Low Peclet Number Heat and Mass Transfer from a Drop in an Electric Field

1979 ◽  
Vol 101 (3) ◽  
pp. 484-488 ◽  
Author(s):  
S. K. Griffiths ◽  
F. A. Morrison
Keyword(s):  
Mass Transfer ◽  
Electric Field ◽  
Exact Solutions ◽  
Heat And Mass Transfer ◽  
Digital Computer ◽  
Peclet Number ◽  
Perturbation Expansion ◽  
Regular Perturbation ◽  
Péclet Number

An electric field, when applied to a dielectric drop suspended in another such fluid, generates a circulating motion. The low Peclet number transport from the drop is investigated analytically using a regular perturbation expansion. A digital computer is used to obtain exact solutions to the resulting equations. These solutions yield accurate results up to a Peclet number of at least 60.

Heat/Mass Transfer to a Drop Translating in a Perpendicular Electric Field

2015 ◽  
Author(s):  
Mohamed R. Abdelaal ◽  
Omar A. Huzayyin ◽  
Milind A. Jog
Keyword(s):  
Mass Transfer ◽  
Electric Field ◽  
Mass Transport ◽  
Time Scale ◽  
Peclet Number ◽  
Heat Mass Transfer ◽  
Surface Velocity ◽  
Dielectric Fluid ◽  
Péclet Number ◽  
Transport Enhancement

Enhancement of heat or mass transport in a spherical drop of a dielectric fluid translating in another dielectric fluid in the presence of uniform electric field is investigated. The internal problem or the limit of the majority of the transport resistance being in the dispersed phase is considered. The transient energy conservation equation is solved using a fully implicit finite volume method. In the literature, there is a plenty of studies that had been carried out when the electric field acts in the same plane of translation. In this paper, considering creeping flow regime, numerical computations have been conducted when the electric field acts perpendicular to the plane at which translation acts. As such the flow is no longer a two dimensional flow as a third component velocity comes to picture. At the first glance, thoughts of transport enhancement come to mind on the presence of a third velocity component that might promote mixing and consequently enhance transport effectiveness. Results are expressed in terms of the Nusselt number. Nusselt numbers are plotted in terms of Peclet number, Fourier number and the parameter L which is defined as the ratio of the maximum electric-field-induced surface velocity to translation-induced surface velocity. The code was validated by comparing, results for Peclet numbers of 500 and 1000 to corresponding cases available in literature. Results showed good agreement with previous results. A 3-D grid of 20×40×60 has been considered to cover the computational domain. A grid independence study has been carried out by doubling the whole grid. Results show acceptable results compromising accuracy and code running time. The effect of electric field is expressed in terms of parameter L. For low Peclet numbers (Pe ≤ 250), the application of electric field perpendicular to the plane at which translation acts leads to enhancement of heat/mass transport compared to that in pure translation. Such enhancement is about the same when the electric field and translation act in the same plane. On the other hand, for moderate Peclet numbers (Pe= 250∼1000), the transport enhancement is significant when compared to the enhancement obtained by an electric field acts in the same plane of action of translation as well as pure translation. These results can be understood by comparing time scales for diffusion and convection. When Peclet number is low the convection time scale is very large and hence mixing is not that effective in promoting heat / mass transfer. Whereas for moderate Peclet number, when the convection time scale gets smaller, heat/mass transfer is considerably enhanced compared to low Peclet numbers.

Forced Heat and Mass Transfer From a Slightly Deformed Sphere at Small but Finite Peclet Numbers in Stokes Flow

2013 ◽  
Vol 135 (8) ◽  
Author(s):  
Zhi-Gang Feng
Keyword(s):  
Mass Transfer ◽  
Nusselt Number ◽  
Singular Perturbation ◽  
Perturbation Method ◽  
Heat And Mass Transfer ◽  
Stokes Flow ◽  
Peclet Number ◽  
Fundamental Problem ◽  
Singular Perturbation Method ◽  
Péclet Number

The fundamental problem of heat and mass transfer from a slightly deformed sphere at low but finite Peclet numbers in Stokes flow is solved by a combined regular and singular perturbation method. The deformed sphere is assumed to be axisymmetric and its shape is described by a power series in a small parameter; the correction to the Nusselt number due to the deformation of the sphere is obtained through a regular perturbation with respect to this parameter. On the contrary, the correction to the Nusselt number due to the small Peclet number is derived by applying a singular perturbation method. The analytical solution is derived for the averaged Nusselt number in terms of the Peclet number and the deformation parameter.

Concentration Distribution in the Wake of a Plane Surface Buried in a Porous Media in Alignment with the Flow Direction

2009 ◽  
Vol 283-286 ◽  
pp. 553-558
Author(s):  
João M.P.Q. Delgado ◽  
M. Vázquez da Silva
Keyword(s):  
Mass Transfer ◽  
Peclet Number ◽  
Numerical Solutions ◽  
Plane Surface ◽  
Flow Direction ◽  
Mathematical Expression ◽  
Mass Conservation ◽  
Mass Transfer Process ◽  
Packed Bed ◽  
Péclet Number

The present work describes the mass transfer process between a moving fluid and a slightly soluble flat surface buried in a packed bed of small inert particles with uniform voidage, by both advection and diffusion. Numerical solutions of the differential equation describing solute mass conservation were undertaken to obtain the concentration profiles, for each concentration level, the width and downstream length of the corresponding contour surface and the mass transfer flux was integrated to give the Sherwood number as a function of Peclet number. A mathematical expression that relates the dependence with the Peclet number is proposed to describe the approximate size of the diffusion wake downstream of the reactive solid mass.

scholarly journals Exact solutions for the formation of stagnant caps of insoluble surfactant on a planar free surface

2021 ◽  
Vol 131 (1) ◽  
Author(s):  
Darren G. Crowdy
Keyword(s):  
Exact Solutions ◽  
Peclet Number ◽  
Burgers Equation ◽  
Initial Conditions ◽  
Implicit Representation ◽  
Péclet Number ◽  
New Exact Solutions ◽  
Kinetics Modelling ◽  
Complex Burgers Equation ◽  
Insoluble Surfactant

AbstractA class of exact solutions is presented describing the time evolution of insoluble surfactant to a stagnant cap equilibrium on the surface of deep water in the Stokes flow regime at zero capillary number and infinite surface Péclet number. This is done by demonstrating, in a two-dimensional model setting, the relevance of the forced complex Burgers equation to this problem when a linear equation of state relates the surface tension to the surfactant concentration. A complex-variable version of the method of characteristics can then be deployed to find an implicit representation of the general solution. A special class of initial conditions is considered for which the associated solutions can be given explicitly. The new exact solutions, which include both spreading and compactifying scenarios, provide analytical insight into the unsteady formation of stagnant caps of insoluble surfactant. It is also shown that first-order reaction kinetics modelling sublimation or evaporation of the insoluble surfactant to the upper gas phase can be incorporated into the framework; this leads to a forced complex Burgers equation with linear damping. Generalized exact solutions to the latter equation at infinite surface Péclet number are also found and used to study how reaction effects destroy the surfactant cap equilibrium.

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