Membrane hydrodynamic forces

Fig. 14.5. Experimental rejection (o) and theoretical prediction of the critical pressure for filtration of BSA in 0.001 M NaCI solution at pH 9 at a membrane of mean pore diameter 84 nm. Rejection is high below the critical pressure as electrical double layer repulsion prevents the protein (effective spherical diameter 6nm) from entering the membrane pores. As the critical pressure is approached, hydrodynamic forces increase and drive the...

Fig. 14.6. Filtration flux as a function of time of filtration for the filtration of O.Oi g/L silica particles in 0.001 M NaCI solution at pH 6 at a membrane of mean pore diameter 84 nm. The particle size was very close to the pore size. The critical transmembrane pressure for these conditions was calculated as 130 kPa. Operation below this pressure gives only a gradual decline in filtration flux with time. Operation above this pressure gives an initially higher filtration flux which declines rapidly with time. In the latter case the intial hydrodynamic force exceeds the electrical double layer repulsion between the membrane and the particles, causing the particles to block the membrane pores.

The extrinsic pathway is activated by tissue injury and is not of major concern in the clinical use of membrane devices. The intrinsic pathway, however, is initiated by a multitude of factors. Including interactions between serum proteins and exogenous materials. Hydrodynamic forces acting on platelets may also lead to the release of platelet factors that trigger the intrinsic pathway. Thus, the selection of membrane materials to minimize thrombogenesls cannot be fully separated from the design of devices to contain them because of this potential for shear forces to activate the clotting cascade. 

Separation and concentration of high-molecular-weight solutes from low-molecular-weight solutes by application of hydrodynamic force over the solution above a semipermeable membrane (ultrafiltration). 

In these expressions, me, Vc, Fd, F, X, a, H, t, 17, p, R, DLVO force, the hydrodynamic force, the scaled distance, the linear radius of the cells, the dimensionless closest half surface-to-surface distance between two cells, the scaled half separation distance between two cells, the time, the viscosity of liquid phase, the hydrodynamic retardation factor, the density of the cells, the gas constant, the scaled DLVO potential, the scaled van der Waals potential, and the Hamaker constant of the system, and i, , and I are dummy variables. Note that the fourth and fifth integral terms on the right-hand side of (25.141) represent, respectively, the contribution to the electrostatic repulsion force when the fixed positive and negative charge in the membrane phase of a cell appears. Equation (25.135) can be rewritten to become... 

DLVO force (kg m/s ) hydrodynamic force (kg m/s ) scaled electrostatic repulsion force (-) friction factor of the cell membrane (-) parameter for expression of electrostatic potential in region 111 (-)... 

Dissipation may also occur by mass transport of particles in the bulk of the phase. Work must be done against the frictional forces of the medium through which the particle moves. In solids, migration and diffusion are usually important in liquids and membranes, hydrodynamic mass transport must also be considered. 

One of the most useful practical operating concepts for membrane processes is that of a critical filtration flux or critical operating pressure. These critical parameters are such that below such critical values rejection will occur and fouling will be minimum, while above these critical values both transmission and fouling may take place. For colloidal particles, the critical values may arise as a balance between the hydrodynamic force driving solutes toward a membrane pore and an electrostatic (electrical double layer) force opposing this motion. 

The dynamical behavior of fluid vesicles in simple shear flow has been stodied experimentally [190-193], theoretically [194-201], numerically with the boundary-integral technique [202,203] or the phase-field method [203,204], and with meso-scale solvents [37,180,205]. The vesicle shape is now determined by the competition of the curvature elasticity of the membrane, the constraints of constant volume V and constant surface area S, and the external hydrodynamic forces. 

The factors to consider in the selection of crossflow filtration include the flow configuration, tangential linear velocity, transmembrane pressure drop (driving force), separation characteristics of the membrane (permeability and pore size), size of particulates relative to the membrane pore dimensions, low protein-binding ability, and hydrodynamic conditions within the flow module. Again, since particle-particle and particle-membrane interactions are key, broth conditioning (ionic strength, pH, etc.) may be necessary to optimize performance. 

Similar instability is caused by the electrostatic attraction due to the applied voltage [56]. Subsequently the hydrodynamic approach was extended to viscoelastic films apparently designed to imitate membranes (see Refs. 58-60, and references therein). A number of studies [58, 61-64] concluded that the SQM could be unstable in such models at small voltages with low associated thinning, consistent with the experimental results. However, as has been shown [60, 65-67], the viscoelastic models leading to instability of the SQM did not account for the elastic force normal to the membrane plane which opposes thickness... 

