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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Viscoelastic effects in circular edge waves
TL;DR: In this article, the eigenvalue problem is equivalent to the classic damped-driven oscillator model on linear operators with viscosity appearing as damping force and elasticity and surface tension as restorative forces, consistent with our physical interpretation of these viscoelastic effects.
A study of inkjet printed line morphology using volatile ink with non-zero receding contact angle for conductive trace fabrication
TL;DR: Shou et al. as mentioned in this paper studied the line morphology of a homogeneous solid substrate with non-zero receding contact angle (NRCA) for conductive trace fabrication and found a new family of line instability, featuring the formation of agglomerations within a line.
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Dynamic stabilisation of Rayleigh–Plateau modes on a liquid cylinder
TL;DR: In this paper , the authors demonstrate dynamic stabilisation of axisymmetric Fourier modes susceptible to the classical Rayleigh-Plateau (RP) instability on a liquid cylinder by subjecting it to a radial oscillatory body force.
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Coalescence-induced droplet spreading: experiments aboard the International Space Station
TL;DR: In this paper , the authors report experiments of centimeter-sized sessile drop coalescence aboard the International Space Station (ISS), where microgravity conditions enable inertial-capillary spreading motions to be explored for a range of hydrophobic wetting conditions.
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.