Measuring hydraulic layer resistance and correlated effects in colloidal fouling of salt-retaining membranes

Colloidal fouling is one of the main reasons for the reduced ef ﬁ ciency of membrane-based water desalination processes. The synchrony of several resistance mechanisms like hydraulic, osmotic, and electro-kinetic as well as numerous coupling effects complicate the analysis of their individual contributions to the fouling extent. A new measuring approach using a dead-end ﬁ ltration test-cell allows exactly this, irrespective of any simultaneously occurring concentration polarization phenomena. First results show that the hydraulic resistance of a fully developed colloidal layer is not exclusively determined by the physicochemical properties of its constituents but seems to be strongly dependent on the speci ﬁ c way of its formation (e.g. ionic strength prevailing during layer build-up or ﬁ ltration sequence of different particle sizes). This time-dependent effect is largely irreversible and therefore most likely due to persistent changes in fouling layer structure. A minor reversible ionic strength effect could also be demonstrated. The extent of this effect is identical irrespective of whether the ionic strength is increased or decreased. Results further indicate that commonly applied models like the Kozeny – Carman equation are lacking a size-dependent parameter that causes a disproportionate decrease of colloidal fouling layer resistance with decreasing foulant particle size.


INTRODUCTION
The deposition of water constituents on the membrane surface in solid or gel-like form (fouling) usually has the effect that a fluid passing the membrane at a constant rate experiences a higher pressure drop than in an equivalent case without fouling. This additional pressure loss significantly influences the total energetic efficiency of the filtration process and is attributed to molecular friction in the stationary fouling layer. This 'hydraulic' resistance is frequently referred to as a pure material parameter that is solely determined by the geometric properties of the substances that form the fouling layer. Since membrane desalination processes are usually applied to treat raw waters with low particulate loads, the relevant fouling substances are mostly in the colloidal size range. Nevertheless the models that are commonly applied to describe colloidal fouling layer resistance are usually based on concepts that have been developed for macroscopic (particulate) systems.
Most of these models only work within the scope of the Darcy equation and incorporate the significant structural parameters of the respectively described layers. Among the most accepted and frequently applied semi-empirical models for the description of densely packed particle layers are the models of Brinkman, Rumpf and Gupte, as well as the well-known model of Kozeny and Carman (Dullien ). For suspended layers and macromolecular gels that lack a defined pore structure mostly cell models like This is an Open Access article distributed under the terms of the Creative that of Happel or Kuwabara are applied (Masliyah & Bhattacharjee ).
The attempt to analytically verify the applicability of such models for the colloidal size range has often failed due to the limitations of the available in-situ visualization techniques. Due to this, the structural properties of colloidal layers, as they usually form under practically relevant operating conditions on desalination membranes, have never been systematically specified in a representative and reliable way. On the other hand, a quantitative evaluation of the predictive accuracy of these resistance models is challenging even under well-controlled laboratory conditions, as the measured increase in transmembrane pressure (TMP), mostly taken as an indicator for changes in the hydraulic resistance, is actually a kind of sum parameter that quantifies the effectiveness of various resistance mechanisms simultaneously.
Besides the 'hydraulic' resistance mechanisms, which are related to molecular friction effects, the TMP increase in membrane-based desalting applications is most significantly affected by osmotic and electro-kinetic mechanisms A colloidal layer structure is particularly susceptible to changes in raw water ionic strength strongly affecting the electrostatic repulsion between like-charged particles. In this context a deviation from the practically relevant filtration conditions for the purpose of a selective experimental analysis of individual resistance mechanisms has to be assessed critically.
The differentiation between individual contributions of superimposed resistance mechanisms is further complicated by the existence of coupling effects that relate the effectiveness of a resistance mechanism (as well as the extent of its contributed resistance) to the simultaneous occurrence and the effectiveness of another resistance mechanism. A prominent example of this kind of coupling effect is the cake enhanced osmotic pressure (CEOP) phenomenon (Hoek & Elimelech ; Sim et al. ), whereby the diffusibility of salt ions that are retained by the membrane is reduced by the predetermined tortuous pathways in the porous colloidal fouling layer (Shen & Chen ). The respectively increased ion concentration at the feed-side membrane surface leads to an increase in concentration polarization (CP) and consequently in transmembrane osmotic pressure. Nevertheless, in the presence of dense fouling layers, which possess salt-retaining properties by themselves, contrary effects were also observed (Kim et al. ). Other coupling effects are, for example, related to fouling-induced changes in the ion retentive characteristics or the water permeability of the applied membrane materials (Lipp et al. ; Mahlangu et al. ). Due to the practically difficult differentiation between resistance mechanisms and coupling effects the contribution of specific coupling effects to the overall resistance has rarely been described quantitatively.
Depending on the considered raw water qualities and the specifically applied operating conditions the existing studies differ widely in the assessment of their relative importance.
The present study aimed to develop a new measuring procedure that enables the quantitative separation between different types of hydraulic layer resistances and correlations with their respective causes. Since the physicochemical circumstances that influence the formation of fouling and/or CP layers are often heterogeneous and difficult to control across the full filtration module length, this goal can hardly be achieved in cross-flow (CF) mode.

