Liquid flow under pressure drop

The clear liquid back-up is obtained from a tray-pressure balance and is normally taken to be the sum of the tray-pressure-drop, the clear liquid height on the active area of the tray, and the pressure-drop of liquid flowing under the downcomer apron onto the active area. 

Fig. 5.3. Profile of border radius of curvature when liquid flows through a foam under pressure drop (a)...

The kinetics of establishing equilibrium pressure provides information not only about foam drainage but also for other important parameters, such as the time for reaching equilibrium state in the borders and films and the radius of border curvature and border profile during liquid flow and drainage under pressure drop. 

The surface area expansion process in Figure 3.5 must obey the basic thermodynamic reversibility rules so that the movement from equilibrium to both directions should be so slow that the system can be continually relaxed. For most low-viscosity liquids, their surfaces relax very rapidly, and this reversibility criterion is usually met. However, if the viscosity of the liquid is too high, the equilibrium cannot take place and the thermodynamical equilibrium equations cannot be used in these conditions. For solids, it is impossible to expand a solid surface reversibly under normal experimental conditions because it will break or crack rather than flow under pressure. However, this fact should not confuse us surface tension of solids exists but we cannot apply a reversible area expansion method to solids because it cannot happen. Thus, solid surface tension determination can only be made by indirect methods such as liquid drop contact angle determination, or by applying various assumptions to some mechanical tests (see Chapters 8 and 9). 

The downflowing liquid is transported from a tray to the tray below by means of conduits called down. comers, and it is evident thet if the downcomer is not sufficiently large to handle (he required liquid load, the pressure drop associated with liquid flow will serve as a constriction and a point of flow rale limitation. In fact, downcomers usually serve to bottleneck operations or high-pressure fractionators and absorbers. They must be sized such that they do not fill completely under the highest flow rates expected for the column. As will be shown, the vapor flow rate contributes toward the liquid cupacity limitation. 

Maximum vapour rates on packed and tray columns are similar, being about 1.4-1.9m/s based on the empty column area. As indicated under Pressure drop , the pressiue drops over trays will be a good deal greater so that the absolute pressure at the column top is likely to be lower in vacuum operation and the mass flow will be correspondingly less. Vendors of column internals, most of whom are able to supply both trays and column packing systems, can provide information on the details of their products in respect of their liquid and vapour performance, but a turndown of 3 1 on packed columns and 5 1 on trays should be attainable (Fig. 4.7). 

The second mechanism can be explained by the wall liquid film flow from one meniscus to another. Thin adsorptive liquid layer exists on the surface of capillary channel. The larger is a curvature of a film, the smaller is a pressure in a liquid under the corresponding part of its film. A curvature is increasing in top s direction. Therefore a pressure drop and flow s velocity are directed to the top. 

When the cake structure is composed of particles that are readily deformed or become rearranged under pressure, the resulting cake is characterized as being compressible. Those that are not readily deformed are referred to as sem-compressible, and those that deform only slightly are considered incompressible. Porosity (defined as the ratio of pore volume to the volume of cake) does not decrease with increasing pressure drop. The porosity of a compressible cake decreases under pressure, and its hydraulic resistance to the flow of the liquid phase increases with an increase in the pressure differential across the filter media. 

The major factors governing the proper design far clearance under the downcomer (see Figure 8-63), and the distance between the bottom of the downcomer and the tray it is emptying onto are [190] (a) downcomer sealing, (b) downcomer pressure drop, and (c) fouling and/or corrosive nature of the fluids. TTie smaller the clearance, the more stable will be the tray start-up due to the greater restriction to vapor flow into and up the empty liquid downcomer. 

We consider the problem of liquid and gas flow in micro-channels under the conditions of small Knudsen and Mach numbers that correspond to the continuum model. Data from the literature on pressure drop in micro-channels of circular, rectangular, triangular and trapezoidal cross-sections are analyzed, whereas the hydraulic diameter ranges from 1.01 to 4,010 pm. The Reynolds number at the transition from laminar to turbulent flow is considered. Attention is paid to a comparison between predictions of the conventional theory and experimental data, obtained during the last decade, as well as to a discussion of possible sources of unexpected effects which were revealed by a number of previous investigations. 

The experimental investigations of boiling instability in parallel micro-channels have been carried out by simultaneous measurements of temporal variations of pressure drop, fluid and heater temperatures. The channel-to-channel interactions may affect pressure drop between the inlet and the outlet manifold as well as associated temperature of the fluid in the outlet manifold and heater temperature. Figure 6.37 illustrates this phenomenon for pressure drop in the heat sink that contains 13 micro-channels of d = 220 pm at mass flux G = 93.3kg/m s and heat flux q = 200kW/m. The temporal behavior of the pressure drop in the whole boiling system is shown in Fig. 6.37a. The considerable oscillations were caused by the flow pattern alternation, that is, by the liquid/two-phase alternating flow in the micro-channels. The pressure drop FFT is presented in Fig. 6.37b. Under... 

In the capillary method, the time required for a liquid to flow through a capillary tube is determined. The melt under investigation flows with a constant rate through a tube with a small, definite cross-sectional area, such as a cylindrical capillary. The viscosity can be measured in an absolute way from the pressure drop. This method can yield the most reliable absolute data, the viscosity being given by a modified Hagen-Poiseuille equation ... 

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