Constitutive Equation and Governing Differential Equation for Filtration Expressed in Moving Coordinate
- Resource Type
- Journal Article
- Authors
- Kenji Okada; Shaoxiang Qian; Youichi Nagase
- Source
- Journal of the Society of Powder Technology, Japan. 2003, 40(10):712
- Subject
- Constitutive equation
Filtration theory
Moving coordinate
Specific filtration resistance
Suspension rheology
- Language
- English
- ISSN
- 0386-6157
1883-7239
Consolidation and permeation through consolidated bed during filtration were experimentally studied using four types of suspensions and the results were compared with the elasticity data obtained in the previous work. As a result, it was found that the consolidation progressed during the filtration up to almostnearly 95% of that at consolidation equilibrium. The stress versus concentration relation (constitutive equation) and the permeation data for filtration were measured with the bed of about 95% consolidation. The elasticity data was applied to extrapolate the constitutive equation to in the lower range of concentration and to estimated the concentration at the surface of the cake. Governing differential equation expressed with in the solid moving (material) coordinate was derived from the constitutive equation and the permeation equation. The moving coordinate facilitated the calculation of solid flow rate, and the specific filtration resistances calculated numerically for four types of suspensions were in good agreed wellment with the experimental data.