Crystallization

Palermo, Joseph A.

doi:10.1021/ie50700a009

Cited by 5 publications

(3 citation statements)

References 15 publications

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“…The strategy is then: (i) solve the population balance using equation (8) and obtain n* = n*{L*, C*, t*}; (ii) solve the mass balance using the dimensionless counterpart of equation (3) and obtain C* = C{L*, t*}; (iii) use C* = C{L*, t*} in equation (8) and obtain n* = n*{L*, t*}; and finally (iv) test the approximation criterion as given by equation (7).…”

Section: Theoretical Developmentmentioning

confidence: 99%

“…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.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

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

Malcata

1994

International Journal of Mathematical Education in Science and

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A simplified, systematic approach to the mathematical simulation of crystallizers is attempted by using the fundamental principles of mass conservation, via a population balance to the solid phase and a solute balance to both solid and liquid phases. A continuous, isothermal and isochoric crystallizer is assumed to be described by the MSMPR model under transient operating conditions with complete micromixing. The birth and death functions are assumed nil. Homogeneous nucleation is considered at a rate which is independent of the solution supersaturation. The growth rate of the crystals is described by McCabe's law. The possibility of solving the population balance and the mass balance independently is explored, and the conditions of validity for such an approach are found. The maximum linear dimension of crystal and the liquor concentration profile as functions of time are obtained. The approximation is found to be generally good for a period of time right after start-up of the crystallizer. A much wider range of time ensuring a satisfactory approximation is possible provided that the system and operation-dependent parameter takes small values.

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Section: Theoretical Developmentmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Malcata

1994

International Journal of Mathematical Education in Science and

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show abstract

“…In this theory, the droplet is considered to precipitate instantaneously when the surface concentration of the solute reaches a certain preset supersaturation limit and the precipitation front engulfs all parts of the droplet wherever the equilibrium concentration is exceeded. These classical nucleation theories were not sufficient to make good predictions regarding the nucleation within the droplets even at low heating rates [8][9][10][11][12]. For high heating rates, as in plasma, this problem is even more critical and the homonuclear precipitation theory comes under serious scrutiny.…”

Section: Introductionmentioning

confidence: 99%