By Yulii D. Shikhmurzaev
Capillary Flows with Forming Interfaces explores a variety of theoretical difficulties that come up within the mathematical description of capillary flows. It specializes in constructing a unified method of various doubtless very diverse capillary flows of sensible significance the place classical fluid mechanics ends up in nonphysical results.The ebook starts off with a overview of the conceptual framework of fluid mechanics after which proceeds to research the roots of singularities, akin to the relocating contact-line challenge and the capillary breakup challenge. the writer then examines how diverse singular flows might be defined as specific situations of a basic actual phenomenon of interface formation. He illustrates the built mathematical types and experimentally verifies them via a few instance difficulties appropriate to engineering applications.The conceptual framework supplied during this reference permits extra development in constructing mathematical versions of capillary flows.The publication additionally permits readers to make knowledgeable strategic offerings concerning to be had numerical codes and the in-house improvement of those codes.
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Extra info for Capillary Flows with Forming Interfaces
Qualitative arguments related to time averaging can be considered in a similar way. 2 Hence the often used term ‘continuum hypothesis’ implying not a hypothesis about any of physical properties of the ﬂuid, which could turn out to be true or false; it refers to the hypothetical ‘continuous medium’ used as a model of the real ﬂuid. 1: A sketch illustrating how a ‘continuum medium’ results from the thermodynamic limit (a)→(b)→(c). For gases, a full ﬂuid-mechanical model can be derived from statistical physics, where the macroscopic quantities are introduced via a more ﬂexible technique of ensemble averaging which considers possible microscopic ‘realisations’ of a macroscopic state of the ﬂuid.
Stress tensor Symmetry of In classical mechanics, for the angular momentum of a system of N material points of mass mi located at ri (i = 1, 2, . . 33) i=1 (i = 1, 2, . . 34) i=1 is, by deﬁnition, the angular momentum. The angular momentum can be also written down in the form N K = r∗ × M u∗ + (ri × mi ui ), i=1 N where M = i=1 mi is the total mass; r∗ and u∗ are the position and velocity of the center of mass; ri and ui are positions and velocities of points in a moving coordinate frame with the origin at the center of mass.
25). 32) include gradients of the stress tensor. 31), for 13 unknown scalar functions: ρ, three components of u and nine components of P. 31), for twelve unknown components of u and P. To add more equations, or, as it will turn out, to reduce the number of unknowns, we have to consider the balance of the angular momentum. 3 Conservation of angular momentum. stress tensor Symmetry of In classical mechanics, for the angular momentum of a system of N material points of mass mi located at ri (i = 1, 2, .