Study on filtration for extremely compressible cakes

Abstract

In this thesis, we propose theoretical models used universally for the filtration of slightly to extremely compressible cakes. In the filtration analysis, i) the relationship between the hydraulic pressure and the compressive drag pressure and ii) the constitutive equation between the specific cake resistance and the compressive drag pressure are important because they directly affect the predictions of the filtrate flow rate. In the first technical chapter, the relationship between the hydraulic pressure and the compressive drag pressure acting on the particles is studied. During the filtration operation, liquid flows along the particles and applies force corresponding to the pressure drop onto the particles. The drag on each particle increases along the flow direction of the liquid because the drag received by the previous particles is added. The relationship between the hydraulic pressure and the compressive drag pressure is very important in an analysis of cake filtration because the compressive drag pressure due to the hydraulic pressure determines the porosity distribution in the cake. In this thesis, the relationship that includes both the frictional drag and the form drag is proposed, unlike previous studies in which the liquid flowing along the pores in the cake transfers the force onto the particles by the frictional drag only. A new dimensionless parameter defining the ratio of the form drag to the frictional drag is introduced, and the drag region in terms of the compressibility of the cake is classified using the dimensionless parameter. In the second technical chapter, analytical studies on the electrostatic effects contributing to the formation of the extremely compressible cake and the filtration characteristics of the cake are carried out. Weak flocculation between particles based on the DLVO theory determines the cake structure, and if the compressive drag exceeds the weak binding force, the porous layer of the cake becomes dense. Using existing constitutive equations, the filtration performance of extremely compressible cakes cannot be predicted reasonably. To overcome the problems of existing constitutive equations, a new form of constitutive equation is proposed. We use the proposed constitutive equations to correct the misunderstanding of the dense layer near the filter medium and derive a new filtrate flow equation based on proposed constitutive equations. In the appendix A, the electroviscous effects on the liquid flowing through the pores in the cake are investigated. In order to predict the electroviscous effects in an electrically-charged channel with highly overlapped electric double layers, a new analytical model employing effective ionic concentrations suitable for determining the boundary conditions at the wall is developed. Using the developed model, a dimensionless parameter which can express the electroviscosity as a single function is introduced. In this thesis, the electrostatic effects as well as the electrokinetic effects are considered for a systematic analysis of cake filtration. The proposed model and relationship are validated by experimental data. Also, the experimental data obtained from the filtration experiments are compared with the predictions of the filtrate flow rate using the electrovisosity instead of the actual viscosity of the liquid.