S.R. Coriell

University of Maryland, Baltimore County

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G. B. McFadden

National Institute of Standards and Technology

119

Robert F. Sekerka

Carnegie Mellon University

B.T. Murray

National Institute of Standards and Technology

M. E. Glicksman

Florida Institute of Technology

W. J. Boettinger

Norwegian University of Science and Technology

Bruce T. Murray

Binghamton University

A. A. Chernov

Lawrence Livermore National Laboratory

W.M.B. Duval

Glenn Research Center

A. A. Wheeler

The Ohio State University

Ronald F. Boisvert

National Institute of Standards

Cooperative Institutions

Carnegie Mellon University

119

Los Alamos National Laboratory

113

Alcoa (United States)

110

University of Alberta

109

University of Alabama

106

Worcester Polytechnic Institute

106

National Institute of Standards and Technology

National Institute of Standards

United States Department of Commerce

Westinghouse Electric (United States)

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Convective instabilities during the solidification of an ideal ternary alloy in a mushy layer

Journal of Fluid Mechanics (2010)

Daniel Anderson G. B. McFadden S.R. Coriell B.T. Murray

We consider a model for the solidification of an ideal ternary alloy in a mushy layer that incorporates the effects of thermal and solutal diffusion, convection and solidification. Our results reveal that although the temperature and solute fields are constrained to the liquidus surface of the phase diagram, the system still admits double-diffusive modes of instability. Additionally, modes of instability exist even in situations in which the thermal and solute fields are each individually stable from a static point of view. We identify these instabilities for a general model in which the base-state solution and its linear stability are computed numerically. We then highlight these instabilities in a much simpler model that admits an analytical solution.

Liquidus

Directional solidification

Double diffusive convection

10.1017/s0022112009993740

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Citations (15)

Oscillatory morphological instabilities due to non-equilibrium segregation

Journal of Crystal Growth (1983)

S.R. Coriell Robert F. Sekerka

Supercooling

Directional solidification

10.1016/0022-0248(83)90179-3

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Citations (174)

Convective instabilities in two liquid layers

Journal of Research of the National Institute of Standards and Technology (2007)

G. B. McFadden S.R. Coriell Katharine Gurski David Cotrell

We perform linear stability calculations for horizontal fluid bilayers, taking into account both buoyancy effects and thermocapillary effects in the presence of a vertical temperature gradient. To help understand the mechanisms driving the instability, we have performed both long-wavelength and short-wavelength analyses. The mechanism for the large wavelength instability is complicated, and the detailed form of the expansion is found to depend on the Crispation and Bond numbers. The system also allows a conventional Rayleigh-Taylor instability if heavier fluid overlies lighter fluid, and the long-wavelength analysis describes this case as well. In addition to the asymptotic analyses for large and small wavelengths, we have performed numerical calculations using materials parameters for a benzene-water system.

Rayleigh–Taylor instability

Convective instability

10.6028/jres.112.020

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Citations (7)

Microgravity processing of immiscible aluminum-indium alloys

Advances in Space Research (1998)

J. B. Andrews Larry Hayes Y. Arikawa S.R. Coriell

10.1016/s0273-1177(98)00154-9

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Citations (3)

Effect of a crystal-melt interface on Taylor-vortex flow with buoyancy

G. B. McFadden Bruce T. Murray S.R. Coriell M. E. Glicksman M. E. Selleck

During crystal growth from the melt, a fundamental problem is to understand the interaction of the crystal-melt interface with fluid flow in the melt.This problem combines the complexities of the Navier-Stokes equations for fluid flow with the nonlinear behavior of the free boundary representing the crystal-melt interface.Some progress has been made by studying explicit flows that allow a base state corresponding to a one-dimensional crystal-melt interface with solute and/or temperature fields that depend only on the distance from the interface.This allows the strength of the interaction between the flow and the interface to be assessed by a linear stability analysis of the simple base state.The case of a Taylor-Couette flow interacting with a cylindrical crystalline interface is currently being investigated both experimentally and theoretically.We con- sider the changes in the linear stability of this system produced by density-driven convection generated by the interaction of the density gradients with the gravitational and centripetal acceleration.1 'o rw»v^^-w

Interface (matter)

10.6028/nist.ir.4364

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Citations (3)

Effect of surface tension anisotropy on cellular morphologies

Journal of Crystal Growth (1988)

G. B. McFadden S.R. Coriell Robert F. Sekerka

Crystal (programming language)

Directional solidification

10.1016/0022-0248(88)90385-5

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Citations (39)

Effects of shear flow and anisotropic kinetics on the morphological stability of a binary alloy

Metallurgical and Materials Transactions A (1996)

