scholarly journals Phoretic self-propulsion at finite Péclet numbers

2014 ◽  
Vol 747 ◽  
pp. 572-604 ◽  
Author(s):  
Sébastien Michelin ◽  
Eric Lauga
Keyword(s):  
Particle Size ◽  
Theoretical Analysis ◽  
Peclet Number ◽  
Chemical Interaction ◽  
Computational Results ◽  
Parallel Study ◽  
Péclet Number ◽  
Interaction Layer ◽  
Small Scales ◽  
The Impact

AbstractPhoretic self-propulsion is a unique example of force- and torque-free motion on small scales. The classical framework describing the flow field around a particle swimming by self-diffusiophoresis neglects the advection of the solute field by the flow and assumes that the chemical interaction layer is thin compared to the particle size. In this paper we quantify and characterize the effect of solute advection on the phoretic swimming of a sphere. We first rigorously derive the regime of validity of the thin-interaction-layer assumption at finite values of the Péclet number (${Pe}$). Under this assumption, we solve computationally the flow around Janus phoretic particles and examine the impact of solute advection on propulsion and the flow created by the particle. We demonstrate that although advection always leads to a decrease of the swimming speed and flow stresslet at high values of the Péclet number, an increase can be obtained at intermediate values of ${Pe}$. This possible enhancement of swimming depends critically on the nature of the chemical interactions between the solute and the surface. We then derive an asymptotic analysis of the problem at small ${Pe}$ which allows us to rationalize our computational results. Our computational and theoretical analysis is accompanied by a parallel study of the influence of reactive effects at the surface of the particle (Damköhler number) on swimming.

Dispersion controlled by permeable surfaces: surface properties and scaling

2016 ◽  
Vol 801 ◽  
pp. 13-42 ◽  
Author(s):  
Bowen Ling ◽  
Alexandre M. Tartakovsky ◽  
Ilenia Battiato
Keyword(s):  
Mass Transport ◽  
Solute Transport ◽  
Surface Properties ◽  
Peclet Number ◽  
Dispersion Coefficient ◽  
Operating Conditions ◽  
Péclet Number ◽  
Porosity And Permeability ◽  
Matrix Porosity ◽  
The Impact

Permeable and porous surfaces are common in natural and engineered systems. Flow and transport above such surfaces are significantly affected by the surface properties, e.g. matrix porosity and permeability. However, the relationship between such properties and macroscopic solute transport is largely unknown. In this work, we focus on mass transport in a two-dimensional channel with permeable porous walls under fully developed laminar flow conditions. By means of perturbation theory and asymptotic analysis, we derive the set of upscaled equations describing mass transport in the coupled channel–porous-matrix system and an analytical expression relating the dispersion coefficient with the properties of the surface, namely porosity and permeability. Our analysis shows that their impact on the dispersion coefficient strongly depends on the magnitude of the Péclet number, i.e. on the interplay between diffusive and advective mass transport. Additionally, we demonstrate different scaling behaviours of the dispersion coefficient for thin or thick porous matrices. Our analysis shows the possibility of controlling the dispersion coefficient, i.e. transverse mixing, by either active (i.e. changing the operating conditions) or passive mechanisms (i.e. controlling matrix effective properties) for a given Péclet number. By elucidating the impact of matrix porosity and permeability on solute transport, our upscaled model lays the foundation for the improved understanding, control and design of microporous coatings with targeted macroscopic transport features.

Impact of Reservoir Permeability on Flowing Sandface Temperatures: Dimensionless Analysis

SPE Journal ◽  
2013 ◽  
Vol 18 (04) ◽  
pp. 685-694 ◽  
Author(s):  
J.F.. F. App ◽  
K.. Yoshioka
Keyword(s):  
Heat Transfer ◽  
Temperature Change ◽  
Expansion Coefficient ◽  
Peclet Number ◽  
Maximum Temperature ◽  
Péclet Number ◽  
Dimensionless Analysis ◽  
Reservoir Permeability ◽  
Layer Flow ◽  
The Impact

