Experiments on the conductivity of suspensions of ionically‐conductive spheres

Abstract

This is a report on t h e ionic conductivity of monodisperse, neutrallybuoyant suspensions of ion-exchange b e a d s , both AC total-ion conductivity a n d DC specific-ion conductivity of an electrochemically-active s p e c i e s . They r e p r e s e n t t h e zero Peclet-number a n d t h e large Pecletnumber limits of mass transfer, respectively.A rotating d i s c e l e c t r o d e w a s employed for t h e DC s t u d i e s a n d a well mixed conductivity cell for t h e AC-for particle volume fractions $ ranging from zero t o a b o u t 45%. Novel t e c h n i q u e s w e r e d e v e l o p e d for rapidly determining t h e particle AC conductivity a n d for modifying t h e relative conductivity a of ion-exchange beads by poisoning with immobilely-bound ions. For a values, 0.044 I a I 1.48, of this study Maxwell's classical relation is s h o w n to be a d e q u a t e for $ I 0.5, which is, in agreement with Turner (1973, 1976).Our results for t h e DC conductivity differ s o m e w h a t from t h o s e of Andersen (1987) land s h o w t h e w e a k d e p e n d e n c e on particle Peclet number predicted by t h e dilute-suspension theory of Nir a n d Acrivos ( 1 9 7 6 ) f o r P e > > 1. IntroductionAs many engineering problems involve the transport of matter and energy through particulate and granular media, it is useful to understand the role of the particle phase in enhancing or inhibiting this transport. Since the transport through such materials depends not only on the particle concentration and shape but also on the particle arrangement and motion, the knowledge of transport properties can also shed light on the structure and dynamics of the medium and thus on its mechanical properties. Thus, the present study was originally motivated by a desire to develop and characterize an idealized conductive granular material, in which both mechanical and scalar transport properties might be studied simultaneously.We recall that many investigators have theoretically and experimentally studied the transport of heat or mass through suspensions of particles, with Maxwell being one of the first to theoretically relate the effective conductivity of a dilute stationary suspension of solid spheres to the properties of the individual phases and the concentration of the spheres. /3 = (a -I)/(a + 2) a = ratio of conductivity of the particle to that K = effective conductivity of the suspension K,,, = conductivity of the matrix 4 = solid volume fraction of the matrix To the order of terms in 4 to which it is exact, Eiq. 1 takes the form:

Heat Transfer and Dissipation Effects in the Flow of a Drilling Fluid

“…In fact, for anisotropic materials, k becomes a second order tensor. (For a discussion of the effective thermal conductivity concept in porous media and multiphase flows, see [33] (p. 129) and [34][35][36]). Jeffrey [37] derived an expression for the effective thermal conductivity which includes the second order effects in the volume fraction [38]:…”

“…where ω is the ratio of conductivity of the particle to that of the matrix, k the effective conductivity of the suspension, k M the conductivity of the matrix, and φ is the solid volume fraction [34]. More recently, Pabst [39] has derived a relationship for the effective thermal conductivity,…”

Effects of Shear Dependent Viscosity and Variable Thermal Conductivity on the Flow and Heat Transfer in a Slurry

“…For complex materials, such as polymers and granular materials, whether stationary or in motion, the thermal conductivity of the material is assumed to depend on parameters such as volume fraction, particle size, shear rate, etc. [1,52,53].…”

Heat Transfer in Complex Fluids

“…where ω is the ratio of conductivity of the particle to that of the matrix, κ the effective conductivity of the suspension, M κ the conductivity of the matrix, and ν is the solid volume fraction (Bashir & Goddard, 1990). Massoudi (2006aMassoudi ( , 2006b) has conjectured, based on arguments in mechanics, that the heat flux vector for a 'reasonably' dense assembly of granular materials where the media is assumed to behave as a continuum in such a way that as the material moves and is deformed, through the distribution of the voids, the heat flux is affected not only by the motion but also by the density (or volume fraction) gradients.…”