Study of a Non-Conventional Aeration System

1987 ◽  
Vol 19 (5-6) ◽  
pp. 869-876
Author(s):  
L. Raschid-Sally ◽  
M. Roustan ◽  
H. Roques ◽  
G. M. Faup
Keyword(s):  
Oxygen Transfer ◽  
Peclet Number ◽  
Péclet Number ◽  
Theoretical Approaches ◽  
Aeration System ◽  
Circulation Velocity ◽  
The Mean ◽  
Oxygen Transfer Capacity ◽  
Mean Circulation ◽  
Conventional Systems

A non-conventional aeration system for oxidation ditches using jets has been developed. The principle of this system is based on the separation of the 2 actions: aeration and circulation. It was concluded that the flow of the liquid in the channel can be successfully modelled using various theoretical approaches. The mean circulation velocity VC, the power dissipated P, and the Peclet number Pe are the 3 important parameters governing the circulation. The oxygen transfer capacity of the system has been studied and compares favourably with that of conventional systems. The advantage of such systems over conventional ones has been discussed.

Sedimentation in a dilute polydisperse system of interacting spheres. Part 1. General theory

1982 ◽  
Vol 119 ◽  
pp. 379-408 ◽  
Author(s):  
G. K. Batchelor
Keyword(s):  
Distribution Function ◽  
Brownian Motion ◽  
Peclet Number ◽  
Pair Distribution Function ◽  
Brownian Diffusion ◽  
Mean Velocity ◽  
Péclet Number ◽  
Interparticle Force ◽  
Equal Sphere ◽  
The Mean

Small rigid spherical partials are settling under gravity through Newtonian fluid, and the volume fraction of the particles (ϕ) is small although sufficiently large for the effects of interactions between pairs of particles to be significant. Two neighbouring particles interact both hydrodynamically (with low-Reynolds-number flow about each particle) and through the exertion of a mutual force of molecular or electrical origin which is mainly repulsive; and they also diffuse relatively to each other by Brownian motion. The dispersion contains several species of particle which differ in radius and density.The purpose of the paper is to derive formulae for the mean velocity of the particles of each species correct to order ϕ, that is, with allowance for the effect of pair interactions. The method devised for the calculation of the mean velocity in a monodisperse system (Batchelor 1972) is first generalized to give the mean additional velocity of a particle of species i due to the presence of a particle of species j in terms of the pair mobility functions and the probability distribution pii(r) for the relative position of an i and a j particle. The second step is to determine pij(r) from a differential equation of Fokker-Planck type representing the effects of relative motion of the two particles due to gravity, the interparticle force, and Brownian diffusion. The solution of this equation is investigated for a range of special conditions, including large values of the Péclet number (negligible effect of Brownian motion); small values of the Ptclet number; and extreme values of the ratio of the radii of the two spheres. There are found to be three different limits for pij(r) corresponding to different ways of approaching the state of equal sphere radii, equal sphere densities, and zero Brownian relative diffusivity.Consideration of the effect of relative diffusion on the pair-distribution function shows the existence of an effective interactive force between the two particles and consequently a contribution to the mean velocity of the particles of each species. The direct contributions to the mean velocity of particles of one species due to Brownian diffusion and to the interparticle force are non-zero whenever the pair-distribution function is non-isotropic, that is, at all except large values of the Péclet number.The forms taken by the expression for the mean velocity of the particles of one species in the various cases listed above are examined. Numerical values will be presented in Part 2.

scholarly journals Unsteady feeding and optimal strokes of model ciliates

2013 ◽  
Vol 715 ◽  
pp. 1-31 ◽  
Author(s):  
Sébastien Michelin ◽  
Eric Lauga
Keyword(s):  
Peclet Number ◽  
Feeding Rate ◽  
Diffusion Problem ◽  
Advective Transport ◽  
Péclet Number ◽  
Fixed Energy ◽  
Advection Diffusion ◽  
The Mean ◽  
Micro Organisms ◽  
Time Periodic

