Rhodes equation

The Rhodes equation [9] for expressing hypo- and hyperchromism may be written in terms of the above difference in dipole strength [4]... 

It should be noted that eqs. (3.458) and (3.459) do not give the same results. In the case of the gas fluidization equation, eq. (3.459) is considered to be more suitable for particles larger than 100 pin and 0.1 < Relm < 1000, whereas the minimum fluidization velocity for particles less dian 100 pm is better estimated using the correlation of Bayens (Rhodes, 1998 Abrahamsen and Geldart, 1980) ... 

In the above equations, no account has been made for the use of polarized light that Is typically used In SALS. In a classic SALS experiment, the Incident light Is vertically polarized, and the scattered radiation Is passed through a second rotatable polarizer referred to as the analyzer. Stein and Rhodes ( ) give the relationship for the amplitude of a scattered ray of polarized light (E)... 

Many empirical formulas have been proposed to render the effect of internal phase ratio on the emulsion viscosity, but they are only valid in specific cases. Pal and Rhodes (84, 85) proposed and used a semi-empirical equation, that makes use of experimental data O qq as the internal phase fraction O at which the relative viscosity qj. = 100. This experimental value must be attained in the same formulation and emulsification conditions, particularly stirring characteristics, which is maybe why it significantly embodies the overall effects of all remaining variables ... 

Wilder Dwight Bancroft (Middletown, Rhode Island, U.S.A., i October 1867-New York, 7 February 1953) was professor of physical chemistry in Cornell University, Ithaca, New York, and editor of the Journal of Physical Chemistry, He also published on the phase rule (see p. 638), colloid chemistry (see p. 739), and structure colours. He showed that two immiscible liquids become miscible if a third substance, soluble in each, is added investigated ternary mixtures, equilibrium in 2-component systems, analysis of solid phases, suggested that all miscible liquids whose vapour pressure curves cut one another form mixtures of maximum or minimum boiling-point, and stated the equations for electromotive forces in terms of chemical potentials. ... 

In practice, however, the two-phase flow theory overestimates the volume of gas passing through the bed as bubbles, that is, the visible bubble flow rate (Rhodes, 1998) and better estimates of bed expansion may be obtained by replacing (Q - Q ,f) in Equation 7.19 with the following relationship for the bubble flow rate ... 

Additionally, this robust method employing simple statistics based upon the calculation of a spectral best fit permits near-infrared tablet hardness prediction across a range of drug concentrations. In 1997, Morisseau and Rhodes [105] published a paper similar to the work by Drennen and Kirsch wherein they used NIR to determine the hardness of tablets. Four formulations (two of hydrochlorothiazide (HCTZ) and two of chlorpheniramine (CTM)) and a placebo were prepared with hardness levels between 2 and 12 kg. Using MLR and partial least-squares (PLS), equations were generated that allowed good prediction of hardness for all the products. 

Numerical calculations of the complete flowfield, using axially symmetric flow models and solving the full viscous equations of motion, have been carried out by Boyson, Ayers and Swithenbank and by Rhodes, Pericleous and Drake. These simulations are suitable for assessing parameters in design optimization provided they are based on realistic boundary conditions and a comprehensive flow model. Bloor, Ingham and Ferguson have also produced a numerical simulation for viscous flow in a hydrocyclone but at unrealistically low Reynolds numbers. Unlike the others they did not, however, ignore the three-dimensional character of the flow around the entry point and used three different models to simulate the entry flow. 

The isothermal sintering of Zr02-CaO specimens at 1350°C yielded a straight line plot for log LjL versus log time. The diffusion coefficient calculated from the volume diffusion equation of Johnson and Cutter ( ) was 7 X 10" cm /sec (using an estimated value of 0.5 for the particle radius). This compared with 1.3 x 10" for the zirconium diffusion coefficient obtained by extrapolating the tracer data of Rhodes and Carter ( ). 

A first attempt to formulate such a theory was made by Stein et al (3), but this was a two-dimensional approach only. Moreover the resulting equations are rather cumbersome. A different approach was made by Keyzers et al (11), who interpreted their measurements on semi-crystalline polypropylene and polystyrene on the basis of a linear combination of the random orientation correlation approach and the spherulite model of Stein and Rhodes (6). Although this worked rather well in practice, the combination of two fundamentally different kinds of theory for one sample is not entirely satisfactory. The present author has therefore developed a new theory which will be published separately (12). 

Gavrilov, N. K. and Shilnikov, A. L. [1996] On a blue sky catastrophe model, Proc. Int. Conf. Comtemp. Problems of Dynamical Systems Theory, ed. Lerman, L. (Nizhny Novgorod State University Nizhny Novgorod). [1999] An Example of blue sky catastrophe, in Ams Transl Series II. Methods of qualitative theory of differential equations and related topics. (AMS, Providence, Rhode Island). 

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