydraulic fractures

2014 ◽  
Vol 760 ◽  
pp. 567-590 ◽  
Author(s):  
E. V. Dontsov ◽  
A. P. Peirce
Keyword(s):  
Boundary Layer ◽  
Approximate Solution ◽  
Hydraulic Fracturing ◽  
Transport Model ◽  
Fluid Velocity ◽  
Spherical Particles ◽  
Hydraulic Fractures ◽  
Gravitational Settling ◽  
Proppant Transport ◽  
Two Dimensional Flow

AbstractThe goal of this study is to analyse the steady flow of a Newtonian fluid mixed with spherical particles in a channel for the purpose of modelling proppant transport with gravitational settling in hydraulic fractures. The developments are based on a continuum constitutive model for a slurry, which is approximated by an empirical formula. It is shown that the problem under consideration features a two-dimensional flow and a boundary layer, which effectively introduces slip at the boundary and allows us to describe a transition from Poiseuille flow to Darcy’s law for high proppant concentrations. The expressions for both the outer (i.e. outside the boundary layer) and inner (i.e. within the boundary layer) solutions are obtained in terms of the particle concentration, particle velocity and fluid velocity. Unfortunately, these solutions require the numerical solution of an integral equation, and, as a result, the development of a proppant transport model for hydraulic fracturing based on these results is not practicable. To reduce the complexity of the problem, an approximate solution is introduced. To validate the use of this approximation, the error is estimated for different regimes of flow. The approximate solution is then used to calculate the expressions for the slurry flux and the proppant flux, which are the basis for a model that can be used to account for proppant transport with gravitational settling in a fully coupled hydraulic fracturing simulator.

scholarly journals Settling Velocity of Microplastics Exposed to Wave Action

2021 ◽  
Vol 9 (2) ◽  
pp. 142
Author(s):  
Annalisa De Leo ◽  
Laura Cutroneo ◽  
Damien Sous ◽  
Alessandro Stocchino
Keyword(s):  
Laboratory Experiments ◽  
Settling Velocity ◽  
Transport Model ◽  
Stokes Drift ◽  
Inertial Effects ◽  
Sea Waves ◽  
Heavy Particles ◽  
Analytical Formulation ◽  
Simplified Approach ◽  
Remote Areas

Microplastic (MP) debris is recognized to be one of the most serious threats to marine environments. They are found in all seas and oceanic basins worldwide, even in the most remote areas. This is further proof that the transport of MPs is very efficient. In the present study, we focus our attention on MPs’ transport owing to the Stokes drift generated by sea waves. Recent studies have shown that the interaction between heavy particles and Stokes drift leads to unexpected phenomena mostly related to inertial effects. We perform a series of laboratory experiments with the aim to directly measure MPs’ trajectories under different wave conditions. The main objective is to quantify the inertial effect and, ultimately, suggest a new analytical formulation for the net settling velocity. The latter formula might be implemented in a larger scale transport model in order to account for inertial effects in a simplified approach.

Settling Behavior of Particles in Bubble Containing Newtonian Fluids: Experimental Study and Model Development

2021 ◽  
Author(s):  
Silin Jing ◽  
Xianzhi Song ◽  
Zhaopeng Zhu ◽  
Buwen Yu ◽  
Shiming Duan
Keyword(s):  
Reynolds Number ◽  
Drag Coefficient ◽  
Volume Concentration ◽  
Settling Velocity ◽  
Particle Density ◽  
Particle Diameter ◽  
Newtonian Fluids ◽  
Spherical Particles ◽  
Bubble Volume ◽  
Particle Reynolds Number

Abstract Accurate description of cuttings slippage in the gas-liquid phase is of great significance for wellbore cleaning and the control accuracy of bottom hole pressure during MPD. In this study, the wellbore bubble flow environment was simulated by a constant pressure air pump and the transparent wellbore, and the settling characteristics of spherical particles under different gas volume concentrations were recorded and analyzed by highspeed photography. A total of 225 tests were conducted to analyze the influence of particle diameter (1–12mm), particle density (2700–7860kg/m^3), liquid viscosity and bubble volume concentration on particle settling velocity. Gas drag force is defined to quantitatively evaluate the bubble’s resistance to particle slippage. The relationship between bubble drag coefficient and particle Reynolds number is obtained by fitting the experimental results. An explicit settling velocity equation is established by introducing Archimedes number. This explicit equation with an average relative error of only 8.09% can directly predict the terminal settling velocity of the sphere in bubble containing Newtonian fluids. The models for predicting bubble drag coefficient and the terminal settling velocity are valid with particle Reynolds number ranging from 0.05 to 167 and bubble volume concentration ranging from 3.0% to 20.0%. Besides, a trial-and-error procedure and an illustrative example are presented to show how to calculate bubble drag coefficient and settling velocity in bubble containing fluids. The results of this study will provide the theoretical basis for wellbore cleaning and accurate downhole pressure to further improve the performance of MPD in treating gas influx.