AbstractThe flow field created by swimming micro-organisms not only enables their locomotion but also leads to advective transport of nutrients. In this paper we address analytically and computationally the link between unsteady feeding and unsteady swimming on a model micro-organism, the spherical squirmer, actuating the fluid in a time-periodic manner. We start by performing asymptotic calculations at low Péclet number ($\mathit{Pe}$) on the advection–diffusion problem for the nutrients. We show that the mean rate of feeding as well as its fluctuations in time depend only on the swimming modes of the squirmer up to order ${\mathit{Pe}}^{3/ 2} $, even when no swimming occurs on average, while the influence of non-swimming modes comes in only at order ${\mathit{Pe}}^{2} $. We also show that generically we expect a phase delay between feeding and swimming of $1/ 8\mathrm{th} $ of a period. Numerical computations for illustrative strokes at finite $\mathit{Pe}$ confirm quantitatively our analytical results linking swimming and feeding. We finally derive, and use, an adjoint-based optimization algorithm to determine the optimal unsteady strokes maximizing feeding rate for a fixed energy budget. The overall optimal feeder is always the optimal steady swimmer. Within the set of time-periodic strokes, the optimal feeding strokes are found to be equivalent to those optimizing periodic swimming for all values of the Péclet number, and correspond to a regularization of the overall steady optimal.

Approximate analysis of the containment of contaminated sites prior to remediation

2000 ◽  
Vol 42 (1-2) ◽  
pp. 319-324 ◽  
Author(s):  
H. Rubin ◽  
A. Rabideau
Keyword(s):  
Steady State ◽  
Peclet Number ◽  
Dimensionless Parameter ◽  
Contaminated Sites ◽  
Unsteady State ◽  
Péclet Number ◽  
Vertical Barrier ◽  
Time Period ◽  
Barrier Performance ◽  
Vertical Barriers

This study presents an approximate analytical model, which can be useful for the prediction and requirement of vertical barrier efficiencies. A previous study by the authors has indicated that a single dimensionless parameter determines the performance of a vertical barrier. This parameter is termed the barrier Peclet number. The evaluation of barrier performance concerns operation under steady state conditions, as well as estimates of unsteady state conditions and calculation of the time period requires arriving at steady state conditions. This study refers to high values of the barrier Peclet number. The modeling approach refers to the development of several types of boundary layers. Comparisons were made between simulation results of the present study and some analytical and numerical results. These comparisons indicate that the models developed in this study could be useful in the design and prediction of the performance of vertical barriers operating under conditions of high values of the barrier Peclet number.

Convective diffusion toward the sphere in laminar flow around the sphere

1979 ◽  
Vol 44 (4) ◽  
pp. 1218-1238
Author(s):  
Arnošt Kimla ◽  
Jiří Míčka
Keyword(s):  
Laminar Flow ◽  
Velocity Profile ◽  
Peclet Number ◽  
Convective Diffusion ◽  
Péclet Number ◽  
Stability Of The Solution

The problem of convective diffusion toward the sphere in laminar flow around the sphere is solved by combination of the analytical and net methods for the region of Peclet number λ ≥ 1. The problem was also studied for very small values λ. Stability of the solution has been proved in relation to changes of the velocity profile.

Convective diffusion to a slowly rotating spherical electrode; Basic model for Re → O, Pe → ∞

1983 ◽  
Vol 48 (6) ◽  
pp. 1571-1578 ◽  
Author(s):  
Ondřej Wein
Keyword(s):  
Boundary Layer ◽  
Flow Regime ◽  
Peclet Number ◽  
Convective Diffusion ◽  
Creeping Flow ◽  
Péclet Number ◽  
Spherical Electrode ◽  
Basic Model ◽  
Boundary Layer Solution ◽  
Layer Solution

Theory has been formulated of a convective rotating spherical electrode in the creeping flow regime (Re → 0). The currently available boundary layer solution for Pe → ∞ has been confronted with an improved similarity description applicable in the whole range of the Peclet number.

