Larkins equation

Using the strong-coupling diagram technique the following equation, which resembles the Larkin equations for ferromagnets [60], was derived [39-43] for the Fourier transform of Green s function (12) ... 

The exact solution of the instanton equation in the large ohmic friction limit has been found by Larkin and Ovchinnikov [1984] for the cubic parabola (3.18). At T = 0... 

Pressure drop Using the Ergun equation, the liquid and die gas pressure drop are 0.726 and 2.12 kPa/m, respectively. Then, by using the correlation of Larkins et al., die two-phase pressure drop is equal to 10.8 kPa/m, ten times lower than in die pulsing-flow regime and low enough to assure diat the gas density is almost constant. Thus, die condition (e) is satisfied. 

There are a number of pressure drop correlations for two-phase flow in packed beds originating from the Lockhart-Martinelli correlation for two-phase flow in pipes. These correlate the two-phase pressure drop to the single-phase pressure drops of the gas and the liquid obtained from the Ergun equation. See, for instance, the Larkins correlation [Larkins, White, and Jeffrey, AIChE J. 7 231 (1967)]... 

The Larkins and Sweeney equations were developed for downward bubble flow. In trickle bed operation, the liquid and gas flow rate are not as high as in packed absorbers, so that there is much less interaction. Single-phase flow pressure drop equations could be used as a first approximation, with the void fraction reduced to... 

If the parameters Aij, aij and Eij are all known, the initial concentrations and a temperature profile are given, the rate equations would predict the behaviour of the reaction. For very large systems a program LARKIN that integrates the, in general stiff, system of equations [27]. The initial value problems may be solved by routines like METANl [29] or SODEX [30, 31]. Both methods are based on a semi-implicit midpoint rule. 

Larkin BK (1964) Some stable explicit difference approximations to the diffusion equation. Math Comput 18 196-202... 

Larkin BK (1967) Numerical solution of the equation of capillarity. J Colloid Interface 8d 23 305-312... 

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