Measurement of the filtration diffusivity D(ϕ) of a flocculated suspension

Authors

  • Kerry A. Landman,

    Corresponding author
    1. Advanced Mineral Products Centre, Dept. of Mathematics and Statistics, University of Melbourne, Parkville 3052, Victoria, Australia
    • Advanced Mineral Products Centre, Dept. of Mathematics and Statistics, University of Melbourne, Parkville 3052, Victoria, Australia
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  • J. M. Stankovich,

    1. Advanced Mineral Products Centre, Dept. of Mathematics and Statistics, University of Melbourne, Parkville 3052, Victoria, Australia
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  • Lee R. White

    1. Advanced Mineral Products Centre, Dept. of Mathematics and Statistics, University of Melbourne, Parkville 3052, Victoria, Australia
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Abstract

In modeling the pressure filtration of flocculated suspensions using compressional rheology, the filtration diffusivity function D(ϕ) plays the role of a diffusion coefficient in determining the time scale of the filtration process. Its dependence on volume fraction is an important factor in filtration process design. The volume of filtrate expressed per unit membrane is V = βt1/2. The value of β depends on D(ϕ) and various relationships between the two that involve data differentiation have been discussed in the literature. These involve an unknown but bounded parameter. Here a physical approximation is made that justifies setting this parameter to zero. Further, a new approximate expression for β2 in terms of D(ϕ) that avoids data differentiation is determined. Alternatively, the hindered settling factor can be recovered from an analytic expression involving data differentiation of β data with applied pressure. The accuracy of each of these approximations is assessed.

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