Mathematical modelling of deep bed filtration

Numerous mathematical models have been developed to evaluate both initial and transient stage removal efficiency of deep bed filters. Microscopic models either using trajectory analysis or convective-diffusion equations were used to compute the initial removal efficiency. These models predicted the removal efficiency under favorable filtration conditions quantitatively, but failed to predict the removal efficiency under unfavorable conditions. They underestimated the removal efficiency under unfavorable conditions. Thus, semi-empirical formulations were developed to compute initial removal efficiencies under unfavorable conditions. Also, correction for the adhesion of particles onto filter grains improved the results obtained for removal efficiency from the trajectory analysis. Macroscopic models were used to predict the transient stage removal efficiency of deep bed filters. O’Melia and Ali’s model assumed that the particle removal is due to filter grains as well as the particles that are already deposited onto the filter grain. Thus, semi-empirical models were used to predict the ripening of filtration. Several modifications were made to the model developed by O’Melia and Ali to predict the deterioration of particle removal during the transient stages of filtration. Models considering the removal of particles under favorable conditions and the accumulation of charges on the filter grains during the transient stages were also developed. This paper evaluates those models and their applicability under different operating conditions of filtration.

Deep bed filtration : mathematical models and observations

Numerous mathematical models have been developed to evaluate both initial and transient stage removal efficiency of deep bed filters. Microscopic models either using trajectory analysis or convective diffusion equations were used to compute the initial removal efficiency. These models predicted the removal efficiency under favorable filtration conditions quantitatively, but failed to predict the removal efficiency under unfavorable conditions. They underestimated the removal efficiency under unfavorable conditions. Thus, semi-empirical formulations were developed to compute initial removal efficiencies under unfavorable conditions. Also, correction for the adhesion of particles onto filter grains improved the results obtained for removal efficiency from the trajectory analysis. Macroscopic models were used to predict the transient stage removal efficiency of deep bed filters. The O’Melia and Ali1 model assumed that the particle removal is due to filter grains as well as the particles that are already deposited onto the filter grain. Thus, semi-empirical models were used to predict the ripening of filtration. Several modifications were made to the model developed by O’Melia and Ali to predict the deterioration of particle removal during the transient stages of filtration. Models considering the removal of particles under favorable conditions and the accumulation of charges on the filter grains during the transient stages were also developed. This article evaluates those models and their applicability under different operating conditions of filtration.

Surface coverage of filter medium in deep bed filtration : mathematical modelling and experiments

This paper highlights the importance of surface coverage in modeling the removal of particles in deep bed filtration. A model that considers the saturation of sites on which particle deposition occurs is used. Experimental results obtained with monodispersed suspensions of 0.46 and 0.816 μm latex particles at different influent concentrations and ionic strengths were used to calculate the fraction of filter grain surface (β1) on which actual particle deposition occurs. This will be useful in evaluating the filter performance in terms of the utilization of available surface area of the filter medium. Further, the level of dendrite formation of particles on filter grains during filtration is expressed in terms of β1 and the specific surface coverage, θT (the fraction of a filter grain surface that is covered by particles at time T, assuming that the filter grain is covered by a monolayer of particles). This can be used to compare the contribution of deposited particles in the removal efficiency of deep bed filtration for suspensions with different physical and chemical characteristics.

Influence of particle size and size distribution in deep bed filtration and dynamic microfiltration

Particle size and size distribution is an important parameter in solid liquid separation process especially in granular bed filtration and in dynamic microfiltration. This paper discusses their effects on the above processes from extensive experimental data obtained. In granular bed filtration, the experimental results showed that the initial efficiency follows the pattern reported by previous experimental and theoretical studies, i.e., lower efficiency for particles which fall in the range of critical size of 1 m. However, the particle removal during the transient stage increased with an increase in particle size for the range of sizes studied. An attempt was made to quantify these effects in granular bed filtration using semi-empirical approach. In dynamic membrane filtration also, the particle size plays a major role in the retention. However, despite the relative thickness of the membrane (compared to particle size) dynamic microfiltration appears more as a sieving process; the retention is mainly related to the largest pore size.

Angiotensin converting enzyme inhibition lowers body weight and improves glucose tolerance in C57BL/6J mice maintained on a high fat diet

The renin–angiotensin system (RAS) is functional within adipose tissue and angiotensin II, the active component of RAS, has been implicated in adipose tissue hypertrophy and insulin resistance. In this study, captopril, an angiotensin converting enzyme (ACE) inhibitor that prevents angiotensin II formation, was used to study the development of diet-induced obesity and insulin resistance in obesity prone C57BL/6J mice. The mice were fed a high fat diet (w/w 21% fat) and allowed access to either water or water with captopril added (0.2 mg/ml). Body weight was recorded weekly and water and food intake daily. Glucose tolerance was determined after 11–12 weeks. On completion of the study (after 16 weeks of treatment), the mice were killed and kidney, liver, epididymal fat and extensor digitorum longus muscle (EDL) were weighed. Blood samples were collected and plasma analysed for metabolites and hormones. Captopril treatment decreased body weight in the first 2 weeks of treatment. Food intake of captopril-treated mice was similar to control mice prior to weight loss and was decreased after weight loss. Glucose tolerance was improved in captopril-treated mice. Captopril-treated mice had less epididymal fat than control mice. Relative to body weight, captopril-treated mice had increased EDL weight. Relative to control mice, mice administered captopril had a higher plasma concentration of adiponectin and lower concentrations of leptin and non-esterified fatty acids (NEFA). The results indicate that captopril both induced weight loss and improved insulin sensitivity. Thus, captopril may eventually be used for the treatment of obesity and Type 2 diabetes.