Pressure drop, in capillaries

Convergent flow at the die entrance provides strong elongational flow. In 1989, Laun and Schuch, discussing the approximate methods of T g determination, derived the following relation between the entrance pressure drop in capillary flow and the shear stress at the capillary wall ... 

The analysis of power input and mass transfer in this chapter was Umited to scaling, and the results serve to demonstrate the opportunities that arise when alternatives to the contacting workhorse, turbulence, are considered. The works of BerCiC and Pintar [32] and Van Baten and Krishna [2] have elucidated the most important aspects of G/L mass transfer, and two-phase pressure drop in capillary channels is discussed in detail by Kreutzer et al. [1], but more experimental mass-transfer data is needed, in particular with using different fluids at controlled, independently varied bubble and slug lengths. 

Fig. 7.44 Entrance-exit pressure drop in capillary flow of polypropylene, polyamide-6, and commercial PP/PA-6 blend, Orgalloy at 230 °C - line computed from Eq. 7.132...

Entrance-exit pressure drop in capillary flow Heat received by the system Wavevector... 

M. Suo, Pressure drop in capillary slug Rov/.JoumalofBasic Engineering, 1968, 90, 140. 

The measured elongational viscosity, ] , for two homopolymers agreed quite well with the value calculated from the entrance-exit pressure drop in capillary flow, Pe [34] ... 

The primary contributions to pressure drop, in approximately decreasing order, will be (1) inline filters (2) needle valves (3) check valves (4) the spectroscopic cells and (5) capillary tubing. Methods for detailed calculations can be found in Ref [21]. Our experience is that total recycle pressure drop is a small fraction of a bar with normal flow rates. 

Capillary Flow Rheometry Next we examine the experimentally obtained results with the capillary flow rheometer shown in Fig. 3.1, which are directly relevant to polymer processing flows, since the attainable shear rate values are in the range encountered in polymer processing. The required pressure drop AP does not increase linearly with increases in the volumetric flow rate Q, as is the case with Newtonian fluids. Rather, increasingly smaller increments of AP are needed for the same increases in Q. The Newtonian Poiseuille equation, relating flow rate to pressure drop in a tube, is linear and given by... 

The capillary pressure was measured by two independent methods by a compensatory and closed micromanometers and by an optical method for determination of the radius of border curvature [57,58], The data in Table 5.2 indicate that at Apo = 104 Pa the final capillary pressure is equal to the applied pressure drop in all cases studied. At Ap0 = 2104 Pa the capillary pressure reaches an equilibrium value only in foams from non-ionic surfactants. For... 

A significant effect of pressure on the rate of foam destruction was not established for coarsely dispersed foams with NBF, formed by blowing air through a single capillary in a NaDoS solution (10 3 mol dm 3 containing 0.4 mol dm 3 NaCl). In these experiments the pressure drop in the Plateau borders changed from 103 to 4.5-104 Pa and the maximum... 

The viscous pressure drop in the continuous (wetting) phase provides the force necessary to sustain motion of a ganglion in spite of the capillary forces. Darcy s Law for the wetting phase may be written as ... 

In axisymmetric flow situations, the global pressure drop in a capillary rheometer is well described by the three constitutive equations. If one focuses on the entrance pressure drop, the numerical entrance pressure drop related to Bagley correction is foimd to be less important than the corresponding experimental data for the differential models for LDPE and LLDPE melts. For the Wagner integral constitutive equation, the computed entrance pressure drops are found to be lower for both fluids, but the computed values are closer to the experimental data for LLDPE than those related to the LDPE melt. This descrepancy, previously reported in the literature, needs further investigation. 

The difference in curvature radii creates a pressure drop in ceil capillaries in accordance with Laplace-Young s law... 

The total pressure drop in segmented flow, which is of the greatest interest for monolith applications for three-phase processes, may be represented as the sum of the frictional pressure drop, hydrostatic head, and capillary pressure ... 

Fukano, T., Kariyasaki, A., and Kagawa, M. (1989) Flow Patterns and Pressure Drop in Isothermal Gas-Liquid Concurrent Flow in a Horizontal Capillary Tube, Proceedings of the 1989 ANS National Heat Transfer Conference, Philadelphia, Pennsylvania, Vol. 4, pp. 153-161. 

Drainage (i.e., displacement of a wetting fluid by a non-wetting fluid) was modelled by an invasion-percolation process (Wilkinson and Willemsen, 1983). This implies that viscous forces may be ignored (i.e., pressure drops in both fluids may be ignored) and that capillary forces (pressure difference AF between the two fluids) control the process ... 

All reactions were carried out in a thermostated, magnetically stirred 50 ml autoclave (baffles, two thermocouples, X-shaped stirrer, 1=25 mm, max. 900 rpm). A reservoir and a pressure regulator allowed experiments to be carried out under isobaric conditions, p and T in the autoclave and in the reservoir were recorded every 10 s. Usually, the reactions were stopped after 10 min corresponding to conversions of 10 - 50%. Conversion and e.e. were determined by GLC-analysis of the crude reaction mixture (30 m capillary 3-Dex 100, 75°C). In all experiments with HCd modifier, the R-enantiomer was the major enantiomer. The initial rates of hydrogenation were calculated with a linear least square method from the pressure drop in the reservoir, accounting for the compressibility of hydrogen. In all series, one experiment was carried out without modifier to determine k (see below). 

In Figure 4.7, the pressure at the liquid level and at point a just above the meniscus is atmospheric. The height of the column of liquid, h, will be such that the pressure at point c in the column is also atmospheric, due to the balanced effects of hydrostatic and capillary pressures in the liquid column. The pressure at point b, just below the meniscus, will be less than atmospheric by an amount (2ylr).kt equilibrium, AP is also equal to the hydrostatic pressure drop in the liquid column in the capillary. Thus,... 

EC differs from MEKC in that it uses a real stationary phase. In essence, it is conventional LC in which the mobile phase is driven by electro-osmotic flow rather than pressure. However, as in MEKC, the mechanism of separation is mixed, with electrophoretic mobility affecting the retention of charged solutes. The stationary phase particles can be very small, as there is no pressure drop in the column. Typically, 1.5 /rm particles of Cig-modified silica are used. Promising results were also obtained with monolithic columns for EC. Capillary EC provides about twice as many plates as HPLC for the same particle size and column length. 

In these equations, is the shear stress at the capillary wall, AP. is the total pressure drop in the capillary, L is the capillary length, is an apparent length, and e is the Bagley entrance correction. 

Rapid separations are clearly desirable where sufficient selectivity exists for the particular component(s) of interest. The low pressure drop across capillary SFC columns allows the solvating properties of the fluid to be controlled by changing the pressure on a nearly instantaneous basis ( ). Additional advantages are related to the ease of pressure control and the absence of stationary phase modification which decreases reproducibility in HPLC. 

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