Growth kinetics of potassium alum crystal in a well-agitated vessel

Tai, Chun‐Hwei; Yu, Kuo‐Hsuan

doi:10.1016/0022-0248(89)90645-3

Cited by 13 publications

(8 citation statements)

References 15 publications

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“…However, there is a growing body of literature that contradicts the constant growth law. Proportionate growth, evidenced in both natural and synthetic crystal systems, appears to account better for observed CSDs, and has been found in a variety of synthetic crystal systems studied by Canning and Randolph (1967), Mullin and Gaska (1969), Garside and Jaňcić (1976), Jones et al (1986), Tai and Yu (1989), and Tai et al (1993). Proportionate growth also has been noted in geologic systems [e.g., Nordeng and Sibley (1996), Kile and Eberl (1999), Makowitz andSibley (1999, 2001), and Meth and Carlson (2002)].…”

Section: Growth Equationsmentioning

confidence: 91%

On the origin of size-dependent and size-independent crystal growth: Influence of advection and diffusion

Kile

Eberl

2003

American Mineralogist

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Crystal growth experiments were conducted using potassium alum and calcite crystals in aqueous solution under both non-stirred and stirred conditions to elucidate the mechanism for size-dependent (proportionate) and size-independent (constant) crystal growth. Growth by these two laws can be distinguished from each other because the relative size difference among crystals is maintained during proportionate growth, leading to a constant crystal size variance (b 2 ) for a crystal size distribution (CSD) as the mean size increases. The absolute size difference among crystals is maintained during constant growth, resulting in a decrease in size variance. Results of these experiments show that for centimeter-sized alum crystals, proportionate growth occurs in stirred systems, whereas constant growth occurs in non-stirred systems. Accordingly, the mechanism for proportionate growth is hypothesized to be related to the supply of reactants to the crystal surface by advection, whereas constant growth is related to supply by diffusion. Paradoxically, micrometer-sized calcite crystals showed proportionate growth both in stirred and in non-stirred systems. Such growth presumably results from the effects of convection and Brownian motion, which promote an advective environment and hence proportionate growth for minute crystals in non-stirred systems, thereby indicating the importance of solution velocity relative to crystal size. Calcite crystals grown in gels, where fluid motion was minimized, showed evidence for constant, diffusion-controlled growth. Additional investigations of CSDs of naturally occurring crystals indicate that proportionate growth is by far the most common growth law, thereby suggesting that advection, rather than diffusion, is the dominant process for supplying reactants to crystal surfaces.

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Section: Growth Equationsmentioning

confidence: 91%

On the origin of size-dependent and size-independent crystal growth: Influence of advection and diffusion

Kile

Eberl

2003

American Mineralogist

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“…The coefficients of mass transfer and surface integration steps can be determined using the equation derived, on the basis of a second-order surface integration rate with respect to supersaturation, by Tai and Yu [13] from the two-step model of crystal growth:…”

Section: Crystallization Kinetic Expressionsmentioning

confidence: 99%

Effect of Solvent Composition on Crystallization Process of Ascorbic Acid

Omar

2006

Chem Eng & Technol

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The crystal growth kinetics of ascorbic acid in water and in the solvent systems water/ethanol, water/methanol, and water/ propanol is determined by means of seeded isothermal batch crystallization experiments. The measurements are correlated by a power low equation of the form (G = k g r n ). The composition of the solvent system is found to have a significant influence on the kinetic parameters of growth of ascorbic acid. An increase in growth rate in the presence of alcoholic solvents (20 wt %) is measured compared to experiments with pure water. The thermodynamic effect of the solvent on the growth kinetics is approached by the UNIFAC method. The kinetic effect of solvent composition is explained using the two-step model. Both thermodynamic and kinetic analyses give the same result: The addition of alcoholic solvents (20 wt % ethanol, methanol, and propanol) to the ascorbic acid/water system slightly reduces the diffusion rate and significantly accelerates the surface integration process.

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“…Crystal growth and contact nucleation of soluble substances have been studied extensively. Important features of the system include the observation of size-dependent growth over a wide range of crystal sizes (Tai and Yu, 1989), the requirement of a critical crystal size about 195-225 prn for the generation of secondary nuclei (Cayey andEstrin, 1967 andRousseau et al, 1976) and more nuclei are produced at higher supersaturation and magma density (Garside and Shah, 1980). Similar studies of sparingly soluble salt are limited, because large single crystals are difficult to prepare.…”

mentioning

confidence: 98%

“…The evaluation method was developed in the course of this study. Then, growth rate data were analyzed by the two-step model, which has been used by many investigators to study the growth kinetics of soluble substances (Karpinski, 1985;Tai and Yu, 1989;Qiu and Rasmuson, 1990). After growth experiments, the Teflon impeller was replaced by a stainless-steel one to generate secondary nuclei at various operating conditions.…”

mentioning

confidence: 99%

Size‐Dependent growth and contact nucleation of calcite crystals

1993

Self Cite

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The growth kinetics and contact nucleation of calcite crystals were studied in a pH-stat crystallizer. Large seed crystals up to 230 pm were successfully prepared by the gel growth technique. The crystal growth data over a wide range of crystal sizes were evaluated from titration curves by an initial slope method and then analyzed by the two-step model. The mass-transfer and surface integration rates were found to be functions of crystal size with the exception of mass-transfer rates of small crystals less than 10 pm. The controlling step of crystal growth process was tested using the effectiveness factor concept. Large seed crystals of calcite induced contact nucleation when a stainless-steel impeller was used for agitation. The important features of contact nucleation for calcite crystals were explored and compared with those of soluble substances.

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Growth kinetics of potassium alum crystal in a well-agitated vessel

Cited by 13 publications

References 15 publications

On the origin of size-dependent and size-independent crystal growth: Influence of advection and diffusion

On the origin of size-dependent and size-independent crystal growth: Influence of advection and diffusion

Effect of Solvent Composition on Crystallization Process of Ascorbic Acid

Size‐Dependent growth and contact nucleation of calcite crystals

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