A generalized model to predict the viscosity of solutions with suspended particles. I

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Abstract
Several suspension equations available in the literature have been found to have a common derivative form. This common derivative was found to be equivalent to a ratio of the intrinsic viscosity, [η], and a quantity, Vint, defined as the ldquo;relative suspension interaction volume” available for particle flow. Vint was, in general, found to be a relatively simple function of the suspension particle volume fraction, φ, the maximum particle packing fraction, φn, and a new variable, σ, defined as the particle interaction coefficient. Different forms of this common derivative were obtained by modifying VInt with a simple adjustment for the value for the interaction coefficient, σ. Integration of this generalized derivative yielded a generalized suspension viscosity equation that was found to predict the form of many suspension equations that have previously appeared in the literature. For example, by varying the interaction coefficient, σ, the Arrhenius equation resulted when σ = 0, the Kreiger‐Dougherty equation resulted when σ = 1, and when σ = 2, the Mooney equation resulted. Fractional values for the particle interaction coefficient were also found to be useful when optimizing the empirical fit of the literature data of Vand and Eiler. Additional insight from such a data fit can also be obtained from the magnitude of both the particle interaction coefficient, σ, and the packing fraction, φn. © 1993 John Wiley & Sons, Inc.