Lianfa Song

Flux decline in crossflow microfiltration and ultrafiltration: mechanisms and modeling of membrane fouling

Flux decline in crossflow ultrafiltration and microfiltration was investigated by perceiving membrane fouling as a dynamic process from non-equilibrium to equilibrium. Under the influence of the boundary condition at the initial section and cross flow, the equilibrium is first reached at the initial section of the crossflow filter and the front of the equilibrium region progresses with time toward the end of the filter. A mathematical model was developed to describe this dynamic process and a closed-form solution of the model was provided. With the model, the time-dependent flux and the time required to reach the steady state in a crossflow filtration can be easily determined. The fouling process under different conditions is simulated as an illustration and demonstration of the newly developed model.

Theory of concentration polarization in crossflow filtration

A novel theory is developed for concentration polarization of non-interacting particles in crossflow-filtration systems. This theory reveals that the extent of concentration polarization, as well as the behaviour of the permeate flux, are characterized by an important dimensionless filtration number (NF= 4πa3pΔP/3kT). There is a critical value of the filtration number for a given suspension and operational conditions. When the filtration number is smaller than the critical value, a polarization layer exists directly over the membrane surface and the wall particle concentration is determined by the pressure and temperature. At higher filtration numbers, a cake layer of retained particles forms between the polarization layer and the membrane surface. Mathematical models are constructed for both cases and analytical solutions for the permeate flux are derived. An increase in permeate flux with increasing pressure is predicted for all operational conditions.

Kinetics of Colloid Deposition onto Heterogeneously Charged Surfaces in Porous Media.

general theoretical approach for the calculation of colloid deposition rate onto heterogeneously charged surfaces is presented. Patchwise and random distribution models are used to quantitatively describe surface charge het- erogeneity and its effect on the kinetics of colloid deposi- tion. It is shown that unfavorable surfaces with only minor amounts of charge heterogeneity have particle deposition rates that are orders of magnitude larger than similar surfaces having no charge heterogeneity. Furthermore, the sensitivity of particle deposition rate to solution ionic strength decreases as the degree of surface charge het- erogeneity increases. Parameters characterizing the sur- face charge heterogeneity of collectors in porous media are identified from experimental data of colloid deposition by using the inverse procedure of parameter estimation. These heterogeneity parameters can be used in conjunction with current theories of particle deposition to explain experimental results of colloid deposition rates under chemical conditions that are unfavorable for particle deposition.

Dynamics of colloid deposition in porous media: Modeling the role of retained particles

Abstract A model for the dynamics of colloid deposition in porous media is developed by combining macroscopic and microscopic theories of particle deposition. The model considers the non-uniform coverage of collector surfaces by retained particles during the deposition process. A flux-correcting function is introduced that enables the determination of the overall colloid deposition rate as a function of surface coverage. A non-linear dependence of particle deposition rate on surface coverage is obtained, in agreement with experimental data of particle deposition. It is shown that the model is successful in describing the blocking (excluded-area) effect in particle deposition dynamics.

A new model for the calculation of the limiting flux in ultrafiltration

The occurrence of the limiting flux in ultrafiltration is elucidated with the formation of a cake (gel) layer on the membrane surface. Before cake formation, the pressure drop on the concentration polarization layer, as well as the permeate flux, increases with the applied pressure. The pressure drop on the concentration polarization layer, however, will no longer change with the applied pressure after the formation of the cake layer. The limiting flux will be obtained if the hydrodynamic conditions in the filtration channel are not affected by the cake layer. A mechanistic model for predicting the limiting flux in ultrafiltration is developed. A procedure to correlate the model with experimental ultrafiltration data is also presented.

Performance limitation of the full-scale reverse osmosis process

The mechanisms controlling the performance of a full-scale reverse osmosis (RO) process (typically a pressure vessel holding six 1 m long modules in series) under various operating conditions are carefully examined in this study. We demonstrate that thermodynamic equilibrium imposes a strong restriction on the performance of a full-scale RO process under certain circumstances. This thermodynamic restriction arises from the significant increase in osmotic pressure downstream of an RO membrane channel (owing to the phenomenon of salt accumulation within the RO channel as a result of permeate production). The behavior of the full-scale RO process under thermodynamic restriction is much different from that of the process when it is controlled by mass transfer. The conditions for an RO process to shift from mass transfer-controlled regime to thermodynamically restricted regime are delineated and discussed.

Emergence of thermodynamic restriction and its implications for full-scale reverse osmosis processes

The production rate of permeate in a reverse osmosis (RO) process controlled by mass transfer is proportional to the net driving pressure and the total membrane surface area. This linear relationship may not be the only mechanism controlling the performance of a full-scale membrane process (typically a pressure vessel holding six 1-m-long modules in series) which utilizes highly permeable membranes. The mechanisms that control the performance of an RO process under various conditions were carefully examined in this study. It was demonstrated that thermodynamic equilibrium can impose a strong restriction on the performance of a full-scale RO process under certain circumstances. This thermodynamic restriction arises from the significant increase in osmotic pressure downstream of an RO membrane channel due to the accumulation of rejected salt within the RO channel as a result of permeate water production. Concentration polarization is shown to have a weaker influence on the full-scale RO process performance than the thermodynamic restriction. The behavior of the process under thermodynamic restriction is quite different from the corresponding behavior that is controlled by mass transfer. The transition pressure for an RO process to shift from a mass transfer controlled regime to a thermodynamically restricted regime was determined by the basic parameters of the full-scale RO process.

Calculation of particle deposition rate under unfavourable particle–surface interactions

When repulsive colloidal interactions are involved, calculating the rate of particle deposition becomes particularly difficult. To overcome the difficulty, a new (constant migration flux) boundary condition and a sophisticated numerical procedure are introduced. With these procedures, smooth solutions of the equation are obtained for the entire domain, including the region beyond the energy barrier adjacent to the collector surface. Numerical calculations demonstrate that the dependence of particle deposition rate on flow velocity is quite different from that reported previously. The difficulty of using the ‘perfect-sink’ boundary condition in numerical solutions and the inadequacy of previous numerical methods are discussed.

Theoretical investigation of colloid separation from dilute aqueous suspensions by oppositely charged granular media

Abstract A theoretical investigation of removal of colloidal particles from aqueous suspensions by oppositely charged granular (porous) media is presented in th

Deposition of Brownian particles in porous media: Modified boundary conditions for the sphere-in-cell model

Abstract Modified boundary conditions for solving the convective diffusion equation for Brownian particles as applied in the Happel sphere-in-cell porous medium model are presented. With the modified boundary conditions, the convective diffusion equation correctly predicts the deposition rates of Brownian particles at low Peclet numbers. At moderate and large Peclet numbers, colloid deposition rates are similar to those calculated with existing models.