scholarly journals Asymmetrical Induced Charge Electroosmotic Flow on a Herringbone Floating Electrode and Its Application in a Micromixer

Micromachines ◽  
2018 ◽  
Vol 9 (8) ◽  
pp. 391 ◽  
Author(s):  
Qingming Hu ◽  
Jianhua Guo ◽  
Zhongliang Cao ◽  
Hongyuan Jiang
Keyword(s):  
Electrode Surface ◽  
Slip Velocity ◽  
Fluid Velocity ◽  
Laminar Flows ◽  
Fluid Mixing ◽  
Electrode Pair ◽  
Great Opportunity ◽  
Mixing Performance ◽  
Induced Charge ◽  
Floating Electrode

Enhancing mixing is of significant importance in microfluidic devices characterized by laminar flows and low Reynolds numbers. An asymmetrical induced charge electroosmotic (ICEO) vortex pair generated on the herringbone floating electrode can disturb the interface of two-phase fluids and deliver the fluid transversely, which could be exploited to accomplish fluid mixing between two neighbouring fluids in a microscale system. Herein we present a micromixer based on an asymmetrical ICEO flow induced above the herringbone floating electrode array surface. We investigate the average transverse ICEO slip velocity on the Ridge/Vee/herringbone floating electrode and find that the microvortex generated on the herringbone electrode surface has good potential for mixing the miscible liquids in microfluidic systems. In addition, we explore the effect of applied frequencies and bulk conductivity on the slip velocity above the herringbone floating electrode surface. The high dependence of mixing performance on the floating electrode pair numbers is analysed simultaneously. Finally, we investigate systematically voltage intensity, applied frequencies, inlet fluid velocity and liquid conductivity on the mixing performance of the proposed device. The microfluidic micromixer put forward herein offers great opportunity for fluid mixing in the field of micro total analysis systems.

TECHNIQUES TO ENHANCE FLUID MICRO-MIXING AND CHAOTIC MICROMIXERS

2005 ◽  
Vol 19 (28n29) ◽  
pp. 1567-1570 ◽  
Author(s):  
Y. T. CHEW ◽  
H. M. XIA ◽  
C. SHU ◽  
S. Y. M. WAN
Keyword(s):  
Chaotic Advection ◽  
Chaotic Mixing ◽  
Inertial Effects ◽  
Passive Mixer ◽  
Poincaré Plot ◽  
Mixer Design ◽  
Recent Developments ◽  
Fast Development ◽  
Active Mixing ◽  
Working Mechanisms

With fast development of microfluidic systems, fluid micro-mixing becomes a very important issue. In this paper, recent developments on various micromixers and their working mechanisms are reviewed, including the external agitation methods applied in active mixing and the channel geometries adopted in passive mixer design. The chaotic mixing and the influences of Re would be mainly discussed. At moderate and high Re , the fluid inertial effects usually facilitate the chaotic mixing. At low Re , generation of chaotic advection becomes more difficult but can still be achieved through fluid manipulations such as stretching and folding. Chaotic mixers can be characterized using dynamical system techniques, such as Poincaré plot, and Lyapunov exponent.

Closure to “Settling Velocity of Spherical Particles in Calm Water”

1982 ◽  
Vol 108 (12) ◽  
pp. 1548-1549
Author(s):  
Jean L. Boillat ◽  
Walter H. Graf
Keyword(s):  
Settling Velocity ◽  
Spherical Particles ◽  
Calm Water

Settling Velocity of Spherical Particles in Calm Water

1981 ◽  
Vol 107 (10) ◽  
pp. 1123-1131
Author(s):  
Jean L. Boillat ◽  
Walter H. Graf
Keyword(s):  
Settling Velocity ◽  
Spherical Particles ◽  
Calm Water
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