Modeling temperature rise in multi-track reciprocating frictional sliding

2021 ◽  
pp. 135065012098823
Author(s):  
Thierry A Blanchet
Keyword(s):  
Temperature Rise ◽  
Peclet Number ◽  
Maximum Temperature ◽  
Uniform Heat Flux ◽  
Heat Accumulation ◽  
Stroke Length ◽  
Péclet Number ◽  
Maximum Temperature Rise ◽  
Rectangular Patch ◽  
Accumulation Effect

As in various manufacturing processes, in sliding tests with scanning motions to extend the sliding distance over fresh countersurface, temperature rise during any pass is bolstered by heating during prior passes over neighboring tracks, providing a “heat accumulation effect” with persisting temperature rises contributing to an overall temperature rise of the current pass. Conduction modeling is developed for surface temperature rise as a function of numerous inputs: power and size of heat source; speed and stroke length, and track increment of scanning motion; and countersurface thermal properties. Analysis focused on mid-stroke location for passes of a square uniform heat flux sufficiently far into the rectangular patch being scanned from the first pass at its edge that steady heat accumulation effect response is adopted, focusing on maximum temperature rise experienced across the pass' track. The model is non-dimensionalized to broaden the applicability of the output of its runs. Focusing on practical “high” scanning speeds, represented non-dimensionally by Peclet number (in excess of 40), applicability is further broadened by multiplying non-dimensional maximum temperature rise by the square root of Peclet number as model output. Additionally, investigating model runs at various non-dimensional speed (Peclet number) and reciprocation period values, it appears these do not act as independent inputs, but instead with their product (non-dimensional stroke length) as a single independent input. Modified maximum temperature rise output appears to be a function of only two inputs, increasing with decreasing non-dimensional values of stroke length and scanning increment, with outputs of models runs summarized compactly in a simple chart.

scholarly journals Effect of temperature gradient on the cross-stream migration of a surfactant-laden droplet in Poiseuille flow

2017 ◽  
Vol 835 ◽  
pp. 170-216 ◽  
Author(s):  
Sayan Das ◽  
Shubhadeep Mandal ◽  
Suman Chakraborty
Keyword(s):  
Temperature Field ◽  
Temperature Gradient ◽  
Poiseuille Flow ◽  
Peclet Number ◽  
Marangoni Number ◽  
Stream Velocity ◽  
Small Surface ◽  
Péclet Number ◽  
Surfactant Transport ◽  
The Cross

The motion of a viscous droplet in unbounded Poiseuille flow under the combined influence of bulk-insoluble surfactant and linearly varying temperature field aligned in the direction of imposed flow is studied analytically. Neglecting fluid inertia, thermal convection and shape deformation, asymptotic analysis is performed to obtain the velocity of a force-free surfactant-laden droplet. The droplet speed and direction of motion are strongly influenced by the interfacial transport of surfactant, which is governed by surface Péclet number. The present study is focused on the following two limiting situations of surfactant transport: (i) surface-diffusion-dominated surfactant transport considering small surface Péclet number, and (ii) surface-convection-dominated surfactant transport considering high surface Péclet number. Thermocapillary-induced Marangoni stress, the strength of which relative to viscous stress is represented by the thermal Marangoni number, has a strong influence on the distribution of surfactant on the droplet surface. The present study shows that the motion of a surfactant-laden droplet in the combined presence of temperature and imposed Poiseuille flow cannot be obtained by a simple superposition of the following two independent results: migration of a surfactant-free droplet in a temperature gradient, and the motion of a surfactant-laden droplet in a Poiseuille flow. The temperature field not only affects the axial velocity of the droplet, but also has a non-trivial effect on the cross-stream velocity of the droplet in spite of the fact that the temperature gradient is aligned with the Poiseuille flow direction. When the imposed temperature increases in the direction of the Poiseuille flow, the droplet migrates towards the flow centreline. The magnitude of both axial and cross-stream velocity components increases with the thermal Marangoni number. However, when the imposed temperature decreases in the direction of the Poiseuille flow, the magnitude of both axial and cross-stream velocity components may increase or decrease with the thermal Marangoni number. Most interestingly, the droplet moves either towards the flow centreline or away from it. The present study shows a critical value of the thermal Marangoni number beyond which the droplet moves away from the flow centreline which is in sharp contrast to the motion of a surfactant-laden droplet in isothermal flow, for which the droplet always moves towards the flow centreline. Interestingly, we show that the above picture may become significantly altered in the case where the droplet is not a neutrally buoyant one. When the droplet is less dense than the suspending medium, the presence of gravity in the direction of the Poiseuille flow can lead to cross-stream motion of the droplet away from the flow centreline even when the temperature increases in the direction of the Poiseuille flow. These results may bear far-reaching consequences in various emulsification techniques in microfluidic devices, as well as in biomolecule synthesis, vesicle dynamics, single-cell analysis and nanoparticle synthesis.

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