Pressure Drop - With Film

To calculate the pressure drop using the above equation, the film thickness is crucial. It can be estimated using Bretherton s or Aussillon and Quere s correlations depending on the capillary number (Equations 7.2 or 7.3) as demonstrated in Example 7.6. 

Example 7.6 Pressure drop in liquid-liquid slug flow 

A liquid-liquid system flows in a circular cross section capillary with ( = 0.8mm diameter forming a continuous water phase and a dispersed toluene phase. The flow rate of the continuous phase is Smlmin while the flow rate of the dispersed phase is 4mlmin k Estimate the pressure drop in the microchannel assuming dispersed slug velocity equals the two-phase velocity. 

As the two-phase systems form dispersed and continuous phase. Equation 7.53 can be used. It requires single-phase pressure drop and k. The singlephase pressure drop can be calculated using Hagen-Poisseuille equation (Equation 7.42). 

The single phase pressure drop of the continuous phase is calculated with the velocity of the two-phase system (n = + Uc) or flow rate two phases. 

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It is necessary to mention that an avalanche-like destruction is also observed in a NaDoS foam but it occurs at significantly higher pressure drops with respect to the equilibrium pressure pa (see Fig. 6.12,a). That is why it is important to distinguish between the destruction at equilibrium critical Apcr,e and at non-equilibrium critical Apcrne pressures since probably the causes are different. Foam destruction at Apcre is perhaps due to foam film rupture while at Apcr ne the destruction results from other phenomena occurring in the disperse... 

The film pressure is defined as the difference between the surface tension of the pure fluid and that of the film-covered surface. While any method of surface tension measurement can be used, most of the methods of capillarity are, for one reason or another, ill-suited for work with film-covered surfaces with the principal exceptions of the Wilhelmy slide method (Section II-6) and the pendant drop experiment (Section II-7). Both approaches work very well with fluid films and are capable of measuring low values of pressure with similar precision of 0.01 dyn/cm. In addition, the film balance, considerably updated since Langmuir s design (see Section III-7) is a popular approach to measurement of V. 

Some empirical equations to predict cyclone pressure drop have been proposed (165,166). One (166) rehably predicts pressure drop under clean air flow for a cyclone having the API model dimensions. Somewhat surprisingly, pressure drop decreases with increasing dust loading. One reasonable explanation for this phenomenon is that dust particles approaching the cyclone wall break up the boundary layer film (much like spoiler knobs on an airplane wing) and reduce drag forces. 

Zirconium is a highly active metal which, like aluminum, seems quite passive because of its stable, cohesive, protective oxide film which is always present in air or water. Massive zirconium does not bum in air, but oxidizes rapidly above 600°C in air. Clean zirconium plate ignites spontaneously in oxygen of ca 2 MPa (300 psi) the autoignition pressure drops as the metal thickness decreases. Zirconium powder ignites quite easily. Powder (<44 fim or—325 mesh) prepared in an inert atmosphere by the hydride—dehydride process ignites spontaneously upon contact with air unless its surface has been conditioned, ie, preoxidized by slow addition of air to the inert atmosphere. Heated zirconium is readily oxidized by carbon dioxide, sulfur dioxide, or water vapor. 

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