Summary Layer flow contributions are increasingly being quantified through the analysis of measured sandface flowing temperatures. It is commonly known that the maximum temperature change is affected by the magnitude of the drawdown and the Joule-Thomson expansion coefficient of the fluid. Another parameter that strongly impacts layer sandface flowing temperatures is the layer permeability. Aside from determining the drawdown, the layer permeability also affects the ratio of heat transfer by convection to conduction within a reservoir. The impact of permeability can be represented by the Péclet number, which is a dimensionless quantity representing the ratio of heat transfer by convection to conduction. The Péclet number is directly proportional to reservoir permeability. Through dimensionless analysis, it will be shown that for a given drawdown (based on a dimensionless Joule-Thomson expansion coefficient JTD) the temperature change diminishes at low Péclet numbers and increases at high Péclet numbers. This implies that for low-permeability reservoirs such as shale gas or tight oil, the temperature changes will be minimal (less than 0.1ºF) despite the large drawdowns in many instances. Dimensionless analysis is performed for both steady-state and transient thermal models. Results from multilayer transient simulations illustrate the ability to identify contrasting permeability layers on the basis of the Péclet number effect.

scholarly journals Particle-size and -density segregation in granular free-surface flows

2015 ◽  
Vol 779 ◽  
pp. 622-668 ◽  
Author(s):  
J. M. N. T. Gray ◽  
C. Ancey
Keyword(s):  
Particle Size ◽  
Steady State ◽  
Parameter Space ◽  
Peclet Number ◽  
Particle Density ◽  
Critical Concentration ◽  
Free Surface Flows ◽  
Size Segregation ◽  
Péclet Number ◽  
Concentration Changes

When a mixture of particles, which differ in both their size and their density, avalanches downslope, the grains can either segregate into layers or remain mixed, dependent on the balance between particle-size and particle-density segregation. In this paper, binary mixture theory is used to generalize models for particle-size segregation to include density differences between the grains. This adds considerable complexity to the theory, since the bulk velocity is compressible and does not uncouple from the evolving concentration fields. For prescribed lateral velocities, a parabolic equation for the segregation is derived which automatically accounts for bulk compressibility. It is similar to theories for particle-size segregation, but has modified segregation and diffusion rates. For zero diffusion, the theory reduces to a quasilinear first-order hyperbolic equation that admits solutions with discontinuous shocks, expansion fans and one-sided semi-shocks. The distance for complete segregation is investigated for different inflow concentrations, particle-size segregation rates and particle-density ratios. There is a significant region of parameter space where the grains do not separate completely, but remain partially mixed at the critical concentration at which size and density segregation are in exact balance. Within this region, a particle may rise or fall dependent on the overall composition. Outside this region of parameter space, either size segregation or density segregation dominates and particles rise or fall dependent on which physical mechanism has the upper hand. Two-dimensional steady-state solutions that include particle diffusion are computed numerically using a standard Galerkin solver. These simulations show that it is possible to define a Péclet number for segregation that accounts for both size and density differences between the grains. When this Péclet number exceeds 10 the simple hyperbolic solutions provide a very useful approximation for the segregation distance and the height of rapid concentration changes in the full diffusive solution. Exact one-dimensional solutions with diffusion are derived for the steady-state far-field concentration.

scholarly journals A closer look: High-resolution pore-scale simulations of solute transport and mixing through porous media columns

2021 ◽  
Author(s):  
Guillem Sole-Mari ◽  
Diogo Bolster ◽  
Daniel Fernandez-Garcia
Keyword(s):  
Grain Size ◽  
Porous Media ◽  
Peclet Number ◽  
Reactive Transport ◽  
Hydrodynamic Dispersion ◽  
Local Concentration ◽  
Péclet Number ◽  
Incomplete Mixing ◽  
Size Variability ◽  
The Impact

Abstract Mixing is pivotal to conservative and reactive transport behaviors in porous media. Methods for investigating mixing processes include mathematical models, laboratory experiments and numerical simulations. The latter have been historically limited by the extreme computational resources needed for solving flow and transport at the microscopic scale within the complex pore structure of a three-dimensional porous medium, while dealing with a sufficiently large domain in order to generate meaningful emergent continuum-scale observables. We present the results of such a set of virtual column experiments, which have been conducted by taking advantage of modern High-Performance Computing infrastructure and Computational Fluid Dynamics software capable of massively parallel simulations. The computational approach has important advantages such as full control over the experimental conditions as well as high spatial and temporal resolution of measurements. We study the roles of Péclet number and grain size variability on emergent conservative and reactive transport behaviors. Hydrodynamic dispersion results agree with the empirical and theoretical literature and link dispersivity to median grain size, while elucidating the impact of grain-size variability on the critical Péclet number. Reactive transport results also indicate that the relative degree of incomplete mixing is related to the granular material's mean hydraulic radius, and not to the median grain size. When compared to a well-known laboratory experiment with similar configuration, less incomplete mixing is observed in our simulations. We offer a partial explanation for this discrepancy, by showing how an apparent non-linear absorbance-concentration relationship may induce laboratory measurement error in the presence of local concentration fluctuations.