MATERIALS AND METHODS
The measuring procedure has been specifically developed in order to quantify individual resistances of typical fouling layer types. Due to the well controllable and highly reproducible physicochemical filtration conditions, a dead-end (DE) filtration method is chosen instead of more commonly applied CF filtration methods. Thereby, the limited practical relevance of the method in desalting applications is accepted in favor of the potentially significant lesser susceptibility against system-specific measuring artifacts. The direct comparison of DE and CF measuring methods, however, is beyond the scope of the present article and will be a topic of future publications. In order to evaluate the accuracy of the method and allow for comparison of measuring results and predictions of geometry-based resistance models, only model foulants with ideal geometrical properties are applied.

Methodological considerations
When a membrane is operated in CF mode, CP is affected twofold. Firstly CF induced flow field instabilities within the feed flow channel limit the thickness of the CP-layer. According to film-layer theory this instance has a direct effect on the salt concentration gradient and the mass transfer in the layer. Secondly the total amount of salt within the membrane module and therewith the maximum extent of CP is restricted.
When a fouling layer is established at the membrane surface, which partially or fully superimposes the CP-layer, the hydrodynamic conditions that the CP-layer is exposed to change and CP as well as its related effect on TMP are affected to an unknown (highly situation-specific) extent.
The implications of further influences that change the mass transfer within the CP-layer, e.g. CEOP, can hardly be distinguished from that effect. Therefore, with respect to the notations given in Figure 1 (1) c s,p c s,b ¼ 1 and respectively ℜ app M,s ¼ considered as a limiting concentration for a given filtration situation that is independent of the applied (constant) water flux according to condition 3.

Filtration apparatus
Colloidal fouling experiments were performed using a was experimentally determined to be 2.43(±0.07)·10 13 m À1 .
Surface zeta potential was determined to be À46.2(±1.9) mV using Zetasizer Nano ZS with a measuring cell ZEN1020 (Malvern Instruments Ltd, Malvern, UK). For each experiment a new membrane was used, which was thoroughly rinsed with water and kept soaking in ultrapure water for a minimum of 12 h before usage.

Feed waters
Particle-and salt-free water (PW) was generated from tapwater by applying mixed bed ion exchange (TKA DI 2800, Thermo Scientific, Waltham, MA, USA) followed by an in- In this relation the index 0 indicates that the corresponding parameter is measured under steady-state conditions (after a steady state in TMP has been reached); η w represents the dynamic viscosity of pure water.
Since for each fouling experiment a new membrane was applied, each experiment started with determining the pressure loss across the membrane Δ p 0 M by filtering ultrapure water at a constant rate of 50 lm À2 h À1 . In the subsequent phases the osmotic pressure loss Δπ 0 M and the pressure loss across a fouling layer Δ p 0 F were individually determined by measuring the increase in TMP 0 tot associated with a respective (temporal) change in the feed water quality. In the case of Δ p 0 F the feed water was temporarily spiked with foulant particles that settled onto the membrane surface. The temporal filtration of a salt solution was found to have no permanent effect on Normalization of R 0 F with respect to the filtered foulant mass M F per membrane area A M gives the specific hydraulic resistance at steady state α 0 in whichM M is the surface loading of the membrane or 'membrane load'.

