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Method of matched asymptotic expansions

About: Method of matched asymptotic expansions is a research topic. Over the lifetime, 4233 publications have been published within this topic receiving 73311 citations.


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TL;DR: In this article, a matched asymptotic expansion of a small parameter L/a, where a is the particle radius and L is the length scale characteristic of the physical interaction between solute and particle surface, was used to obtain an expression for particle velocity.
Abstract: When a particle is placed in a fluid in which there is a non-uniform concentration of solute, it will move toward higher or lower concentration depending on whether the solute is attracted to or repelled from the particle surface. A quantitative understanding of this phenomenon requires that the equations representing conservation of mass and momentum within the fluid in the vicinity of the particle are solved. This is accomplished using a method of matched asymptotic expansions in a small parameter L/a, where a is the particle radius and L is the length scale characteristic of the physical interaction between solute and particle surface. This analysis yields an expression for particle velocity, valid in the limit L/a → 0, that agrees with the expression obtained by previous researchers. The result is cast into a more useful algebraic form by relating various integrals involving the solute/particle interaction energy to a measurable thermodynamic property, the Gibbs surface excess of solute Γ. An important result is that the correction for finite L/a is actually O(Γ/C∞ a), where C∞ is the bulk concentration of solute, and could be O(1) even when L/a is orders of magnitude smaller.

426 citations

Journal ArticleDOI
TL;DR: In this paper, it was shown that level surfaces of solutions to the Cahn-Hilliard equation tend to solutions of the Hele-Shaw problem under the assumption that classical solutions for the latter exist.
Abstract: We prove that level surfaces of solutions to the Cahn-Hilliard equation tend to solutions of the Hele-Shaw problem under the assumption that classical solutions of the latter exist. The method is based on a new matched asymptotic expansion for solutions, a spectral analysis for linearizd operators, and an estimate for the difference between the true solutions and certain approximate ones.

393 citations

Journal ArticleDOI
TL;DR: In this paper, the authors applied matched asymptotic expansions to investigate the effects of heat losses on linear stability of a planar flame, which is governed by a one-step irreversible Arrhenius reaction.

372 citations

Journal ArticleDOI
TL;DR: In this paper, a solution describing the spatial evolution of small-amplitude instability waves and their associated sound field of axisymmetric supersonic jets is found using the method of matched asymptotic expansions (see Part 1, Tam & Burton 1984).
Abstract: A solution describing the spatial evolution of small-amplitude instability waves and their associated sound field of axisymmetric supersonic jets is found using the method of matched asymptotic expansions (see Part 1, Tam & Burton 1984). The inherent axisymmetry of the problem allows the instability waves to be decomposed into azimuthal wave modes. In addition, it is found that because of the cylindrical geometry of the problem the gauge functions of the inner expansion, unlike the case of two-dimensional mixing layers, are no longer just powers of e. Instead they contain logarithmic terms. To test the validity of the theory, numerical results of the solution are compared with the experimental measurements of Troutt (1978) and Troutt & McLaughlin (1982). Two series of comparisons at Strouhal numbers 0.2 and 0.4 for a Mach-number 2.1 cold supersonic jet are made. The data compared include hot-wire measurements of the axial distribution of root-mean-squared jet centreline mass-velocity fluctuations and radial and axial distributions of near-field pressure-level contours measured by microphones. The former is used to test the accuracy of the inner (or instability-wave) solution. The latter is used to verify the correctness of the outer solution. Very favourable overall agreements between the calculated results and the experimental measurements are found. These very favourable agreements strongly suggest that the method of solution developed in Part 1 paper is indeed valid. Furthermore, they also offer concrete support to the proposition made previously by a number of investigators that instability waves are important noise sources in supersonic jets.

364 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202321
202244
202110
202023
201913
201835