An Inverse Problem in the Darcian Mechanics of Porous Media
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The constitutive relation between the solid-phase stress and the solid-phase concentration is sought. Since this characteristic is difficult to measure, the equations of Darcian mechanics are applied in order to derive a correspondence between the studied quantities and a set of data which are easy to measure. The utilized data originate from a set of 50 experiments carried out with a suspension of water and kaolin; the height of a suspension column was measured as a function of time. Inversion based on the equations of porous media mechanics makes it possible to convert the obtained relationship between mass and height of the suspension column to the sought relationship between the solid-phase stress and the solid-phase concentration. Two different forms of the result are found and presented. A particular result is the threshold value of concentration at which the solid-phase stress becomes nonzero.
KeywordsPorous medium Darcian mechanics Monotonous process Solid-phase concentration Solid-phase stress
The research was supported by the Grant Agency of Charles University under Grant 126408. The authors are indebted to the Central laboratory of the Sedlecký Kaolin, a. s. for the data presented in Table 1.
- Coe, H.S., Clevenger, G.H.: Methods for determining the capacity of slime-settling tanks. AIME Trans. 55, 356–384 (1916)Google Scholar
- Satava, V.: Theory of ceramic casting-slips liquefaction and optimization of the casting process. Sklav. Keram. 23, 195–199 (1973)Google Scholar
- Usher, S.P., Scales, P.J.: Steady state thickener modelling from the compressive yield stress and hindered settling function. Chemical Engineering Journal 111(2–3, SI):253–261. doi: 10.1016/j.cej.2005.02.015, ECI Conference on Solid-Liquid Separation Systems IV, Pucon, Chile, Dec 14–19, 2003 (2005)
- van Olphen, H.: An Introduction to Clay Colloid Chemistry. Interscience, New York (1963)Google Scholar