RESULTS AND DISCUSSION
Effect of membrane load in a salt-free environment  Figure 3 shows a strictly linear relationship between particle load and hydraulic resistance, which is a basic requirement for the application of model relations based on Darcy's law.
However, the declining progression of the specific hydraulic resistance plotted on the right vertical axis shows that the relation cannot be considered linear over the complete range of particle loadings. This finding is most possibly due to the well-known effect that the particle layers that are immediately adjacent to the membrane surface usually create a significantly higher hydraulic resistance than the   repulsion force acting between two spherical particles 1 and 2 can be estimated by using the following equation: in which d eff is the effective particle diameter with By using the parameter values specified in Table 2, Equation (3) yields 1.9·10 À13 N for the maximum repulsing force (attractive forces are disregarded). This force is counteracted by the combined structural and frictional force F fr imposed on a single particle.
Considering a monodisperse colloidal layer as consisting of an unknown number of particle sublayers, each containing an equivalent number of particles that are exposed to identical structural and frictional forces F fr , and further assuming that the pressure drop, as presumed by Darcy's law, linearly increases sublayer by sublayer with layer depth, then F fr is a function of the ratio of layer thickness at point z (' z ) to the total layer thickness (' F ) and the inflow cross-section of a representative particle A p : With respect to the measured data shown in Figure 3, Δ p 0 F for a relatively thin 28 nm PS layer (membrane load 10 g/m 2 ) is ∼23,000 Pa. Equating Equations (3) and (5) and solving yields 0.14 for ' z =' F . This result indicates that, even for rather thin fouling layers, only in less than 1% of all constituting sublayers (monolayers) repulsive forces are not overcome by frictional forces.
In this simple estimation the pressure loss is assumed to be a linear function of the layer depth. This assumption is, to some extent, unrealistic since, due to the influence of neighboring particles, densely packed particle layers produce higher hydraulic resistances (and therefore pressure loss) than electrostatically stabilized monolayers with comparably high porosities. Nevertheless, the consideration of this instance as well as the incorporation of the effect of attractive van der Waals forces in this context yields only a slightly higher value of 5.5% (Keller ).
By taking into account these considerations it can be accepted that monodisperse layers that are built up (and consolidated until reaching a steady state) in PW feature porosities close to 36%, which corresponds to the densest random packing of equal spheres (Gotoh & Finney ).
If, however, a layer porosity of 36% is applied in calculations with the traditional models of Kozeny-Carman (KC), using κ ¼ 5 as the porosity-dependent constant, Rumpf, Happel, and Kuwabara (see the Introduction), these models strongly overestimate the respectively measured resistance, as depicted in Figure 4.
Effect of colloid size and particle size distribution in a salt-free environment In Figure 5 the measured specific resistances of different colloid size (28 nm; 280 nm; mixture of both) PS fouling layers are compared to the respective KC-predictions. Since smaller-size particles (diameter d d ) fill-up spaces between the larger-size particles (diameter d D ), a bi-disperse particle layer is generally considered to have a lower porosity than a monodisperse layer made from identical material. To account for this effect the semi-empirical correlation of Dias et al. (2004) is used to calculate the porosity ε bi of the bi-disperse mixture from the given volume fraction of larger-size particles in the mixture X D : In accordance with the prior considerations the porosity of a monodisperse layer of the smaller-size particle fraction ε 0 d is assumed to be 36%. The results depicted in Figure 5 show that the overestimation of layer resistance by the model theory, as described in the preceding section, only applies to layers that contain 28 nm particles. For monodisperse 280 nm particle layers, the KC-results (cf. markers labeled 'Kozeny-Carman' in Figure 5) agree with measured values within the acceptable margin of error. This result indicates that in the colloidal size range an additional strongly sizespecific effect has to be considered that reduces the measured hydraulic resistance with decreasing particle size. Since both applied particle sizes are considerably bigger than the pore size of the applied nanofiltration membrane, obstruction of pores (as proposed by classical pore-blocking models) is not considered a significant reason for the measured fouling-related resistance increase.   When the initially described assumption, regarding the balance of inter-particle hydrodynamic and electrostatic forces, is correct, a colloidal fouling layer in steady state should have reached a consolidated state where the strongly distance-dependent adhesive forces are fully established and the particle arrangement is mostly fixed. Thus, it is hypothesized that if a bi-disperse particle layer is formed by subsequent filtration of particle sizes (with an intermediate consolidation phase between the filtration steps) the structure of the first built layer should be at least partially maintained when the second particle layer is generated on top. It is to be expected that the resulting layer structure causes a different specific hydraulic resistance than the mixed layer shown in Figure 5. This hypothesis is confirmed by the results of the respective layer formation experiment shown in Figure 6. In the case of the layers built in a twostep procedure (280 on 28 nm; 28 on 280 nm) the second particle size was filtered after the initially produced layer had adopted a steady-state hydraulic resistance. The depicted results basically confirm the assumption of a rather strong structural integrity of once consolidated layers.
The results indicate that, when 280 nm particles are filtered on top of a consolidated layer of 28 nm particles, an almost ideal two-layer structure is formed (cf. Figure 7(a)) that is only marginally higher than the value calculated from the individually measured monodisperse layer resistances (labeled 'sum of separate measurements'). The significantly higher resistance of a layer built with an opposite particle size sequence (28 on 280 nm) is most likely due to the infiltration of 28 nm particles into the existing skeleton of larger-size particles. While passing the skeleton it is quite likely that a portion of the smaller-size particles is retained within the skeleton by some 'deep bed filtration effect' (cf. Figure 7(b)). The retained fraction does not contribute to the formation of a highly compact particle zone in the vicinity of the membrane (compaction zone). Since this compaction zone is assumed to be the major source of resistance in the bi-disperse layer, the deep bed filtration effect potentially reduces the hydraulic resistance of the bi-disperse layer. When particle sizes are filtered simultaneously this deep bed filtration effect is absent, which leads to the formation of the compaction zone in its maximum extent (cf. Figure 7(c)) and a maximum hydraulic resistance respectively (cf. Figure 6). A rather perfect accumulation of all 28 nm particles in the compaction zone was confirmed by scanning electron microscopy (results provided elsewhere (Keller )).

