1992 Fiscal Year Final Research Report Summary
STUDY ON PATTERN FORMATION AND MORHOLOGICAL TRANSITION
| Project/Area Number |
03640353
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| Research Category |
Grant-in-Aid for General Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Research Field |
物理学一般
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| Research Institution | YAMAGUCHI UNIVERSITY |
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Principal Investigator |
FURUKAWA Hiroshi Faculty of Education, Yamaguchi University, Professor, 教育学部, 教授 (10108269)
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| Project Period (FY) |
1991 – 1992
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| Keywords | Phase Separation / Phase Transition / Spinodal Decomposition / Pattern Formation / Morphological Transition / Growth Law / Perfect Crystal / Polymer |
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| Research Abstract |
We examined the mechanism of the phase separation under the inhomogeneous spatio-temporal external conditions, in order to examine the response of the phase separating system to the external conditions. In particular the change in the external condition in the initial stage of the phase separation drastically affects the pattern formation in later stages. An example corresponding to the present theoretical investigation is the case of the formation of large perfect crystal by drawing up a piece of crystal from molten material. We also propose the same experiment for the polymer and the polymer blend with solvent. These experiments are significant from practical purpose offering an efficient method of producing perfect crystem, and from academic point of view offering morphological transition in nonequilibrium state which should be solved. In this project we aim the phase separation not only of solid but also of liquid. We therefore examined the growth law of the length scale for the spinodal decomposition of liquid. Due to the scaling properties of the phase separation the length scale L(t) grows in proportion to t^a as a function of time t. Here a is called the growth exponent and is given as a = 1/3 for solid and a = 1 for fluid. On the other hand, the exponent a = 1 for fluid is known to contradict with the hydrodynamic evolution law in the long time limit ( t * *), and a is considered to become 2/3 in the long time limit. We confirmed the growth exponent a = 2/3 by the simulation The importance is that the cross-over from a = 1 * 2/3 gives rise to the slowing down of the growth of the length scale. For instance, for water + vapor system, the fluid velocity (7000 cm/sec) predicted with a = 1 is large by three degree than 10 cm/sec predicted with a = 2/3 (at L(t) = 1 cm). Such a remarkable slowing down has an important effect to the composition of material in the absence of the gravitational field (such as in the space laboratory).
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Research Products
(6 results)
