Journal ArticleDOI
Moving contact lines and rivulet instabilities. Part 1. The static rivulet
TLDR
In this paper, a linearized stability theory for small, static rivulets whose contact (common or three-phase) lines (i) are fixed, (ii) move but have fixed contact angles or (iii) have contact angles smooth functions of contact-line speeds is presented.Abstract:
A rivulet is a narrow stream of liquid located on a solid surface and sharing a curved interface with the surrounding gas. Capillary instabilities are investigated by a linearized stability theory. The formulation is for small, static rivulets whose contact (common or three-phase) lines (i) are fixed, (ii) move but have fixed contact angles or (iii) move but have contact angles smooth functions of contact-line speeds. The linearized stability equations are converted to a disturbance kinetic-energy balance showing that the disturbance response exactly satisfies a damped linear harmonic-oscillator equation. The ‘damping coefficient’ contains the bulk viscous dissipation, the effect of slip along the solid and all dynamic effects that arise in contact-line condition (iii). The ‘spring constant’, whose sign determines stability or instability in the system, incorporates the interfacial area changes and is identical in cases (ii) and (iii). Thus, for small disturbances changes in contact angle with contact-line speed constitute a purely dissipative process. All the above results are independent of slip model at the liquid–solid interface as long as a certain integral inequality holds. Finally, sufficient conditions for stability are obtained in all cases (i), (ii) and (iii).read more
Citations
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Gravity-driven draining of a thin rivulet with constant width down a slowly varying substrate
TL;DR: In this article, the authors investigated the locally unidirectional gravity-driven draining of a thin rivulet with constant width but slowly varying contact angle down a slowly varying substrate.
Journal ArticleDOI
Nonlinear Marangoni waves in a two-layer film with reflecting lateral boundaries
TL;DR: In this article, a two-layer film of a finite lateral extent is considered and the analysis is carried out in the lubrication approximation in the case of oscillatory instability, which takes place by heating from above.
Journal ArticleDOI
Steiner triangular drop dynamics
Elizabeth Wesson,Paul H. Steen +1 more
TL;DR: The Steiner triangle is a deforming triangle with one side making sliding contact against a planar basal support, and the center of mass of the triangle is governed by Newton's law.
Dissertation
Case Studies In Interfacial Stability And Solidification
TL;DR: In this article, a crack propagation view of natural detachment was used to predict catastrophic adhesion in a semi-empirical way, and the authors showed how the interfacial strength of adhesion, a property only of the pair of adhering materials, might be measured based on sticking distance experiments.
Journal ArticleDOI
Multiple equilibrium shapes of partially constrained menisci: A quasi-static mechanism for instability of a coating bead
Brian G. Higgins,Robert S. Brown +1 more
TL;DR: In this paper, the upstream meniscus of an extrusion coating bead operating in the capillary limit is modelled as a cylindrical menisus that pins to the die and inte
References
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Book
Methods of Mathematical Physics
Richard Courant,David Hilbert +1 more
TL;DR: In this paper, the authors present an algebraic extension of LINEAR TRANSFORMATIONS and QUADRATIC FORMS, and apply it to EIGEN-VARIATIONS.
Journal ArticleDOI
Methods of Mathematical Physics
TL;DR: In this paper, the authors present an algebraic extension of LINEAR TRANSFORMATIONS and QUADRATIC FORMS, and apply it to EIGEN-VARIATIONS.
Journal ArticleDOI
On the Spreading of Liquids on Solid Surfaces: Static and Dynamic Contact Lines
TL;DR: In this article, it is shown that the mutual interaction between the three materials in the immediate vicinity of a contact line can significantly affect the statics as well as the dynamics of an entire flow field.
Liquids on solid surfaces: static and dynamic contact lines
TL;DR: In this paper, it is shown that the mutual interaction between the three materials in the immediate vicinity of a contact line can significantly affect the statics as well as the dynamics of an entire flow field.