Brown equation

The principal factor that determines the column diameter is the vapour flow-rate. The vapour velocity must be below that which would cause excessive liquid entrainment or a high-pressure drop. The equation given below, which is based on the well-known Souders and Brown equation, Lowenstein (1961), can be used to estimate the maximum allowable superficial vapour velocity, and hence the column area and diameter,... 

Furthermore, Venuto (77, 78) has applied a special type of LFER, the Brown selectivity relationship (79), to the deuteration (series 50) and ethylation (series 51) of toluene and benzene catalyzed by zeolites. The Brown equation... 

Although the work of Gomberg and those who followed provided good evidence for the existence of arylmethyl radicals, there was still skepticism regarding simple aliphatic radicals such as methyl and ethyl. As noted above, the modern history of these species began with the suggestions of Crum Brown (equation 2). ... 

In countercurrent operation of several stages in series, feed enters This is of the same form as the Kremser-Brown equation for gas the first stage and final extract leaves it, and fresh solvent enters the... 

The Souders and Brown constant CSB is the C-factor [Eq. (14-77)] at the entrainment flood point. Most modern entrainment flooding correlations retain the Souders and Brown equation (14-80) as the basis, but depart from the notion that CSB is a constant. Instead, they express CSb as a weak function of several variables, which differ from one correlation to another. Depending on the correlation, CSB and us,flood are based on either the net area or on the bubbling area AB. 

Resuming the main line of our consideration, let us show how to consistently take into account the effect of the particle magnetic anisotropy by solving the Brown equation (4.90). Taking n as the polar axis of the coordinate framework, we recover the situation considered as an illustration in Section II.B. Namely, the dimensionless particle magnetization is expressed as Eq. (4.54) and the particle energy as Eq. (4.55). Then the nonstationary solution of the kinetic equation (4.90), which is equivalent to Eq. (4.27), is presented in the form of expansion (4.56) whose amplitudes satisfy Eqs. (4.60) and (4.61). 

For the quantitative treatment of substituent effects in such reactions, Brown proposed (Brown and Okamoto, 1957) a new Hammett-type structure-reactivity relationship, the Brown equation (1), in terms of substituent constant instead of a in the original Hammett equation. 

The use of the Brown equation as a probe of reaction mechanism is essentially based on the alternative use of substituent parameters tr and a- the better correlation with one of the reference scales, i.e. in this analysis, indicates closer similarity in the mechanism or in the structure of the transition state to that of the reference reaction, solvolysis of a-cumyl chlorides [2]. While the broad applicability of the Brown treatment is widely appreciated, this (T treatment has the inevitable limitations of a single reference parameter relationship. 

Gassman and Fentiman (1970) used the Brown equation to investigate participation by a remote ir-bond in solvolysis reactions. They compared substituent effects in the solvolyses of 7-aryl-7-norbornyl [6], and syn-l-aryl-anri-7-norbornenyl [7] systems. The saturated bicyclic system [6] gave a linear... 

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