Pulsatile Instability in Rapid Directional Solidification: Strongly-Nonlinear Analysis

Merchant, G. J.; Braun, R. J.; Brattkus, K.; Davis, Stephen H.

doi:10.1137/0152074

Cited by 22 publications

(11 citation statements)

References 26 publications

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“…[1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18] In contrast, in many industrial [19][20][21][22] and natural processes [23][24][25] the temperature changes are gradual and slow rather than being quenches. Most of these studies considered the behavior of systems quenched ͑cooled rapidly͒ from the isotropic phase into the biphasic region.…”

Section: Introductionmentioning

confidence: 99%

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Oscillatory instabilities in phase separation of binary mixtures: Fixing the thermodynamic driving

Auernhammer

Vollmer

2005

The Journal of Chemical Physics

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Binary liquid mixtures can show pronounced oscillations in the differential scanning calorimeter signal for the specific heat and in the turbidity when phase separation is induced by continuously ramping the temperature. For a fixed ramp rate, i.e., a linear temporal drift of temperature, only a small number of oscillations have been observed. In the present manuscript we describe an experimental setup where simultaneous video-microscopy and shadow-graph measurements can be performed on mixtures subjected to an arbitrary temporal temperature evolution. In particular, it can be adjusted to fix the thermodynamic driving force, which characterizes the rate of change of the composition of the coexisting phases. With this novel technique both the number of oscillations and the temperature interval where oscillations are observed increase significantly. This technique can easily be applied to a great variety of binary mixtures, permitting detailed investigations of their phase-separation kinetics under slowly ramping temperature.

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Section: Introductionmentioning

confidence: 99%

“…They separate into two liquid phases. 19,20,[24][25][26][27][28][29][30][31][32] Irrespective of the ramp rate only a small number of oscillations is observed when linearly cooling a sample. Phase separation leads to a polymer-poor liquid phase and a polymerrich gel phase.…”

Section: Introductionmentioning

confidence: 99%

Oscillatory instabilities in phase separation of binary mixtures: Fixing the thermodynamic driving

Auernhammer

Vollmer

2005

The Journal of Chemical Physics

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“…Как правило, ассоциированные с такими ПС физикохимические процессы предполагаются медленными, скорости роста порядка µm/s, зачастую и на несколько порядков ниже. Исследования авторов второй группы работ сосредоточены на построении теории ПС, возникающих при быстрой направленной кристаллизации (БНК) ряда сплавов [14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29], скорости роста порядка 1−10 m/s,. Поскольку статья посвящена расчету профилей примесных ПС при БНК, то ниже мы приводим краткий обзор результатов предшествующих заметных работ, относящихся лишь ко второй группе.…”

Section: Introductionunclassified

Нелинейная Динамика Формирования Периодической Сверхструктуры Примесных Полос При Быстрой Направленной Кристаллизации Бинарных Сплавов

Чеврычкина¹,

Бессонов²,

Корженевский³

2019

Физика Твердого Тела

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The article offers an analytical description of the nonlinear dynamics of the formation of regular impurity superstructures during the rapid crystallization of binary alloys, supplemented by numerical model calculations. The existence of a stable limit cycle is shown and the spatial profiles of the impurity concentration in a solid product are calculated. It has been established that considering the finiteness of the velocity of jumps of impurity atoms leads to a very significant decrease in the size of the cycles and a change in the profiles of the impurity superstructures.

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“…Several important dynamical systems modelled by equation (2) include nerve conduction [2], rapid directional solidi®cation of a dilute binary alloy [3], and the relativistic harmonic oscillator [4]. The a priori absence of a small parameter in equation (2) means that the usual perturbative procedures [1] cannot be applied.…”

mentioning

confidence: 99%

“…where n is a positive integer [2,3]. (The relativistic harmonic oscillator is also of the form given by equation (2); however, its detailed analysis is presented in Mickens [4].)…”

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confidence: 99%

Letters to the Editor

Mickens

Jackson

1999

Journal of Sound and Vibration

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A vast effort has gone into constructing analytical approximations to oscillatory systems that can be modelled by equations taking the formwhere the parameter e is small and F is a polynomial function of its arguments. A summary of many of these techniques is given by Mickens [1]. This paper presents preliminary results on a class of non-linear oscillators for which the frequency is a function of the velocity, i.e.,

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Pulsatile Instability in Rapid Directional Solidification: Strongly-Nonlinear Analysis

Cited by 22 publications

References 26 publications

Oscillatory instabilities in phase separation of binary mixtures: Fixing the thermodynamic driving

Oscillatory instabilities in phase separation of binary mixtures: Fixing the thermodynamic driving

Нелинейная Динамика Формирования Периодической Сверхструктуры Примесных Полос При Быстрой Направленной Кристаллизации Бинарных Сплавов

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