On the possibility of using information entropy as a quantitative description of porous media structural characteristics

This paper deals with possibility of information entropy usage for porous media structure characteristics description. The paper presents the results of preliminary investigation of the possibility using information entropy parameter for porous media. The first approach of the method presented in the paper confirmed the possibility to get the join characteristic of porous media. The method may give a new point of view on the problem of porous media modelling. The examples of entropy calculation for distributions of pore by size and length as well as for multi-layers porous media joint entropy are given.Junta de Investigação Científica e Tecnológica (JNICT

Extending Kozeny-Carman permeability model to highly porous media

Anomalous normalised permeability as a ratio of permeability to square of particle size for snow, diatomite, kieselgel was considered using Kozeny-Carman model and tortuosity factor defined as the square of average tortuosity pathway. Since the Kozeny-Carman model is based on the geometrical models of a capillary tube, the model adopted for high porous media with shaped particles (often with fractal properties) becomes complex. To show how the problem of permeability may be complex, two types of particles are analysed in porous media: snowflakes and diatomite and kieselguhrs. Snowflakes are typical fractal particles, whereas diatomite and kieselguhr can form pores with fractal tortuosity. Based on theoretical investigation a model including fractal measurements for void and solid phases and dependence of tortuosity on packing porosity is proposed. The obtained results show that within the developed model we can describe a wide range of porous media with different fractality and tortuosity. Based on presented numerous examples it was concluded that further experimental investigation should be useful to improve the model and validate the application range

Hindered motion in highly porous media : steric and fractal approaches

Two-dimensional simulation of porous media using a pore fractal dimension D was performed. Obtained results can be outlined as follows: 1). Starting from large pores with aspect ratio of micro-particle size to pore size λ > 0.001, molecules (or test object) recognise the pore volume as a partially restricted space with reduced fractal dimension. 2). The restriction effect on a molecule depends on pore topology (in the present case on the type of packing). 3). Dramatic reduction of D is observed when λ overcomes 0.01 and approaches λ ~ 0.1 in a 2-D approach, meaning that the test object recognises the pore as one dimensional rather than a 2-D space; in turn, a 3-D system will be recognised by the the test object as a 2-D system. 4). Concerning the hydrodynamic chromatography (HDC) the simulation explains why micro-objects become significantly retarded even at λ ~ 0.01, that is, even when the ratio between the Stokes-Einstein diameter of the diffusing micro-object to the equivalent pore diameter is very small. The developed approach confirms that even for micro-object with a very simple geometry (a square test box) a molecule might be much more sensitive to pore topology than what could be expected by a steric effect. It is possible to expect a more pronounced effect for asymmetric micro-objects in tortuous channels. These results show that the problem of molecular sensitivity towards pore topology may be understood using fractal analysis. Further work will apply this fractal approach to diffusivity behaviour in gel-like and fibre-like or foam structures

Equation for fitting dispersed systems gravity and centrifuge settling data

Liquid phase accumulation kinetics during sedimentation and centrifugation serves as a source of information about the average settling properties of dispersed systems. A power order fitting function is proposed for describing the dependence of accumulated liquid phase volume on settling time. The function validity was tested for numerous experimental settling data under gravitational and centrifugal forces for different dispersed systems. The obtained results give good correlation between experimental data and fitting curves even when settling displays a lag period. The main advantage of the proposed model is the possibility to fit the liquid phase accumulation kinetics in a wide range of settling time and solids concentration. The power order fitting function allows simulating the liquid phase accumulation in the case of limited experimental data.Fundação para a Ciência e a Tecnologia (FCT)FEDE

Influence of cell-shape on the cake resistance in dead-end and cross-flow filtrations

The problems related to tortuosity variation whenever filter cakes are composed of cells with different shapes and compressible biosuspensions are discussed. Presented examples show that neglecting the tortuosity variation may lead to significant miscalculations of cake porosity or of specific cake resistance. Specific cake resistance of rod-like particles in cross-flow filtration depends on the higher tortuosity obtained by the shear-induced ordered arrangement. In turn, spheroid cells such as baker’s yeast cells do not affect tortuosity as much as the rod-shaped cells. By including tortuosity as a parameter of compressible cakes, a more precise representation of cakes’ behaviour may be obtained. The tortuosity becomes a highly significant parameter with the increase in filtration pressure.North Atlantic Treaty Organisation (NATO) - Science fellowships Programme

