Deep bed filtration is an effective method of submicron and micron particle removal from the fluid stream. There is an extensive body of literature regarding particle deposition in filters, often using the classical continuum approach. However, the approach is not convenient for studying the influence of particle deposition on filter performance (filtration efficiency, pressure drop) when non-steady state boundary conditions have to be introduced. For the purposes of this work the lattice-Boltzmann model describes fluid dynamics, while the solid particle motion is modeled by the Brownian dynamics. For aggregates the effect of their structure on displacement is taken into account. The possibility of particles rebound from the surface of collector or reentrainment of deposits to fluid stream is calculated by energy balanced oscillatory model derived from adhesion theory. The results show the evolution of filtration efficiency and pressure drop of filters with different internal structure described by the size of pores. The size of resuspended aggregates and volume distribution of deposits in filter were also analyzed. The model enables prediction of dynamic filter behavior. It can be a very useful tool for designing filter structures which optimize maximum lifetime with the acceptable values of filtration efficiency and pressure drop.

A model of bacterial filtration on fibrous filter media is developed. The single fibre efficiency as well as the efficiency of the whole filter - at the onset of the process and the evolution of those quantities - are analysed. The differences between the numerical modelling of colloidal particles and bacteria are stressed in detail. The main differences are the active motion ability of bacteria and biofilm formation. The parameters of the model were identified based on the literature data.

The modelling of colloidal fouling and defouling of hollow fibre membranes in the presence of membrane oscillations is analysed by means of numerical simulations as an effect of complex coupling between hydrodynamic and surface forces. To describe the latter the Derjaguin-Landau- Vervey-Overbeek (DLVO) model has been employed. We have investigated the influence of various parameters of the process like flow rate, mean particle diameter, amplitude and frequency of the oscillations, and others, on the efficiency of the defouling process. The investigated parameters is close to that of a silica suspension in , a typical system modelling used to investigate membrane separation. On the basis of numerical simulation results e have defined an optimal set of parameters preventing membrane fouling.

A simple model of behaviour of a single particle on the bulging membrane was presented. As a result of numerical solution of a motion equation the influence of the amplitude and frequency of bulging as well as the particle size on particle behaviour, especially its downstream velocity was investigated. It was found that the bulging of a membrane may increase the mean velocity of a particle or reinforce its diffusive behaviour, dependeing on the permeation velocity. The obtained results may help to design new production methods of highly fouling-resistant membranes.

The motion of submicron particles involves the deterministic terms resulting from the aerodynamic convection and/or electrostatic attraction, and the stochastic term from the thermal displacement of particles. The Langevin equation describes such behavior. The Brownian dynamics algorithm was used for integration of the Langevin equation for the calculation of the single fiber deposition efficiency. Additionally the deterministic and stochastic of the particle motion were derived, using the Lagrangian and Eulerian approaches of particle movement and balance, for the calculation of the single fiber deposition efficiency due to both mechanisms separately. Combination of the obtained results allows us for calculation of the coupling effect of inertia and interception with the Brownian diffusion in a form of correlation. The results of calculation show that the omitting of the coupling effect of particular mechanism and using the simple additive rule for determination of the single fiber deposition efficiency introduces significant error, especially for particles with diameter below 300 nm.