Pinch-off of rods by bulk diffusion

L. K. Aagesen; A. E. Johnson; J. L. Fife; P. W. Voorhees; M. J. Miksis; S. O. Poulsen; E. M. Lauridsen; F. Marone; M. Stampanoni

doi:10.1016/j.actamat.2011.04.036

Pinch-off of rods by bulk diffusion

L. K. Aagesen, A. E. Johnson, J. L. Fife, P. W. Voorhees, M. J. Miksis, S. O. Poulsen, E. M. Lauridsen, F. Marone, M. Stampanoni

Research output: Contribution to journal › Article › peer-review

27 Scopus citations

Abstract

The morphology of a rod embedded in a matrix undergoing pinching by interfacial-energy-driven bulk diffusion is determined near the point of pinching. We find a self-similar solution that gives a unique temporal power law and interfacial shape prior to pinching and self-similar solutions after pinching. The theory is compared to experiments that employ in situ four-dimensional X-ray tomographic microscopy for rods of liquid or solid pinching by solute diffusion in the high-diffusivity liquid phase. The excellent agreement between experiment and theory confirms that the interfacial morphology near the singularity is universal both before and after pinching; the shape holds regardless of the material system and initial condition. This also implies that the predictions of the time-dependence of the process can be used to determine the time to pinching for a wide variety of physical systems, and thus provide estimates of the time required for capillarity-driven break-up of microstructures from the detachment of secondary dendrite arms to polymer blends.

Original language	English (US)
Pages (from-to)	4922-4932
Number of pages	11
Journal	Acta Materialia
Volume	59
Issue number	12
DOIs	https://doi.org/10.1016/j.actamat.2011.04.036
State	Published - Jul 2011

Funding

This work was partially supported by NSF RTG Grant DMS-0636574 (L.K.A.). M.J.M. acknowledges support from US National Science Foundation RTG grant DMS-0636574 and NSF Grant DMS-0616468. A.E.J., J.L.F. and P.W.V. acknowledge the US Department of Energy, Grant DE-FG02-99ER45782, for financial support, and J.L.F. also acknowledges the National Science Foundation Graduate Research Fellowship. E.M.L. and S.O.P acknowledge the Danish National Research Foundation for supporting the Center for Fundamental Research: Metal Structures in 4D, within which part of this work was performed. The authors thank the Paul Scherrer Institut for beamtime at the TOMCAT beamline. We would also like to thank Gordan Mikuljan from the TOMCAT team for his technical expertise during the initial setup of the experiments at the beamline.

Keywords

Bulk diffusion
Capillary phenomena
Coarsening
Self-organization and patterning
X-ray and neutron techniques

ASJC Scopus subject areas

Electronic, Optical and Magnetic Materials
Ceramics and Composites
Polymers and Plastics
Metals and Alloys

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10.1016/j.actamat.2011.04.036

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title = "Pinch-off of rods by bulk diffusion",

abstract = "The morphology of a rod embedded in a matrix undergoing pinching by interfacial-energy-driven bulk diffusion is determined near the point of pinching. We find a self-similar solution that gives a unique temporal power law and interfacial shape prior to pinching and self-similar solutions after pinching. The theory is compared to experiments that employ in situ four-dimensional X-ray tomographic microscopy for rods of liquid or solid pinching by solute diffusion in the high-diffusivity liquid phase. The excellent agreement between experiment and theory confirms that the interfacial morphology near the singularity is universal both before and after pinching; the shape holds regardless of the material system and initial condition. This also implies that the predictions of the time-dependence of the process can be used to determine the time to pinching for a wide variety of physical systems, and thus provide estimates of the time required for capillarity-driven break-up of microstructures from the detachment of secondary dendrite arms to polymer blends.",

keywords = "Bulk diffusion, Capillary phenomena, Coarsening, Self-organization and patterning, X-ray and neutron techniques",

author = "Aagesen, {L. K.} and Johnson, {A. E.} and Fife, {J. L.} and Voorhees, {P. W.} and Miksis, {M. J.} and Poulsen, {S. O.} and Lauridsen, {E. M.} and F. Marone and M. Stampanoni",