Immobilized particles in gel matrix-type porous media: nonhomogeneous cell distribution

The conventional random pore model assumes a homogeneous cell distribution in the gel matrix used to immobilize cells. However, the validity of this model is restricted to values of the exponent R, between 1.8 and 2.25, of a model power function relating the diffusivity coefficient in the matrix with the overall cell volume fraction in the system. Based on the analysis of published data for diffusion in gels with immobilized cells and on the homogeneous approach for the random pore model developed in a previous work, a new, nonhomogeneous approach is proposed for R values outside the range 1.8-2.25. To explain these data, two main types of nonhomogeneous cell distribution were considered: (1) nonhomogeneous cell distribution in the gel for R > 2.25 (type 1) and (2) nonhomogeneity related with anisotropy of cell space orientation when R < 1.8 (type 2). In the case of nonhomogeneity of type 1, the cell volume fraction in the layers occupied by cells must be considered in place of the concept previously used for homogeneous distribution, viz., the average cell volume fraction. This model underlines that accumulation of cells in a thin layer close to the surface improves their nutrient intake. For nonhomogeneity of type 2, the tortuosity of such a system is smaller than should be expected if spherical cells were considered, thereby changing the effective diffusion. The model proposed in this work proved to fit into several real cases reported in the literature.Organização do Tratado do Atlântico Norte (NATO). Science Fellowships Program (Portugal)

Dependence of Saccharomyces cerevisiae filtration through membrance on yeast concentration

Filtration of baker’s yeast in an isotonic solution through a 0.45 micron membrane was investigated for yeast concentrations in the range 0.14 – 51 g/L at filtration pressures between 40 and 80 kPa. Yeast filtration through membranes depends on applied filtration pressure and on slurry concentration. It was found that for a yeast volume fraction in suspension above 0.06 the porosity of the yeast cake becomes weakly dependent on the suspension concentration. For highly diluted suspension the specific cake resistance approaches to the minimum value, which is sensitive to the filtration pressure. Correlation functions of the cake porosity and specific cake resistance were obtained in the investigated concentration range. It was found that the Kozeny-Carman coefficient is increased with increasing applied pressure. Both filtration pressure and slurry concentration can be subject of process control. In the range of moderate yeast concentration, manipulation of filtration pressure and of slurry concentration might increase the filtrate flux. Obtained results and assumptions made indicate that complex behavior of yeast cake at high slurry concentration can be further described within the framework of conventional model by increasing complexity of subsystems due to aggregation effect.Fundação para a Ciência e a Tecnologia (FCT) – Programa Operacional “Ciência, Tecnologia, Inovação” (POCTI) - POCTI/EQU/37500/2001

Baker’s yeast filtration through mixed beds of filtration aids and large glass beads

Filtration of baker´s yeast through a mixed particulate bed of filter aid and glass beads was investigated. Glass beads form the large size particle fraction in the mixture, whereas the small size particle fraction was made by the following filter aids: kieselgel, kieselguhr-G, and industrial kieselguhr of different grades. Investigated particle size ratio of beads and filter aids was in the range around 20 – 100. Obtained results show that the large size particles do not influence the cake filtration performance up to a volume fraction of large particles in the layer of 0.8 ÷ 0.85. Bench filtration through a composite layer was performed, being the mixed layer built by filtering a kieselguhr suspension through the glass beads packing formed on a support. Regeneration of the glass beads by fluidization allows its use as a non-disposal fraction of the filter bed. Obtained results clearly demonstrate that the amount of filter aid used is less than required in conventional processes, showing advantages in what concerns saving of filter aid and reduction of pollution levels. From the tested filter aids, the coarse grade kieselguhr proved to be the most adequate as it was the component that allowed for the higher initial filtration velocity in the large size particle volume fraction in the mixture of 0.82 – 0.85.Fundação para a Ciência e a Tecnologia (FCT) - Programa Operacional “Ciência, Tecnologia, Inovação” (POCTI) - POCTI/EQU/37500/2001.União Europeia (UE). Fundo Europeu de Desenvolvimento Regional (FEDER)