Capillaries pressure drop

The capillary pressure drop, AP caused by pores with an efiective radius r for each capillary is given by... 

In the real LHP design capillary pressure drop APc depends on some LHP parameters ... 

In the slip-casting process a capillary pressure drop AP between the support pores (with radius r in case of cylindrical capillaries) and the liquid drives the liquid into the support and through the formed gel layer. This is schematically shown in Fig. 8.3. The total pressure drop AP. (generated by the support pores)... 

The assumption that the aqueous foam film is plane parallel avoids introducing a pressure gradient in the film because the Laplace pressure jump is therefore everywhere zero. The resulting condition for equilibrium of the bridging drop is then only that the capillary pressure drop across the oil-water surface should equal that across the air-oil surface as is the case for a lens. However, a later treatment by Denkov [55] relaxes this requirement that the film be plane parallel. Here we consider the simpler plane-parallel case first before considering the latter. 

Substituting the appropriate values shows that the capillary pressure drop will increase from 78% to 100% of the applied pressure as the melt flow indexer goes from completely filled to empty. Thus, a 50% increase in the output rate is possible, as has been shown for polyethylene (PE) by Skinner [13]. With PF, the position is shown to be worse by Charley [IS], who performed extensive experiments for using the MFI test for molten PP. Despite this time-dependent deformation behavior, there is no conection recommended for entrance and exit abnormalities. This would also be difficult to specify, because the conections would be expected to vary from polymer to polymer. 

The acoustic pressure that is required to eject an ink droplet is shown schematically in Figure 6.9. To eject an ink drop, the acoustic pressure that is generated by the electrostatic actuator must overcome the viscous pressure drop required to push the ink through the nozzle ( 0.5-1 atm), the capillary pressure drop due to surface tension ( 0.1 atm), and the dynamic pressure of the liquid associated with its kinetic energy ( 0.5 atm). The total acoustic pressure required to eject a drop will be on the order of 1-2 atm of pressure. 

The lumped elements between A and B, C and D, and E and F have pressure drop due to friction. The pressure drop between B and C, and D and E is attributed to the interface. The advancing and receding interface contributes either positively or negatively to the capillary pressure drop, which is a function of contact angle. For a spherical interface of curvature radius of the advancing front, the pressure difference can be written based on Young-Laplace equation as... 

In a similar way, we may solve the same problem for two droplets of different composition with different interfacial tensions, y, and 72, of the first and the second droplet, respectively. In this case, even for the droplets of the same radius, the interlayer on the whole proves to be curved owing to the appearance of a capillary pressure drop, AP = (yj - 72)// . 

First, we determine the value of the static advancing contact angle, 0. For the motion of the meniscus in front of the capillary, the pressure in the liquid phase must be increased, which diminishes the capillary pressure drop at the meniscus-gas interface. Consequently, in this case, P < Pe and AP < 0. This means that curve /(fi, P) (curve 4) is located below curve /(fi, P ) (curve 3) in... 

Several conclusions can be drawn from Fig. 7. First, the capillary pressure drops. Pc, determined from the Bagley plot and from calcixlations using Eq. 8 and 9, agree with each other. Secondly, the Bagley plots are slightly curved at high L/D values. This upward curvature is attributed to a combination of compressibility of the melt and the pressure dependence of viscosity [16]. Thirdly, Pe increases when the temperature decreases and when the capillary ratio (L/D) decreases. 

To study the effect of phase separation on die pressures, we compared measurements of Pdie with the calculated capillary pressure drops (Pc) using Eq. 8 and 9. The calculations made use of the single-phase viscosity... 

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