Patrice Bacchin

A unifying model for concentration polarization, gel-layer formation and particle deposition in cross-flow membrane filtration of colloidal suspensions

Abstract A model is proposed to describe the cross-flow filtration of colloidal particles and molecules. This two-dimensional model depicts both concentration polarization and gel or cake formation in a tubular filtration device. A description of transport phenomena in a concentrated colloidal suspension is the core of the model. Surface and hydrodynamic interactions are used to predict the variation of the osmotic pressure and diffusion coefficient with the volume fraction of the suspension. The mathematical development leads to an analytical equation used for calculating the stationary permeate flux from integral calculations. The two-dimensional concentration profile along the membrane, together with the corresponding permeate flux is obtained. This paper illustrates how mass transfer equations coupled with a realistic description of the fluid can describe both concentration polarization and gel or cake formation. The paper includes a discussion on the differences between limiting and critical fluxes, and between particles and macromolecular cross-flow filtrations.

On an experimental method to measure critical flux in ultrafiltration

The following study presents an improvement of previous techniques to determine critical flux in ultrafiltration. The data treatment allows having accurate values of the critical flux and the rate of irreversibility of the created deposit on the membrane. Measures of critical flux were run with different hydrodynamic conditions and were in accordance with the expected results (critical flux increases with hydrodynamics). To confirm this method, the experiments were run with stable suspensions of PVC latex in water with different ionic strength to induce a change in stability. A significant difference was noticed in the measure of critical flux showing the sensibility of the method.

Influence of surface interaction on transfer during colloid ultrafiltration

Experimental ultrafiltration (UF) of clay suspensions having different salinity shows that the presence of salt affects the transfer mechanisms, such as deposition kinetics, hydraulic resistance of the deposit and salt retention by the deposit. Such changes are the results of the variation in surface repulsive interaction between particles with the salt concentration (DLVO theory). With respect to the deposition kinetics, it is observed that as salt concentration increases the critical flux decreases to zero: this coincides with the occurrence of an adhesion mechanism. These phenomena are modelled by considering transport by surface interaction of the particles near the surface. Variations in hydraulic resistance of the cake are explained through a modified Kozeny-Carman equation. A reduction in porosity due to a decrease in repulsive interaction and a particle size increase due to coagulation are involved. Salt retention is described by considering (i) electrostatic partition (ii) salt transport by convection and diffusion in the boundary layer and in the porous medium. Analysis of salt retention and of hydraulic resistance of the cake lead to the same conclusions about the deposit properties. An important result is that surface interactions (hence the suspension stability) are as important as operating conditions for the membrane processing of colloidal suspensions.

Modelling of filtration: from the polarised layer to deposit formation and compaction☆

A theoretical study is developed for the modelling of mass accumulation from the polarised layer to the formation of a deposit. Concentrated suspension properties are accounted for through a solid pressure corresponding to osmotic pressure in the suspension and to compression resistance in the deposit. Mass and solvent transfer are depicted through balanced permeation/diffusion transport in the polarised layer and balanced friction/compaction forces in the deposit. The modelling applied to transient state for dead end filtration gives information about the coupling between mass transfer in the polarised layer and in the deposit. Consequences on specific cake resistance are presented and discussed.

Colloidal surface interactions and membrane fouling: Investigations at pore scale

In this paper, we examine the contributions of colloidal surface interaction in filtration processes. In a first part, we describe the way surface interactions affect the transport of colloidal particles or macromolecules towards a membrane, and its theoretical description. The concept of critical flux is introduced and linked to particle-membrane wall and particle-particle surface interactions. From this review, it seems important to consider how surface interactions occur at pore scale and control the development of fouling layers. In this context, we report in a second part experiments where the capture of micron-sized particles is observed in a poly-dimethylsiloxane (PDMS) microfluidic filtration device. Direct observations of the filtering part by video-microscopy allow to investigate the way the fouling of the microchannels by the particles is taking place. The experimental results underline the important role played by the particle-wall interactions on the way particles are captured during filtration. A small change in surface properties of the PDMS has important consequences in the way pore clogging occurs: in more hydrophobic conditions the particles first form arches at the microchannels entrance, then leading to the growth of a filtration cake, whereas in more hydrophilic conditions the particles are captured on the walls between the microchannels, then leading to the progressive formation of dendrites. To conclude, both experimental and theoretical approaches show the important role played by surface interactions in filtration processes. The complex interplay between multi-body surface interactions and hydrodynamics at nanometric scale leads to clogging phenomena observed experimentally in microfluidic systems that have not been predicted by numerical simulations. In the future, the two way coupling between simulation and experimental approaches at the pore scale have to progress in order to reach a full understanding of the contribution of colloid science in membrane processes.