As follows from the hydrodynamic properties of systems involving phase boundaries (see e.g. [86a], chapter 2), the hydrodynamic, Prandtl or stagnant layer is formed during liquid movement along a boundary with a solid phase, i.e. also at the surface of an ISE with a solid or plastic membrane. The liquid velocity rapidly decreases in this layer as a result of viscosity forces. Very close to the interface, the liquid velocity decreases to such an extent that the material is virtually transported by diffusion alone in the Nernst layer (see fig. 4.13). It follows from the theory of diffusion transport toward a plane with characteristic length /, along which a liquid flows at velocity Vo, that the Nernst layer thickness, 5, is given approximately by the expression,... 

The hydrodynamic shear forces at the membrane surface tend to reduce the boundary layer and keep the membrane clean. 

Plasmapheresis typically employs a membrane module of similar configuration as a high-flux hemodialyzer. Alternatively, a rotating membrane separation element is used in which the tendency of the blood cells to deposit on the membrane surface is counteracted with hydrodynamic lift forces created by the rotation. The membrane element and the associated plasmapheresis circuitry are shown in Fig. 49. Worldwide, about 6 million plasmapheresis procedures are performed annually using this system, making this one of the largest biomedical membrane applications after hemodialysis. 

A further experimental problem is caused by the action of hydrodynamic lift forces in A-Fl-FFF. As the mean carrier fluid velocity varies along the channel length in the rectangular channel geometries, the equilibrium positions of the particles also vary. Hence conditions may be encountered where the carrier velocity close to the outlet of a rectangular A-Fl-FFF channel falls to such a low level that lift forces are unable to counter the drag of the flow through the membrane. These particles then make contact with the membrane and do not elute [250]. 

In Fl-FFF, the channel is created by placing a mylar spacer with the channel cut out between two porous frits. A membrane hlter of a specihc molecular weight cutoff is placed on one of the frits and acts as the accumulation wall to permit flow, without loss of particles. The applied force is then a perpendicular flow of the carrier solution across the porous frits. Fl-FFF is a versatile technique capable of separating macromolecules as small as roughly 1000 Da, in which case it is comparable to gel permeation (size exclusion) chromatography. However, Fl-FFF can also be applied to the separation of colloidal particles. In this case the hydrodynamic diameter of the colloidal particle is related to the retention volume, V by the equation... 

Under an applied driving force (pressure, voltage or concentration difference), the fluid streams in a membrane reactor arc split or combined possibly at various locations of the reactor. The hydrodynamics of the fluid streams, its interactions with the process and reactor parameters and the fluid management method largely determine the reactor behavior. 

Most commercial systems like Mustang from Pall and Sartobind from Sartorius make use of functionalized microporous membranes. The fibrils reinforced membranes are (pleated) layered around a porous core. The feed is forced to permeate through the membranes in radial direction. This approach results in high area to volume ratio. The 3M and Mosaic Systems approach is different. Instead of functionalization of a porous support they make use of already functionalized beads, which are embedded in a porous support. In this approach, the beads are responsible for the capacity and selectivity where the porous matrix controls the hydrodynamics. The 3M modules consist of stacked flat sheet or pleated membranes, while Mosaic Systems makes use of porous fibers in which the active particles are embedded (Figure 3.23). 

The aggregation rate of colloidal and particulate materials is dependent on the permeation rate, hydrodynamics, and surface forces between the membrane and colloid material, therefore fouling rates are system dependent. However, certain broad trends are evident with respect to fouling. Below a certain permeation rate the TMP varies linearly with flux and above this transition flux, a sharp increase in TMP is observed concomitant with a permeate flux decline. A time-dependent flux decline is also... 

Membrane Formation. In earlier work. 2.) it was found that fumed silica particles could be dispersed in aqueous suspension with the aid of ultrasonic sound. Observations under the electron microscope showed that the dispersion contained disc-like particles, approximately 150-200 1 in diameter and 70-80 1 in height. Filtration experiments carried out in the "dead-end" mode (i.e., zero crossflow velocity) on 0.2 urn membrane support showed typical Class II cake formation kinetics, i.e., the permeation rate decreased according to equation (12). However, as may be seen from Figure 7, the decrease in the permeation rate observed during formation in the crossflow module is only t 1, considerably slower than the t 5 dependence predicted and observed earlier. This difference may be expected due to the presence of lift forces created by turbulence in the crossflow device, and models for the hydrodynamics in such cases have been proposed. 

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