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)

Immobilized particles in gel matrix-type porous media: homogeneous porous media model

Diffusion in pure gels and gels with immobilized cells was analyzed. A model of diffusion assuming a homogeneous cell distribution in gel was improved by introducing a tortuosity value. By theoretical analysis and numerical modeling it was shown that the tortuosity of a gel with immobilized cells is the product of two factors: (1) tortuosity generated by the cells, Tc, and (2) tortuosity of the gel matrix, Tg, both variables being a function of cell volume fraction. Total tortuosity is thus T=TcTg. On the basis of this approach, it was possible to analyze diffusivity data for gels with immobilized cells. It was shown that, in these systems, the diffusivity = De/D0 is a complex function of (1) diffusivity in the gel, and (2) diffusivity in immobilized cells. The developed model allowed for the description of the dependence of De/D0 on fi_c. Comparison with numerous published experimental data showed a good fit. Observed deviations might be explained by nonhomogeneous cell distributions inside the gel matrix.PRAXIS XXI - BBC/6440/95

Image analysis of packed beds of spherical particles of different sizes

Two-dimensional simulations of packed beds composed of binary and ternary particle mixtures were made and image analysis of the bed structure was used to determine the bed porosity and tortuosity. Both the porosity and tortuosity were found to be dependent upon the volume fraction of the large particles. However, the volume fraction alone does not totally determine either the porosity or the tortuosity. For a bed of two different sizes of particles, its tortuosity may be considered a product of two quantities, the macro- and micro-tortuosity, each of which can be determined from the corresponding monosized particle beds.Junta Nacional de Investigação Científica e Tecnológica (JNICT) - PRAXIS XXI - BBC/6440/95

Effect of the particle shape on flow through porous media

In order to study the performance of shaped particles flow in porous media, filtration of two different shape - spherical and rod-like – micro particles was performed through a porous bed. Filtration was investigated at a constant flow rate of 0.04 cm/s with yeast cells, diameter 5 microns, micro spheres, diameter 1 micron, and rod-like bacilli Lactobacillus bulgaricus with 6 microns average length and 0.5 micron diameter. Yeast diameter is close to the bacillus length and micro-sphere diameter is in the scale of the bacillus diameter. All particles have similar density. For the packing, the following glass beads were used: coarse particles, size 1.125 mm; fine particles, size 0.1115 mm. Experiments were carried out using a column loaded with a binary packing (volume fraction of coarse particles in the mixture 0.7) or with a monosize packing with the same amount of coarse or fine particles as used in the binary packing. The analysis of the experimental results was based on two models: pure exclusion effect and hydrodynamic separation model (HDC). Results for spheres show that the classic HDC model ( B = 1.0) fits well the data whenever the ratio of particle size to the bend scale is high (~ 1/100, as for micro spheres). However, if this ratio increases and becomes ~ 1/20, the HDC model needs to be corrected due to the effect of channel wall curvature on the exclusion effect. This assumption leads to a modified HDC equation - R = B/ (1+2λ -2.8λ²), where B ≥ 1 and λ represents the ratio of microparticle size to the pore size. The effect of pore topology plays an important role in the separation of shaped particles when the aspect ratio λ approaches 0.1 and, in the case of bacillus, separation occurs by an exclusion mechanism. For the binary packing, the rod-like particles behave differently from the spherical particles having a length or a diameter in the same scale of bacillus length and diameter. The explanation is the interference of rod-like particles with the pore topology. The exclusion model for particles was formulated in a general form as R = A/(1-λ)², where A is a coefficient proportional to the tortuosity and parameter z = 1, 2 or 3 depends mainly on the pore shape. For instance, in a parallel-plate channel flow: R ~ 1/(1-λ), for a cylindrical pore R ~ 1/(1-λ)² , and for 3-D pore R ~ 1/(1- λ)³ . Further investigation is needed to clarify the particle – pore topology interaction and its effect on particle separation