note = "Funding Information: This work was partially supported by NSF RTG Grant DMS-0636574 (L.K.A.). M.J.M. acknowledges support from US National Science Foundation RTG grant DMS-0636574 and NSF Grant DMS-0616468. A.E.J., J.L.F. and P.W.V. acknowledge the US Department of Energy, Grant DE-FG02-99ER45782, for financial support, and J.L.F. also acknowledges the National Science Foundation Graduate Research Fellowship. E.M.L. and S.O.P acknowledge the Danish National Research Foundation for supporting the Center for Fundamental Research: Metal Structures in 4D, within which part of this work was performed. The authors thank the Paul Scherrer Institut for beamtime at the TOMCAT beamline. We would also like to thank Gordan Mikuljan from the TOMCAT team for his technical expertise during the initial setup of the experiments at the beamline.",

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AU - Johnson, A. E.

AU - Fife, J. L.

AU - Voorhees, P. W.

AU - Miksis, M. J.

AU - Poulsen, S. O.

AU - Lauridsen, E. M.

AU - Marone, F.

AU - Stampanoni, M.

N1 - Funding Information: This work was partially supported by NSF RTG Grant DMS-0636574 (L.K.A.). M.J.M. acknowledges support from US National Science Foundation RTG grant DMS-0636574 and NSF Grant DMS-0616468. A.E.J., J.L.F. and P.W.V. acknowledge the US Department of Energy, Grant DE-FG02-99ER45782, for financial support, and J.L.F. also acknowledges the National Science Foundation Graduate Research Fellowship. E.M.L. and S.O.P acknowledge the Danish National Research Foundation for supporting the Center for Fundamental Research: Metal Structures in 4D, within which part of this work was performed. The authors thank the Paul Scherrer Institut for beamtime at the TOMCAT beamline. We would also like to thank Gordan Mikuljan from the TOMCAT team for his technical expertise during the initial setup of the experiments at the beamline.

PY - 2011/7

Y1 - 2011/7

N2 - The morphology of a rod embedded in a matrix undergoing pinching by interfacial-energy-driven bulk diffusion is determined near the point of pinching. We find a self-similar solution that gives a unique temporal power law and interfacial shape prior to pinching and self-similar solutions after pinching. The theory is compared to experiments that employ in situ four-dimensional X-ray tomographic microscopy for rods of liquid or solid pinching by solute diffusion in the high-diffusivity liquid phase. The excellent agreement between experiment and theory confirms that the interfacial morphology near the singularity is universal both before and after pinching; the shape holds regardless of the material system and initial condition. This also implies that the predictions of the time-dependence of the process can be used to determine the time to pinching for a wide variety of physical systems, and thus provide estimates of the time required for capillarity-driven break-up of microstructures from the detachment of secondary dendrite arms to polymer blends.

AB - The morphology of a rod embedded in a matrix undergoing pinching by interfacial-energy-driven bulk diffusion is determined near the point of pinching. We find a self-similar solution that gives a unique temporal power law and interfacial shape prior to pinching and self-similar solutions after pinching. The theory is compared to experiments that employ in situ four-dimensional X-ray tomographic microscopy for rods of liquid or solid pinching by solute diffusion in the high-diffusivity liquid phase. The excellent agreement between experiment and theory confirms that the interfacial morphology near the singularity is universal both before and after pinching; the shape holds regardless of the material system and initial condition. This also implies that the predictions of the time-dependence of the process can be used to determine the time to pinching for a wide variety of physical systems, and thus provide estimates of the time required for capillarity-driven break-up of microstructures from the detachment of secondary dendrite arms to polymer blends.

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KW - Capillary phenomena

KW - Coarsening

KW - Self-organization and patterning

KW - X-ray and neutron techniques

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JO - Acta Materialia

JF - Acta Materialia

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ER -

Pinch-off of rods by bulk diffusion

Abstract

Funding

Keywords

ASJC Scopus subject areas

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