Unsteady processes of combined polymerization and crystallization in continuous apparatuses

Buyevich, Yu.A.; Natalukha, I. A.

doi:10.1016/0009-2509(94)e0052-r

Cited by 51 publications

(32 citation statements)

References 6 publications

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“…Non-stationary contributions entering in the growth rates of spherical particles, their radii, and the distribution of temperature and concentration fields must be taken into account in the theoretical description of the intermediate stage of phase transformation in melts and solutions (the analytical description of crystal growth in dilute solutions is presented in appendix A). For this reason, many theories of growth of crystals or droplike aggregates in supersaturated solutions, supercooled melts, mushy layers, colloids, magnetic fluids and other physical systems (see, among others, [18][19][20][21][22][23][24][25][26][27]) should be reconsidered with allowance for the non-stationary contributions to the particle growth rates.…”

Section: Discussionmentioning

confidence: 99%

On the theory of the unsteady-state growth of spherical crystals in metastable liquids

Alexandrov

Аlexandrova

2019

Phil. Trans. R. Soc. A.

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Section: Discussionmentioning

confidence: 99%

On the theory of the unsteady-state growth of spherical crystals in metastable liquids

Alexandrov

Аlexandrova

2019

Phil. Trans. R. Soc. A.

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“…Estimating β 2 * ∆t/(aΛ) ∼ 10 −2 t s −1 as a typical case for metallic melts, we conclude that the second term in expressions (18) becomes substantial at times t 10 s after nucleation of a certain particle. In other words, the commonly used approximation of the particle growth rate V(t) ≈ β * ∆ [13,14,22,[26][27][28][29] is only the rough estimate that describes the main contribution only. In order to obtain a more precise description of the real nucleation process one can use next terms in the asymptotic expansion of R(t) and V(t) found in expressions (18).…”

Section: Unsteady-state Growth Rate Of Spherical Nucleimentioning

confidence: 99%

Nucleation and evolution of spherical crystals with allowance for their unsteady-state growth rates

Alexandrov¹

2018

J. Phys. A: Math. Theor.

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The growth dynamics of a spherical crystal in a metastable liquid is analyzed theoretically. The unsteady-state contributions to the crystal radius and its growth rate are found as explicit functions of metastability level Δ and time t. It is shown that the fundamental contribution to the growth rate represents the time independent solution of a similar temperature conductivity problem (Alexandrov and Malygin 2013 J. Phys. A: Math. Theor. 46 455101) whereas the next unsteady-state contribution is proportional to ∆ 2 t. On the basis of these explicit unsteady-state solutions, the process of transient nucleation and growth of spherical crystals in a metastable system is theoretically studied at the intermediate stage of phase transformation. A complete analytical solution for the particle-radius distribution function and metastability level is constructed with allowance for the Weber-Volmer-Frenkel-Zel'dovich and Meirs kinetic mechanisms. It is shown that the obtained unsteady-state contribution to the crystal growth rate plays an important role in the nucleation process and drastically changes the particle-radius distribution function.

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“…At the concluding stage, the growth of each particle influences the evolution of neighbouring crystals so that Ostwald ripening, coagulation and fragmentation processes are capable of occurring [13][14][15][16][17]. Let us especially note that such processes as external electromagnetic fields [18], buoyancy forces [19], polymerization [9,20] and withdrawal mechanisms of product crystals from a crystallizer [21][22][23][24] may essentially change the dynamics of particulate assemblages in a metastable liquid as well.…”

Section: Introductionmentioning

confidence: 99%

Dynamics of particulate assemblages in metastable liquids: a test of theory with nucleation and growth kinetics

Аlexandrova

Alexandrov

2020

Phil. Trans. R. Soc. A.

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This manuscript is devoted to the nonlinear dynamics of particulate assemblages in metastable liquids, caused by various dynamical laws of crystal growth and nucleation kinetics. First of all, we compare the quasi-steady-state and unsteady-state growth rates of spherical crystals in supercooled and supersaturated liquids. It is demonstrated that the unsteady-state rates transform to the steady-state ones in a limiting case of fine particles. We show that the real crystals evolve slowly in a more actual case of unsteady-state growth laws. Various growth rates of particles are tested against experimental data in metastable liquids. It is demonstrated that the unsteady-state rates describe the nonlinear behaviour of experimental curves with increasing the growth time or supersaturation. Taking this into account, the crystal-size distribution function and metastability degree are analytically found and compared with experimental data on crystallization in inorganic and organic solutions. It is significant that the distribution function is shifted to smaller sizes of particles if we are dealing with the unsteady-state growth rates. In addition, a complete analytical solution constructed in a parametric form is simplified in the case of small fluctuations in particle growth rates. In this case, a desupercooling/desupersaturation law is derived in an explicit form. Special attention is devoted to the biomedical applications for insulin and protein crystallization. This article is part of the theme issue ‘Patterns in soft and biological matters’.

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Unsteady processes of combined polymerization and crystallization in continuous apparatuses

Cited by 51 publications

References 6 publications

On the theory of the unsteady-state growth of spherical crystals in metastable liquids

On the theory of the unsteady-state growth of spherical crystals in metastable liquids

Nucleation and evolution of spherical crystals with allowance for their unsteady-state growth rates

Dynamics of particulate assemblages in metastable liquids: a test of theory with nucleation and growth kinetics

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