S.R. Coriell B.T. Murray A. A. Chernov G. B. McFadden

Shear velocity

10.1007/bf02648955

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Citations (17)

Influence of a Catalytic Surfactant on Roughness Evolution During Film Growth

Journal of The Electrochemical Society (2004)

Daniel Wheeler T. P. Moffat G. B. McFadden S.R. Coriell D. Josell

A numerical analysis is presented to explain the effect of catalytic surfactant on roughness evolution during film growth mediated by an electrochemical or chemical reaction. The analysis uses the previously published curvature enhanced accelerator coverage (CEAC) mechanism; the CEAC mechanism accounts for the conservation of local coverage of adsorbed catalyst on a deforming interface. It has recently been demonstrated that the CEAC mechanism stabilizes surfaces against the growth of instabilities when the coverage of an adsorbed catalyst is in a steady state governed by catalyst consumption balanced by accumulation from the ambient. Surfaces with global conservation of catalyst during deposition, i.e., experiencing neither accumulation nor consumption, are not predicted to be stable. Experimental evidence suggests otherwise. This paper uses numerical analysis to demonstrate that such surfaces, while not strictly stable to arbitrarily small perturbations, are effectively stabilized through the formation of time dependent oscillatory states with extremely small amplitudes. A simple front tracking algorithm is used to model the evolution of the interface. © 2004 The Electrochemical Society. All rights reserved.

Deposition

Conservation of mass

10.1149/1.1767351

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Citations (34)

Effect of a crystal-melt interface on Taylor-vortex flow

G. B. McFadden S.R. Coriell B.T. Murray

The linear stability of circular Couette flow between concentric infinite cylinders is considered for the case that the stationary outer cylinder is a crystal–melt interface rather than a rigid surface. A radial temperature difference is maintained across the liquid gap, and equations for heat transport in the crystal and melt phases are included to extend the ordinary formulation of this problem. The stability of this two‐phase system depends on the Prandtl number. For small Prandtl number the linear stability of the two‐phase system is given by the classical results for a rigid‐walled system. For increasing values of the Prandtl number, convective heat transport becomes significant and the system becomes increasingly less stable. Previous results in a narrow‐gap approximation are extended to the case of a finite gap, and both axisymmetric and nonaxisymmetric disturbance modes are considered. The two‐phase system becomes less stable as the finite gap tends to the narrow‐gap limit. The two‐phase system is more stable to nonaxisymmetric modes with azimuthal wavenumber n=1; the stability of these n=1 modes is sensitive to the latent heat of fusion.

Interface (matter)

Crystal (programming language)

10.6028/nist.ir.89-4192

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Citations (1)

Equilibrium and stability of axisymmetric drops on a conical substrate under gravity

Physics of Fluids (2015)

A. K. Nurse Sean Colbert-Kelly S.R. Coriell G. B. McFadden

Motivated by recent investigations of toroidal tissue clusters that are observed to climb conical obstacles after self-assembly [Nurse et al., “A model of force generation in a three-dimensional toroidal cluster of cells,” J. Appl. Mech. 79, 051013 (2012)], we study a related problem of the determination of the equilibrium and stability of axisymmetric drops on a conical substrate in the presence of gravity. A variational principle is used to characterize equilibrium shapes that minimize surface energy and gravitational potential energy subject to a volume constraint, and the resulting Euler equation is solved numerically using an angle/arclength formulation. The resulting equilibria satisfy a Laplace-Young boundary condition that specifies the contact angle at the three-phase trijunction. The vertical position of the equilibrium drops on the cone is found to vary significantly with the dimensionless Bond number that represents the ratio of gravitational and capillary forces; a global force balance is used to examine the conditions that affect the drop positions. In particular, depending on the contact angle and the cone half-angle, we find that the vertical position of the drop can either increase (“the drop climbs the cone”) or decrease due to a nominal increase in the gravitational force. Most of the equilibria correspond to upward-facing cones and are analogous to sessile drops resting on a planar surface; however, we also find equilibria that correspond to downward facing cones that are instead analogous to pendant drops suspended vertically from a planar surface. The linear stability of the drops is determined by solving the eigenvalue problem associated with the second variation of the energy functional. The drops with positive Bond number are generally found to be unstable to non-axisymmetric perturbations that promote a tilting of the drop. Additional points of marginal stability are found that correspond to limit points of the axisymmetric base state. Drops that are far from the tip are subject to azimuthal instabilities with higher mode numbers that are analogous to the Rayleigh instability of a cylindrical interface. We have also found a range of completely stable solutions that correspond to small contact angles and cone half-angles.

Dimensionless quantity

10.1063/1.4927697

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Citations (3)