scholarly journals MODELING OF PARTICLE SIZE SEGREGATION: CALIBRATION USING THE DISCRETE PARTICLE METHOD

2012 ◽  
Vol 23 (08) ◽  
pp. 1240014 ◽  
Author(s):  
ANTHONY THORNTON ◽  
THOMAS WEINHART ◽  
STEFAN LUDING ◽  
ONNO BOKHOVE
Keyword(s):  
Particle Size ◽  
Peclet Number ◽  
Particle Method ◽  
Size Ratio ◽  
Size Segregation ◽  
Discrete Particle ◽  
Péclet Number ◽  
Particle Properties ◽  
Chute Flow ◽  
Discrete Particle Method

Over the last 25 years a lot of work has been undertaken on constructing continuum models for segregation of particles of different sizes. We focus on one model that is designed to predict segregation and remixing of two differently sized particle species. This model contains two dimensionless parameters: Sr, a measure of the segregation rate, and Dr, a measure of the strength of diffusion. These, in general, depend on both flow and particle properties and one of the weaknesses of the model is that these dependencies are not predicted. They have to be determined by either experiments or simulations. We present steady-state, periodic, chute-flow simulations using the discrete particle method (DPM) for several bi-disperse systems with different size ratios. The aim is to determine one parameter in the continuum model, i.e. the segregation Péclet number (ratio of the segregation rate to diffusion, Sr/Dr) as a function of the particle size ratio. Reasonable agreement is found; but, also measurable discrepancies are reported; mainly, in the simulations a thick pure phase of large particles is formed at the top of the flow. Additionally, it was found that the Péclet number increases linearly with the size ratio for low values, but saturates to a value of approximately 7.7.

scholarly journals Cu and Cu-SWCNT Nanoparticles’ Suspension in Pulsatile Casson Fluid Flow via Darcy–Forchheimer Porous Channel with Compliant Walls: A Prospective Model for Blood Flow in Stenosed Arteries

2021 ◽  
Vol 22 (12) ◽  
pp. 6494
Author(s):  
Amjad Ali ◽  
Zainab Bukhari ◽  
Muhammad Umar ◽  
Muhammad Ali Ismail ◽  
Zaheer Abbas
Keyword(s):  
Reynolds Number ◽  
Blood Flow ◽  
Fluid Flow ◽  
Peclet Number ◽  
Casson Fluid ◽  
Porous Channel ◽  
Péclet Number ◽  
Compliant Walls ◽  
The Impact ◽  
Prospective Model

The use of experimental relations to approximate the efficient thermophysical properties of a nanofluid (NF) with Cu nanoparticles (NPs) and hybrid nanofluid (HNF) with Cu-SWCNT NPs and subsequently model the two-dimensional pulsatile Casson fluid flow under the impact of the magnetic field and thermal radiation is a novelty of the current study. Heat and mass transfer analysis of the pulsatile flow of non-Newtonian Casson HNF via a Darcy–Forchheimer porous channel with compliant walls is presented. Such a problem offers a prospective model to study the blood flow via stenosed arteries. A finite-difference flow solver is used to numerically solve the system obtained using the vorticity stream function formulation on the time-dependent governing equations. The behavior of Cu-based NF and Cu-SWCNT-based HNF on the wall shear stress (WSS), velocity, temperature, and concentration profiles are analyzed graphically. The influence of the Casson parameter, radiation parameter, Hartmann number, Darcy number, Soret number, Reynolds number, Strouhal number, and Peclet number on the flow profiles are analyzed. Furthermore, the influence of the flow parameters on the non-dimensional numbers such as the skin friction coefficient, Nusselt number, and Sherwood number is also discussed. These quantities escalate as the Reynolds number is enhanced and reduce by escalating the porosity parameter. The Peclet number shows a high impact on the microorganism’s density in a blood NF. The HNF has been shown to have superior thermal properties to the traditional one. These results could help in devising hydraulic treatments for blood flow in highly stenosed arteries, biomechanical system design, and industrial plants in which flow pulsation is essential.

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