Effect of ionic strength
It has been shown in numerous studies that the colloidal fouling layer resistance is strongly affected by the feed ionic strength. The possible reasons for that affection are manifold and will not be discussed in detail at this point. Generally there has to be distinction between dispersion destabilizing effects, which are basically due to shielding of repulsive electrostatic interaction-forces, and the effects which occur after a fouling layer is formed (i.e. CEOP).
While destabilizing effects are considered to (  electrostatic forces is supposed to be biggest in PW (Israelachvili ). When the identified ionic strength dependency of hydraulic layer resistance is solely attributed to the changing inter-particle distances maintained by electrostatic repulsion forces, the porosity of a layer formed in SS (low inter-particle distance) should be significantly lower than that of a layer formed in PW (high inter-particle distance). In order to prove this assumption, the theoretical layer porosities were calculated for each measured resistance value by using the KC-relation (κ ¼ 5). For easier classification of the results the resistance for a hypothetical layer of particles with direct surface contact between the particles (ε ¼ 36%) is shown on the right.
The respective values given in Figure 8 show that even for layers formed in SS, a porosity of more than 50% has to be accepted in order to match predictions with measured values. With respect to the previously provided considerations, such high values appear to be rather unrealistic. A permanent increase in inter-particle spacing due to electrostatic repulsion effects, therefore, seems to be a rather unlikely explanation for the high discrepancy between measured values and model predictions. show a strict linear relation between resistance increase and membrane load. Therefore, in order to describe the layer resistance, Darcy-type relations seem to be applicable when the influence in feed ionic strength is respectively considered.
The respectively measured values are shown in Figure 9.

CONCLUSIONS
Within the presented study a measuring approach is proposed and tested that enables the determination of hydraulic resistances generated by any kind of spatially homogeneous layer that covers the feed site membrane surface. The method particularly distinguished itself from