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.

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.

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.

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.

Do strategy choices matter for nascent firms? Effectuation in the early stages of venture creation

This paper explores empirically effects of Effectuation on nascent firms’ performance. Three potential outcomes for nascent firms using different levels of effectuation and causation are investigated. Innovation, a measure of venture sophistication was introduced as a moderator. We examine a longitudinal random sample of 625 nascent firms collected over two years in Australia and provide support for our hypotheses. Results show that in situation of high uncertainty, nascent firms using effectuation are more likely to reach operational stage than their counterpart using causation.

Early stages of growth of YBa2Cu3O7-δ high Tc superconducting films on (001) Y-ZrO2 substrates

The early stages of growth of high quality YBa2Cu 3O7-δ (YBCO) films grown on (001) Y-ZrO2 (YSZ) substrates by pulsed laser deposition have been studied using a combination of atomic force microscopy and transmission electron microscopy. A one unit cell thick YBCO layer and relatively large CuO particles formed in the initial stages. Additional YBCO grew on top of the first layer in the form of one or a few unit cell high c-axis oriented islands about 30 nm in diameter. The rounded islands subsequently coalesced into faceted domains. Elongated Y 2BaCuO5 particles nucleated after the first layer of YBCO. A highly textured BaZrO3 layer formed between the YSZ and the YBCO with a cube-on-cube dominant orientation relationship with respect to the YBCO film.