A general approach for predicting the filtration of soft and permeable colloids: the milk example.

Membrane filtration operations (ultra-, microfiltration) are now extensively used for concentrating or separating an ever-growing variety of colloidal dispersions. However, the phenomena that determine the efficiency of these operations are not yet fully understood. This is especially the case when dealing with colloids that are soft, deformable, and permeable. In this paper, we propose a methodology for building a model that is able to predict the performance (flux, concentration profiles) of the filtration of such objects in relation with the operating conditions. This is done by focusing on the case of milk filtration, all experiments being performed with dispersions of milk casein micelles, which are sort of ″natural″ colloidal microgels. Using this example, we develop the general idea that a filtration model can always be built for a given colloidal dispersion as long as this dispersion has been characterized in terms of osmotic pressure Π and hydraulic permeability k. For soft and permeable colloids, the major issue is that the permeability k cannot be assessed in a trivial way like in the case for hard-sphere colloids. To get around this difficulty, we follow two distinct approaches to actually measure k: a direct approach, involving osmotic stress experiments, and a reverse-calculation approach, that consists of estimating k through well-controlled filtration experiments. The resulting filtration model is then validated against experimental measurements obtained from combined milk filtration/SAXS experiments. We also give precise examples of how the model can be used, as well as a brief discussion on the possible universality of the approach presented here.

Filtration method characterizing the reversibility of colloidal fouling layers at a membrane surface : Analysis through critical flux and osmotic pressure

A filtration procedure was developed to measure the reversibility of fouling during cross-flow filtration based on the square wave of applied pressure. The principle of this method, the apparatus required, and the associated mathematical relationships are detailed. This method allows for differentiating the reversible accumulation of matter on, and the irreversible fouling of, a membrane surface. Distinguishing these two forms of attachment to a membrane surface provides a means by which the critical flux may be determined. To validate this method, experiments were performed with a latex suspension at different degrees of destabilization (obtained by the addition of salt to the suspension) and at different cross-flow velocities. The dependence of the critical flux on these conditions is discussed and analysed through the osmotic pressure of the colloidal dispersion.

Formation of bacterial streamers during filtration in microfluidic systems

Bacterial behavior during filtration is complex and is influenced by numerous factors. The aim of this paper is to report on experiments designed to make progress in the understanding of bacterial transfer in filters and membranes. Polydimethylsiloxane (PDMS) microsystems were built to allow direct dynamic observation of bacterial transfer across different microchannel geometries mimicking filtration processes. When filtering Escherichia coli suspensions in such devices, the bacteria accumulated in the downstream zone of the filter forming long streamers undulating in the flow. Confocal microscopy and 3D reconstruction of streamers showed how the streamers are connected to the filter and how they form in the stream. Streamer development was found to be influenced by the flow configuration and the presence of connections or tortuosity between channels. Experiments showed that streamer formation was greatest in a filtration system composed of staggered arrays of squares 10 μm apart.

Fouling and Concentration Polarisation in Ultrafiltration and Microfiltration

The chapter summarizes different aspects to be considered in order to understand and analyse fouling and concentration polarisation of porous membranes. In a first part, the properties of fluids and membranes are described, and orders of magnitude of fluxes and forces are given. Then, transport phenomena and interactions are listed, which play a role in the mechanisms at the fluid/membrane interface. Then the modelling of these different phenomena is considered, and allows a comparison between different limiting mechanisms to be proposed.

Bacteria Delay the Jamming of Particles at Microchannel Bottlenecks.

Clogging of channels by complex systems such as mixtures of colloidal and biological particles is commonly encountered in different applications. In this work, we analyze and compare the clogging mechanisms and dynamics by pure and mixture suspensions of polystyrene latex particles and Escherichia coli by coupling fluorescent microscopic observation and dynamic permeability measurements in microfluidic filters. Pure particles filtration leads to arches and deposit formation in the upstream side of the microfilter while pure bacteria form streamers in the downstream zone. When mixing particle and bacteria, an unexpected phenomenon occurs: the clogging dynamics is significantly delayed. This phenomenon is related to apparent “slippery” interactions between the particles and the bacteria. These interactions limit the arches formation at the channels entrances and favour the formation of dendritic structures on the pillars between the channels. When these dendrites are eroded by the flow, fragments of the deposit are dragged towards the channels entrances. However, these bacteria/particles clusters being lubricated by the slippery interactions are deformed and stretched by the shear thus facilitating their passage through the microchannels.