Modulational instability in thin liquid film flowing down an inclined uniformly heated plate

We consider the motion of a cylinder with the same mass and sizeas a curling rock, but with a very different contact geometry.Whereas the contact area of a curling rock is a thin annulus havinga radius of 6.25 cm and width of about 4 mm, the contact area of the cylinderinvestigated takes the form of several linear segments regularly spacedaround the outer edge of the cylinder, directed radially outward from the center,with length 2 cm and width 4 mm. We consider the motion of this cylinderas it rotates and slides over ice having the nature of the ice surfaceused in the sport of curling. We have previously presented a physicalmodel that accounts for the motion of curling rocks; we extend this modelto explain the motion of the cylinder under investigation. In particular,we focus on slow rotation, i.e., the rotational speed of the contact areasof the cylinder about the center of mass is small compared to thetranslational speed of the center of mass.The principal features of the model are (i) that the kineticfriction induces melting of the ice, with the consequence that thereexists a thin film of liquid water lying between the contact areasof the cylinder and the ice; (ii) that the radial segmentsdrag some of the thin liquid film around the cylinder as it rotates,with the consequence that the relative velocity between the cylinderand the thin liquid film is significantly different than the relativevelocity between the cylinder and the underlying solid ice surface.Since it is the former relative velocity that dictates the nature of themotion of the cylinder, our model predicts, and observations confirm, thatsuch a slowly rotating cylinder stops rotating well before translationalmotion ceases. This is in sharp contrast to the usual case of most slowlyrotating cylinders, where both rotational and translational motion ceaseat the same instant. We have verified this prediction of our model bycareful comparison to the actual motion of a cylinder having a contactarea as described.PACS Nos.: 46.00, 01.80+b

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Visualization of Surface Acoustic Waves in Thin Liquid Films

Scientific Reports ◽

10.1038/srep21980 ◽

2016 ◽

Vol 6 (1) ◽

Cited By ~ 20

Author(s):

R. W. Rambach ◽

J. Taiber ◽

C. M. L. Scheck ◽

C. Meyer ◽

J. Reboud ◽

...

Keyword(s):

Liquid Film ◽

Acoustic Waves ◽

Low Cost ◽

Thin Liquid Film ◽

Surface Acoustic Waves ◽

Liquid Films ◽

Theoretical Description ◽

Propagation Path ◽

Microfluidic Channels ◽

Potential Applications

Abstract We demonstrate that the propagation path of a surface acoustic wave (SAW), excited with an interdigitated transducer (IDT), can be visualized using a thin liquid film dispensed onto a lithium niobate (LiNbO3) substrate. The practical advantages of this visualization method are its rapid and simple implementation, with many potential applications including in characterising acoustic pumping within microfluidic channels. It also enables low-cost characterisation of IDT designs thereby allowing the determination of anisotropy and orientation of the piezoelectric substrate without the requirement for sophisticated and expensive equipment. Here, we show that the optical visibility of the sound path critically depends on the physical properties of the liquid film and identify heptane and methanol as most contrast rich solvents for visualization of SAW. We also provide a detailed theoretical description of this effect.

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Thin liquid film resulting from a distributed source on a vertical wall

Physical Review Fluids ◽

10.1103/physrevfluids.5.064004 ◽

2020 ◽

Vol 5 (6) ◽

Author(s):

Yadong Ruan ◽

Ali Nadim ◽

Marina Chugunova

Keyword(s):

Liquid Film ◽

Thin Liquid Film ◽

Vertical Wall ◽

Distributed Source

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