Differential height

Four different electrokinetic processes are known. Two of them, electroosmosis and electrophoresis, were described in 1809 by Ferdinand Friedrich Renss, a professor at the University of Moscow. The schematic of a cell appropriate for realizing and studying electroosmosis is shown in Fig. 31.1a. An electrolyte solution in a U-shaped cell is divided in two parts by a porous diaphragm. Auxiliary electrodes are placed in each of the half-cells to set up an electric held in the solution. Under the inhuence of this held, the solution starts to how through the diaphragm in the direction of one of the electrodes. The how continues until a hydrostahc pressure differential (height of liquid column) has been built up between the two cell parts which is such as to compensate the electroosmotic force. 

Calculation of the pressure drop and flooding rate is particularly important for vacuum columns, in which the pressure may increase severalfold from the top to the bottom of the column. When a heat-sensitive liquid is distilled, the maximum temperature, and hence the pressure, at the bottom of the column is limited and hence the vapour rate must not exceed a certain value. In a vacuum column, the throughput is very low because of the high specific volume of the vapour, and the liquid reflux rate is generally so low that the liquid flow has little effect on the pressure drop. The pressure drop can be calculated by applying equation 4.15 over a differential height and integrating. Thus ... 

In an adiabatic column in which there is 7% salt in the brine at the bottom and essentially no salt at the top, some ice will form as the bed moves upward through the vertical concentration gradient, and this will affect the rate, B, but this effect is small and is ignored below. Following the nomenclature in Figure 7, in the differential height, dLy the rate of salt transfer is... 

An expression for the cumulative pressure drop profile in a spouted bed was derived by Mamuro and Hattori (M6) from a consideration of the balance of forces acting on a differential height dz of the annular solids (Fig. 10) ... 

The acquisition of the spectral information from each single spark separately is now possible with advanced measurement systems, using integration in a small capacitor and rapid computer-controlled readout combined with storage in a multichannel analyzer. With the aid of statistical analysis, sparks with outlier signals can be rejected and the precision improved accordingly. Furthermore, pulse differential height analysis enables discrimination between a number of elements such... 

For continuous contact equipment the material and energy balances are written around a section of column of differential height as shown in Figure 12.8. For the vapor phase the component material balance reads... 

The material balance for A over a differential height dHj) of the column gives... 

Consider a differential height of a packed distillation column of unit cross section as shown in Fig. 5.6 1, For component i. 

The height of packing required to perform a specified amount of mass transfer can be misted to the mess transfer cnefficjent and a meterial balance for the absorbed component at any point in a tower. Referring to Fig. 6.3-2, which represents a packed absorption cower, a material balance within a differential height... 

The amount of solute absorbed in a differential height dZ is d Vy), since both V and y decrease as the gas passes through the tower. 

Consider that the gas rises at a rate GM mole/(area)(time). Let the interfacial surface between gas and liquid be a area/volume of liquid-gas froth. As the gas rises a differential height dh[t the area of contact is a dht per unit active area of the tray. If, while of concentration y, it undergoes a concentration change dy in this height, and if the total quantity of gas is assumed to remain essentially constant, the rate of solute transfer is GM dy ... 

The rate of sensible-heat transfer from the liquid to the interface in a differential height of the packed tower, dz, is... 

A material balance for component A, which is being absorbed over a differential height of column dl, gives... 

Figure 4.11. Hypothetical reactivity-selectivity profile for the interaction of a weakly reactive digitalis compound (D,) or a strongly reactive digitalis compound (Ds) with Na lJC-ATPase isoenzymes or Eg, which differ in the chemotopography of the digitalis binding matrix. Selectivity is shown to be a reflection of the differential height of the activation Gibbs energy barrier, which is equivalent to the association rate constant. In other words, the inhibitor D, will preferentially bind to the isoenzyme Eg, whereas inhibitor D2 will equally bind to both isoenzymes. Eg and Eg (adapted from [251]).

A U-tube manometer is filled with mercury at a specific gravity of 13.6 to measure the pressure of air exiting a pipe. The low pressure end of the pipe is open to atmosphere at a pressure of 99.2 kPa. The differential height of the manometer is 20.5 cm at 25 C. What is the pressure in the pipe ... 

Repeat the first example in Chapter 5 where the cylinder body is charged with 100 ml of acetone and mercury is the operating fluid in the U-tube manometer (differential height is 14 in.). Discuss the potential sources of error in this measurement and how to minimize them. 

Material balance in a fixed bed adsorber with the differential height Az ... 

A material balance of the solute over a differential height dh of the column can now be written as ... 

Figure 8 shows the pertinent details and the assumptions are given in Table 4. A material balance over a differential height gives ... 

If we assume "plug flow" for both phases, setting up a material balance on a differential height of a packed column for absorption of solute A into a liquid containing dissolved reactant gives ... 

The mass transfer can be written in terms of the individual coefficients Eqs. (15-27) or overall coefficients Eqs. fl5-2Rl. For the differential height dz in the rectifying section, the mass transfer rate in terms of the individual coefficients is... 

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