Order-parameter-dependent mobility in the convective-viscous Cahn-Hilliard equation

Abstract

Generally the mobility in the Cahn-Hilliard equation may depend on the order parameter; this was evident already from the original derivation. However, explicit introduction of such dependence results in tremendous calculation difficulties, so the constant mobility approximation was commonly used. On the other hand, in several cases this dependence appeared to be crucial, so more realistic expressions were applied, usually positive powers or polynomials; still, for such dependencies only approximate and/or numerical solution exist. We consider 'reciprocal' linear and quadratic dependencies of mobility on the order parameter; for these dependencies exact traveling wave solutions are obtained. Even more, in a limited interval of the parameters reciprocal quadratic mobilities are rather good approximations to polynomial mobilities.

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BibTeX RIS

BibTeX

@misc{mchedlovpetrosyan2026orderparameterdependent,
  title = {{Order-parameter-dependent mobility in the convective-viscous Cahn-Hilliard equation}},
  author = {P. O. Mchedlov-Petrosyan and L. N. Davydov and O. A. Osmayev},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.25263},
  eprint = {2609.25263},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.25263},
  note = {CC BY 4.0},
}

RIS

TY  - UNPB
TI  - Order-parameter-dependent mobility in the convective-viscous Cahn-Hilliard equation
AU  - P. O. Mchedlov-Petrosyan
AU  - L. N. Davydov
AU  - O. A. Osmayev
PY  - 2026
DA  - 2026/09/26
PB  - arXiv
DO  - 10.48550/arxiv.2609.25263
UR  - https://arxiv.org/abs/2609.25263
AB  - Generally the mobility in the Cahn-Hilliard equation may depend on the order parameter; this was evident already from the original derivation. However, explicit introduction of such dependence results in tremendous calculation difficulties, so the constant mobility approximation was commonly used. On the other hand, in several cases this dependence appeared to be crucial, so more realistic expressions were applied, usually positive powers or polynomials; still, for such dependencies only approximate and/or numerical solution exist. We consider 'reciprocal' linear and quadratic dependencies of mobility on the order parameter; for these dependencies exact traveling wave solutions are obtained. Even more, in a limited interval of the parameters reciprocal quadratic mobilities are rather good approximations to polynomial mobilities.
ER  -

Abstract

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