Thick fluid interface modeling

Prud'Homme, Roger; Gatignol, Renée

doi:10.1016/j.ijthermalsci.2003.08.003

Cited by 1 publication

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“…For what concerns the three-dimensional models of phase interfaces by means of generalized continua, we give here only a very biased list of research papers which exploited and developed the ideas presented by Hellinger. The reader will easily find from them the research streams to which we refer, [2][3][4][5]12,13,24,25,30,31,[51][52][53]74,91,94,95]. Using different methods all the previous papers create also a "limit" model which applies when the thickness of the interface is small.…”

Section: Annotated Translation Of Nomentioning

confidence: 99%

Exegesis of Sect. III.B from “Fundamentals of the Mechanics of Continua” by E. Hellinger

Eugster

Dell’Isola

2017

Z Angew Math Mech

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This is our third and last exegetic essay on the fundamental review article DIE ALLGEMEINEN ANSÄTZE DER MECHANIK DER KONTINUA in the Encyklopädie der mathematischen Wissenschaften mit Einschluss ihrer Anwendungen, Bd. IV-4, Hft. 5 (1913) by Ernst Hellinger which contains the translation and the commentary of the remaining text starting from p. 663. The six subsections, No. 9-15, deal with the applications of the previously developed conceptual tools to formulate: an effective theory of elasticity, the dynamics of ideal fluids, models for internal friction and elastic hysteresis, a theory of capillarity, optics, the fundamental equations of electrodynamics, an introduction of the thermodynamical foundations and the relationship between the theory of continua and the theory of relativity. Hellinger refers to relevant literature while consolidating in an effective way the contemporary knowledge in 1913. Considering notational differences as being irrelevant for the characterization of the presented scientific content, Hellinger's article shows that an effective compendium of a large part of the insights given in Truesdell and Toupin [106] and Truesdell and Noll [105] has already been available in 1913. We include in this paper an assessment of the different roles played by pioneers, who are innovating their scientific discipline, and by erudite scholars whose role consists in re-ordering existent knowledge and advertising to a wider audience the most important technical results already obtained in a given discipline.

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