Fiber fluid dynamics

In a 1991 study by van Reis et al. (5), a filtration operation as applied to harvest of animal cells was optimized by the use of dimensional analysis. The fluid dynamic variables used in the scale-up work were the length of the fibers (L, per stage), the fiber diameter (D), the number of fibers per cartridge (k), the density of the culture (p), and the viscosity of the culture (p). From these variables, scale-up parameters such as wall shear rate (y ) and its effect on flux (L/m /h) were derived. Based on these calculations, an optimum wall shear rate for membrane utilization, operating time, and flux was found. However, because there is no single mathematical expression relating all of these parameters simultaneously, the optimal solution required additional experimental research. 

While several niche applications for OD have been identified, the commercial acceptance of the technology has been hampered by the nonavailability of a suitable membrane-membrane module combination. Fluoropolymer membranes, such as PTFE and PVDF, have been shown to provide superior flux performance, but are still unavailable in hollow fiber form with a suitable thickness for use in OD applications. The inherently low flux of OD requires fhaf membranepacking density be maximized for effective operation, and hence the available flat-sheet form of perfluoro-carbon membranes is unsuitable for commercial use. Four-port hollow fiber modules that provide excellent fluid dynamics are currently available, but only low-flux polypropylene membranes are utilized. 

A major objective of fundamental studies on hollow-fiber hemofliters is to correlate ultrafiltration rates and solute clearances with the operating variables of the hemofilter such as pressure, blood flow rate, and solute concentration in the blood. The mathematical model for the process should be kept relatively simple to facilitate day-to-day computations and allow conceptual insights. The model developed for Cuprophan hollow fibers in this study has two parts (1) intrinsic transport properties of the fibers and (2) a fluid dynamic and thermodynamic description of the test fluid (blood) within the fibers. 

Most of the membrane segregated enzyme systems previously examined suffer some constitutive drawbacks which limit their yield and area of application. When enzymes are entrapped within the sponge of asymmetric membranes, product and substrate mass transfer occur mainly by a diffusive mechanism reactor performance is then controlled only by means of the amount and kind of charged enzyme, and the fluid dynamics of the solution in the core of the fibers. UF or RO fluxes, moreover, result in enzyme losses. Enzyme crosslinking in the membrane pores can reduce these losses, but it can lead to an initial activity loss, as compared to that of the native enzyme. Of course, once the enzyme is deactivated, it makes the reactor useless for further operation. Such immobilization techniques are seldom useful for microbial cells due to their large size. 

Woerdeman, D.L., et al., 2005. Electrospun fibers from wheat protein investigation of the interplay between molecular structure and the fluid dynamics of the electrospinning process. Biomacromolecules 6 (2), 707—712. 

This is far less than the 12 mmHg quoted above for the C-DAK 4000. This difference could be due to the entering and exiting flow of dialysate normal to the fibers, which would increase the pressure drop considerably. A better estimate could be made with a computational fluid dynamics (CFD) program. 

Delaunay D, Le Bot PH, Fulchiron R, Luye JF, Regnier G (2000b) Nature of contact between polymer and mold in injection molding. Part II Influence of mold deflection on pressure history and shrinkage. Polym Eng Sci 40 1692-1700 Denn MM (2001) Extrusion instabilities and wall slip. Annu Rev Fluid Mech 33 265-287 Denn MM (2004) Fifty years of non-Newtonian fluid dynamics. AIChE J 50 2335-2345 Dinh SH, Armstrong RC (1984) A rheological equation of state for semi-concentrated fiber suspensions. J Rheol 28 207-227... 

Sdnchez D, ChertcofFR, Calvo A, Callegari G. (2007) Dewetting in fibers. Poster 31 in Pan-American Advanced Studies Institute on Interfacial Fluid Dynamics From Theory to Applications, Mar del Plata, Argentina, 6—17tb August 2007. 

Fouling deposition in crossflow membrane filtration can be indicated by the deceleration of particles on the membrane surface. PIV was used to identify early fouling phenomena (particle decelerations) and the dead zone during membrane filtration [84]. PIV has the same limitation as other optical methods, like DOTM, as it requires optically transparent solutions. However, how this technique can be extended to real module with a large number of fibers is a challenge and it may be limited to laboratory validation of bubbling and computational fluid dynamic models of MBR systems. 

The models developed in previous sections are for fiber jrartides rising in a static fluid. They do not consider lateral motion and deformation of the fluid, as well as hydrodynamic diffusion effects. Eqns. (16) and (17) are appropaiate for rmderstanding rising behavior of fibers under static conditions. However, this study is to determine the hole cleaning efficiency of the fiber particles in real world situations such as fluid circulating up the annulus and drillstring rotation. The shearing motion of the fluid in the aimulus wfll affect the apparent viscosity that subsequently influences the behavior of fiber particles in the base fluid. To accurately model the behavior of fiber imder dynamic conditions, the overall shear rate must be computed from the piimaiy and secondary flow shear rates, and the annulus is modeled as a narrow slot to obtain analytical solutions (Fig. 13). 

For all fluid-dynamic calculations, it is advisable to correct the Sauter diameter by the sphericity yielding the representative diameter based on equivalent specific surface area d. Equation (3.70) assumes a constant sphericity for all size fractions. For pulverized bituminous coal (<100 pm) sphericities between 0.73 and 0.78 are reported while for coarse bituminous coals (4-22.4 mm) somewhat lower values of 0.66-0.71 occur. For lignite fibers (xylite), sphericity may decrease to 0.38 [114,115]. 

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