# Noncolloidal Suspension Essay

Daniel Galvez-Moreno a)

Missouri University of Science and Technology, 219 Butler-Carlton Hall, 1401 N. Pine St., Rolla, MO 65409, USA.

Synopsis

INTRODUCTION

Noncolloidal suspensions are composed by a liquid and a solid phase, which the latter is constituted by particles where Brownian motion, repulsion/attraction forces and Van Der Waals bonds are often negligible [1]. Nowadays, the success of many industrial processes relies on the ability of controlling and predicting with accuracy the rheological properties of suspensions. Typically, by fitting experimental data to constitutive equations is possible to characterize the rheological properties of simple fluids [2].

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Then, if each interaction generates a displacement Ο(a) and the interaction frequency scales as γ ̇ϕ, the migration velocity scales as γ ̇ϕ(a^2⁄η)∇η. Since the viscosity of concentrated suspensions where the importance of Brownian forces is negligible (Pe≫1) can be expressed approximately as: η_r= (1-ϕ⁄ϕ_max )^(-1.82) ( 2 )

when multiplied by ϕ, the eq. ( 2 ) can be used to express the gradient of viscosity in terms of ∇ϕ and represent the flux attributed to the special variation of viscosity (N_η ) due to particle concentration gradients as follow:

N_η=-K_η γ ̇ϕ^2 (a^2/η) dη/dϕ ∇ϕ ( 3 )

where K_η is a constant that must be determined experimentally. Once that both sources of particle migration are defined, a conservation equation could be modeled following the relative movement of a suspension portion through space and time in the following way:

Suspension balance model

Measuring

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