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 makes a speciality of constructing a unified method of numerous doubtless very diversified capillary flows of useful value the place classical fluid mechanics ends up in nonphysical results.
The publication starts with a evaluation of the conceptual framework of fluid mechanics after which proceeds to research the roots of singularities, reminiscent of the relocating contact-line challenge and the capillary breakup challenge. the writer then examines how assorted singular flows could be defined as specific instances of a common actual phenomenon of interface formation. He illustrates the built mathematical types and experimentally verifies them via a couple of instance difficulties suitable to engineering purposes.
The conceptual framework supplied during this reference allows extra development in constructing mathematical versions of capillary flows.
The e-book 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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Additional resources for Capillary Flows with Forming Interfaces
The material points M0 and M1 by deﬁnition have the same Lagrangian coordinates throughout their motion and the elementary vectors dr and dr both have the same coordinates (dξ 1 , dξ 2 , dξ 3 ). 48) εij = 12 (gij − gij ). 49) will have to transform as © 2008 by Taylor & Francis Group, LLC 38 Fundamentals of ﬂuid mechanics covariant components of a tensor. Thus, unsurprisingly, variations of lengths during ﬂow can be associated with the corresponding variations of the metric tensor generated in the observer’s space by the Lagrangian coordinates.
6: A deﬁnition sketch for the introduction of the stress tensor. 22) S(t) where ρF is the sum of external body forces, p are stresses, acting on the surface S conﬁning volume V , and n is a unit normal vector to S pointing outwards. 22) is the main dynamic relationship postulated in continuum mechanics. This equation requires only that the functions involved are integrable and can be applied to volumes containing surfaces of discontinuity. 22) will take the form ρ V (t) Du dV = Dt ρF dV + V (t) p(n) dS.
1 Conservation of mass Consider an arbitrary volume V whose position is ﬁxed relative to the observer’s reference frame, and let S be a surface conﬁning this volume and n be a unit outward normal to S. Then, if volume V is entirely occupied by ﬂuid of possibly variable density ρ, then ρ dV V is the mass of ﬂuid inside V at any instant. The net rate at which the mass inside the volume changes due to the mass ﬂux across its boundary is given by ρu · n dS. 11) S which describes conservation of mass in an integral form.