Houghton solution

The solution derived by Haarhoff and Van der Linde [14] gives a profile whose equation is very similar to the Houghton solution. It can be written in the same... 

Profiles calculated with the equilibrium-dispersive model and the parabolic isotherm (1) or the Langmuir isotherm (3). 2, Houghton solution. The Haarhoff and Van der Linde solution is identified by squares. Reproduced with permission from S. Golshan-Shirazi and G. Guiochon,J. Chromatogr., 506 (1989) 495 (Figs. 17 and 18). 

Houghton et al. (HI3) have reported data on the size, number, and size-distribution of bubbles. Distinction is made between bubble beds, in which bubble diameter and gas holdup tend to become constant as the gas velocity is increased (these observations being in agreement with those of other workers previously referred to), and foam beds, in which bubble diameter increases and bubble number per unit volume decreases for increasing gas velocity. Pore characteristics of the gas distributor affect the properties of foam beds, but not of bubble beds. Whether a bubble bed or a foam bed is formed depends on the properties of the liquid, in particular on the stability of bubbles at the liquid surface, foam beds being more likely to form in solutions than in pure liquids. 

Houghton, P. G. et al., J. Chem. Soc., Chem. Comm., 1979, 771 Thermolysis of the undiluted tetrazole is violent, but controlled sand or in solution. 

Hummel, Thomas J., Steven S. Zumdahl, and Susan Arena Zumdahl. Chemistry (Student Solutions Manual), 6th Ed. (Houghton Mifflin, 2004). 

Gas Chromatography-Mass Spectrometry Negative-ion chemical ionisation mass spectrom-etry is the best method to identify a wide range of synthetic corticosteroids in horse urine (E. Houghton et at, Biomed. Mass Spectrom., 1982, 9, 459-465). Method. Extract 10 ml of urine with 25 ml of methylene chloride, separate the solvent layer, dry over anhydrous sodium sulphate, and evaporate to dryness in a rotary film evaporator at 30° to 40°. Heat the residue with 100 p.1 of an 8% solution of methoxyamine hychochloride in dry pyridine in a reaction tube at 80° for 30 minutes, add 50 pi of trimeOiylsilylimidazole, [Pg.98]

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Houghton has shown that the limit of Eqs. 10.18 and 10.19 to 10.21 when the apparent dispersion coefficient. Da, tends toward 0 is Eq. 7.4, the solution of the ideal model for the diffuse rear profile [13]. It is significant, however, that the limit solution is different from the rigorous solution of the ideal model for a parabolic isotherm [15]. This shows that the Houghton equation is not self-consistent. This flaw comes from the simplification made to replace Eq. 10.14 by Eq. 10.17. 

DatR,Q- It turns out that this procedure corrects the Houghton equation for its lack of mass conservation. In the Haarhoff-Van der Linde solution, mass is conserved. 

This new simplification is correct to the first order and conserves mass. This observation explains why the Haarhoff-Van der Linde equation conserves mass while the Houghton equation does not, even to the first order. In the next section we discuss the range of validity of these solutions. 

Figure 10.2 Comparison between the band profiles derived from the Houghton equation, the Haarhoff and Van der Linde equation and the numerical solution of the equilibrium-dispersive model using the Rouchon procedure, (a) Influence of the isotherm model used.

Figure 10.4 Comparison of experimental band profiles with the best profiles obtained by fitting experimental data to the Houghton equation. Experimental conditions Erbasil C18 with methanol-water (17 83) at ft, = 3 mL/min and 20°C. Solute benzyl alcohol. Reproduced with permission from A. Jaulmes, C. Vidal-Madjar, H. Colin and G. Guiochon,. Phys. Chem., 90 (1986) 207 (Fig. 1). 1986, American Chemical Society.

However, eventually 5jR > 1 for a dissolving bubble, so that the steady-state solution prevails. For gas bubbles dissolving in water at atmospheric pressure with i (0) <0.2 mm, Houghton, Ritchie, and Thomson (H8) find that the transient term becomes negligible after about 100 sec. After this time the result reduces to the quasi-steady solution, governed by the Laplace equation, whose solutions have been extensively studied. For a bubble attached to a wall with zero contact angle, Liebermann (L6) thus shows that the rate of solution is reduced by a factor of In 2, leading to the result... 

Solutions of alkylamitte/aldehyde condensation products have been used in several sulfur-scavenging processes. The spent solution is fiee of sulfur particles, and no nitrogen oxide gases are formed however, it has a very obnoxious odor. It is reported to have corrosion-inhibition properties and to be approved for Gass I, non-hazardous, deep-well disposal (Houghton and Bucklin, 1994). Examples of processes in this category are Gas Treat 114. Gas Treat 113. and Gas Treat... 

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