The mixed suspension, mixed product removal crystallizer as a concept in crystallizer design

Abstract

Numerals0 = mid axis origin 1 2 1 h = experimental = initial condition or upper phase = final condition or lower phase LITERATURE CITED 1. Cockbain, E. G., and T. S. McRoberts, J. Colloid Sci., 8, 440 ( 1953). Simultaneous population and mass balances have been solved together with a generalizedform of nucleation-growth rate kinetics to obtain the form of crystal size distribution (CSD)for several idealized modes of crystallizer operation, including seed crystal removal, product classification, arbitrary solids concentration, and staged vessels. The effect of holding time and feed supersaturation on crystal size in a mixed suspension, mixed product removal (MSMPR) crystallizer was also studied. A representative CSD from an MSMPR crystallizer plus the relative kinetic order of nucleation to growth rate can be used to predict CSD from any of the above modes of operation.Crystal size distribution (CSD) is one of the most important and troublesome properties of an operating crystallizer and is a property which cannot presently be designed without prior experience with the crystal system and the type of crystallizer used. Saeman (I), in a classical con-A notable addition to the recent literature is a paper by Bennett (7) which tabulates experimental CSD data from a large class of crystallizers and crystal systems. A property of any CSD is the so-called coeficient of variation (C.V.)," or relative size spread over which the majority +a Not to be confused with coefficient of velocity, also referred to as

Principles, approaches, and challenges for predicting protein aggregation rates and shelf life

“…10,45,84 If aggregates are insoluble, alternative particlesizing techniques may be of use; 85 however, the kinetic parameters that are obtained from such measurements are necessarily based on the rates of phase separation and bulk particle growth. 86,87 It remains to be generally shown how the thermodynamics and kinetics of aggregate phase separation can be quantitatively related to the kinetics of soluble aggregate formation. 36,85 Dynamic light scattering provides a z-average diffusion coefficient or a weighted distribution of effective diffusion coefficients.…”

Plantwide operation of processes with crystallization

“…The MSMPR is an idealized model of a continuous crystallizer originally due to Randolph 11 and discussed in detail in the book by Randolph and Larson. 12 Like the well-known CSTR reactor model, it employs a number of assumptions to produce a simple analytical model of the process.…”

Mathematical design of continuous, isothermal crystallizers with homogeneous nucleation: a simplified approach

“…The associated variation with time of the maximum linear dimension of crystal, i.e. L* max = C* t*, is plotted in Figure 2 for the same values of the design parameter Si Op 4 . The size distribution in steady state may be obtained from the asymptotic form of equation (15) Equation (22) cannot be solved in an exact fashion; however, implementation of a Newton method from the starting estimate C* s = 1 converges in less than ten iterations (using a maximum error estimate of 0-005); the variation with Si Op 4 of the steady-state value C* s thus obtained is available in Figure \{b).…”

“…Such progress has made it possible to model some types of crystallizers on the basis of involved systems of partial derivative equations [2][3][4][5][6][7][8][9]; although the integration of such equations demands powerful numerical methods, some typical parameters relating to the crystallization process may be efficiently determined from experimental data [10,11]. Since in the predesign steps of pilot scale or plant scale crystallizers the MSMPR type (i.e.…”