Flows film splitting

Figure 9, A schematic of the film splitting flow in forward roll coating. Reproduced from Coyle et ai, copyright 1986 [40]. Reprinted with the permission of Cambridge University Press.

The Galerkin finite element method is successfully applied to flow in a relatively simple element of roll coating symmetric film-splitting in the nip region between smooth, rigid, counterrotating rolls. 

Thus the objective here is a generally applicable simulation of steady, two-dimensional, incompressible flow between rigid rolls with film splitting. The results reported are solutions of the full Navier-Stokes system including the physically required boundary conditions. The analysis is also extended to a shearthinning fluid. The solutions consist of velocity and pressure fields, free surface position and shape, and the sensitivities of these variables to parameter variations, valuable information not readily available from the conventional approach (10). The rate-of-strain, vorticity, and stress fields are also available from the solutions reported here although they are not portrayed. Moreover, the stability of the flow states represented by the solutions can also be found by additional finite element techniques (11), and the results of doing so will be reported in the future. 

As with any theoretical prediction, the calculation itself must be validated, and the prediction has to be held up against as closely comparable an experiment as is available. Comprehensive validation of the present calculations will be detailed elsewhere. As for experiments, unfortunately few details of the flow field are fully described in the literature. Pitts and Greiller (1) detected the eddies, but did not indicate over what parameter ranges eddies were or were not present. They did, however, measure where the film splits in a number of experiments. 

Coyle, D.J., Macosko, C.W., and Scriven, LE. (1987) Film-splitting flows of shear-thinning liquids in forward roll coating. AIChE J., 33, 741-746. 

Fig. 13. Bubble column flow characteristics (a) data processing system for split-film probe used to determine flow characteristics, where ADC = automated data center (b) schematic representation of primary flow patterns.

As a result of asperity contact, the nominal contact zone is split into a number of discrete areas that can be cataloged either to the lubrication region or asperity contact area (Fig. 2). The mean hydrodynamic pressure in the lubrication regions, pi, can be calculated by the average flow model, while contact pressure is estimated via Eq (7). Consequently, the film thickness is determined through numerical iterations to... 

Chromatographic Conditions. GC/MS-MS analyses were performed on a Varian 3800 gas chromatograph (Varian Chromatography Systems, Walnut Creek, CA) equipped with a 1079 split/splitless injector and a ion trap spectrometer (Varian Saturn 2000, Varian Chromatography Systems) with a waveboard for MS-MS analysis. The system was operated by Saturn GC/MS Workstation v5.4 software. The MS-MS detection method was adapted from reference. PCBs were separated on a 25 m length x 0.32 mm i.d., CPSil-8 column coated with a 0.25-pm film. The GC oven temperature program was as follows 90 °C hold 2 min, ramp 30 °C/min to 170 °C, hold for 10 min, rate 3 °C/ min to 250 °C, rate 20 °C/min to a final temperature of 280 °C, and hold for 5 min. Helium was employed as the carrier gas, with a constant column flow of 1.0 mL/min. 

Heat the sample for 30 min at 30°C while purging helium at a rate of 25 ml/min. Collect volatile compounds on the trap (packed with Tenax or equivalent) and thermally desorb at 180°C onto a 30-m x 0.32-pm i.d. x 1-pm film thickness fused-silica capillary column. After desorption is complete, hold the initial temperature for 1 min at -20°C and then program the temperature to ramp to 220°C at 6°C/min. Set the injector and the detector temperatures at 260°C and 280°C, respectively. Use helium as carrier gas at a flow rate of 3.0 ml/min and a split ratio of 20 1. 

Plastic tube and tubular films are formed continuously by extruding a polymer through an annular die. The annular flow channel is formed by the outer die body and the die mandrel. A number of annular die designs are currently employed. In the first, the mandrel is supported mechanically onto the outer die body by a number of fins called spider legs Fig. 12.41 illustrates this type of die. The flow is axisymmetric, and the only serious problem encountered in the cross-machine direction uniformity of the extruded product is that of weld lines and streaks caused by the presence of the spider legs, which split the flow. 

The refractive index detector is popular in prep units because it is universal and less sensitive. UV detectors are often too sensitive, and short path length cells are needed. Alternatively, the UV detector can be detuned to a less sensitive wavelength, or the effluent stream can be split, sending only part of it through the detector. A unique UV detector uses a thin film instead of a cell and claims typical path lengths around 0.2 mm and flows up to 400 mL/min.78... 

Procedure (See Chromatography, Appendix IIA.) Use a gas chromatograph capable of split and splitless capillary column injection and equipped with a flame ionization detector and a 25-m x 0.53-mm (id) fused-silica capillary column coated with a 2.0-p.m film of 5% phenyl/95% methylsilicone liquid phase, or equivalent, and a 30-m x 0.32-mm (id) fused-silica capillary column, or equivalent, coated with 1.8-p.m film of (6% cyanopropylphenyl) methylpolysiloxane liquid phase, or equivalent, connected in series, with the first column that was described placed behind the second. Set the injector temperature to 150°, the detector to 250°, and the oven to 40° isothermal. Use helium as the carrier gas at a flow rate of 4.4 mL/min. Set the split flow at a rate of 98 mL/min. 

Procedure Inject 1-pL aliquots of the Standard Preparation and the Sample Preparation into a gas chromatograph equipped with a split injector, a flame-ionization detector, and a 25 -m fused silica capillary column coated with a 2-pm film of 7% cyanopropyl-7% phenyl-85% methyl-1% vinylpolysiloxane (CP-Sil 19 CB, Chrompack Middelburg, or equivalent). Maintain the column at 100°, raising the temperature at 8°/min to a final temperature of 300°. Set the injector temperature to 270°and the detector temperature to 270°. Use a mixture of helium and methane, at a split ratio of 1 100, as the carrier gas, flowing at 120 mL/ min. Run the chromatogram for 27 min. 

In actual use for mobility control studies, the network might first be filled with oil and surfactant solution to give a porous medium with well-defined distributions of the fluids in the medium. This step can be performed according to well-developed procedures from network and percolation theory for nondispersion flow. The novel feature in the model, however, would be the presence of equations from single-capillary theory to describe the formation of lamellae at nodes where tubes of different radii meet and their subsequent flow, splitting at other pore throats, and destruction by film drainage. The result should be equations that meaningfully describe the droplet size population and flow rates as a function of pressure (both absolute and differential across the medium). 

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