Mathematical modeling of extraction process for biporous medium and analyze of pressure in particles and extraparticle space

Обґрунтовано математичну модель процесу відтиску матеріалів рослинного походження у одновимірній постановці. Середовище, що піддається відтиску, представляється у вигляді біпористої системи, системою міжчастинкових та внутрішньочастинкових просторів. Сформульовано рівняння фільтрації-консолідації з відповідними початковими та крайовими умовами як для міжчастинкового, так і внутрішньочастинкового просторів у припущенні, що для матеріалів рослинного походження, міжчастинковий шар пор володіє малою місткістю, а пори в частинках – високою. Проведено числове моделювання профілів тисків в мікро- та макро порах біпористого середовища для двох матеріалів з різними степенями попередньої деформованості внутрішньої структури. Отримані результати вказують на відтермінування падіння значення тиску в частинці та уповільнення процесу консолідації для менш деформованого середовища.During solid-liquid expression, the porous layer formed by a whole fruit or fragmentized material is subjected to unidirectional or complex compression in industrial presses. Such compression can be carried out under constant or variable parameters (pressure, deformation rate). Physical model of solid-liquid expression from liquid containing materials is presented in one-dimensional formulation. The layer of sliced cellular material is conceptualized as a double porosity system with extraparticle and intraparticle networks for liquid flowing. The liquid flowing occurs inside the particles (intraparticle space), outside the particles (extraparticle space) and between these two spaces. The sliced particles are rectangular parallelepipeds separated by the porous network. The extraparticles network forms the first porosity with low storage capacity and high hydraulic permeability. The sliced liquid containing particles form a second porosity with high storage capacity and low hydraulic permeability. The filtration-consolidation equations with corresponding initial and boundary conditions were formulated for both extraparticle and intraparticle networks. The extraparticle network was supposed to form the first porosity level, while the intraparticle network forms a second porosity. Using obtained numerical solutions, the liquid pressure distributions inside of porous particles and in the extraparticle space were calculated. The pressure distribution curves are presented in function of time and dimensionless geometrical coordinates. Computational modeling of pressure profiles in macro- and micropores versus time for different layer sections was done for plant material with two different compressibility-permeability characteristics corresponding different degrees of tissue destroying. Results show the delayed pressure drop in the intraparticle network and retardation of consolidation kinetics for the less destroyed plant tissue due to the lower value of consolidation coefficient. Therefore, the degree of destroying of cellular tissue can influence importantly on the pressure profiles and retardation of pressure drops inside the porous particles

Pressure electroosmotic dewatering with continuous removal of electrolysis products

Pressurised electroosmotic dewatering (PED) is usually implemented in classical filters with the electrodes making a direct contact with the material or the filter cloths. Thus, electrolysis products generated at the electrodes (gas, ions) tend to accumulate in the solid/liquid mixture being dewatered. This results in a non-uniform distribution of water content, porosity, electric field intensity, and particle zeta potential throughout the mixture, affecting progress of the PED process. This paper proposes a specific design of filter press to study PED in the absence of disturbances from electrolysis products. An experimental study was carried out on a gelatinous bentonite suspension at 8.5% w/w solid. The influence of the ionic conductivity of suspension (2-25 mS/cm), the current intensity (20-300 mA) and the pressure (2.5-15 bar) were investigated. In order to improve the energetic yield of PED, the conductivity and current intensity should be limited, as observed in earlier works. The pressure increase considerably aids the water removal and leads to better product dryness. For PED at 15 bar and 100 mA, the bentonite reached 40% w/w solid for 0.7 kWh/kg of water removed. This study emphasizes that to analyse PED precisely it is important to clarify the dependence of the electroosmotic flow rate on the porosity and pressure

Phase Splitting for Periodic Lie Systems

In the context of the Floquet theory, using a variation of parameter argument, we show that the logarithm of the monodromy of a real periodic Lie system with appropriate properties admits a splitting into two parts, called dynamic and geometric phases. The dynamic phase is intrinsic and linked to the Hamiltonian of a periodic linear Euler system on the co-algebra. The geometric phase is represented as a surface integral of the symplectic form of a co-adjoint orbit.Comment: (v1) 15 pages. (v2) 16 pages. Some typos corrected. References and further comments added. Final version to appear in J. Phys. A