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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Journal ArticleDOI
Formation of coffee stains on porous surfaces.
Rui Dou,Brian Derby +1 more
TL;DR: Here it is shown that a suspension, optimized to eliminate the formation of coffee stains on a range of solid surfaces, shows coffee staining on a number of porous surfaces, consistent with a mechanism of fluid removal through capillary flow (draining) of the solvent into the porous substrate, combined with filtration of the particles by the small pore size, in addition to the flow from solvent evaporation.
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Self-organized metal nanostructures through laser driven thermocapillary convection
TL;DR: In this article, the authors investigate self-organization and the ensuing length scales when Co films (1-8 nm thick) on SiO(n) surfaces are repeatedly and rapidly melted by non-uniform (interference) laser irradiation.
Book ChapterDOI
Structure Formation in Thin Liquid Films
TL;DR: In this paper, the authors outline some recent developments in the theoretical description of structure formation in thin liquid films and present the physical questions posed by the individual systems and discuss approaches and results for sliding drops on an inclined homogeneous substrate.
Journal ArticleDOI
Boundary‐layer analysis of the dynamics of axisymmetric capillary bridges
Abhay Borkar,John Tsamopoulos +1 more
TL;DR: In this article, the authors examined the small amplitude oscillations of capillary bridges in the limit of large modified Reynolds number and found that the oscillation frequency and damping rate depend on the aspect ratio of the bridge, the mode being excited, and the motion of the contact line.
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.