Stability analysis of a thin film on a rotating cylinder with low airflow

2019 ◽  
Vol 31 (3) ◽  
pp. 034106
Author(s):  
Heather Newell ◽  
Hendrik Viljoen
Keyword(s):  
Thin Film ◽  
Stability Analysis ◽  
Rotating Cylinder

The motion of rotating cylinders sliding on pebbled ice

2000 ◽  
Vol 77 (11) ◽  
pp. 847-862 ◽  
Author(s):  
MRA Shegelski ◽  
M Reid ◽  
R Niebergall
Keyword(s):  
Thin Film ◽  
Liquid Film ◽  
Contact Area ◽  
Relative Velocity ◽  
Thin Liquid Film ◽  
Center Of Mass ◽  
Translational Motion ◽  
Rotating Cylinder ◽  
Outer Edge ◽  
Slow Rotation

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

scholarly journals Temperature Stability Analysis of Thin-Film Lithium Niobate SH0 Plate Wave Resonators

2019 ◽  
Vol 28 (5) ◽  
pp. 799-809 ◽  
Author(s):  
Ming-Huang Li ◽  
Chao-Yu Chen ◽  
Ruochen Lu ◽  
Yansong Yang ◽  
Tao Wu ◽  
...  
Keyword(s):  
Thin Film ◽  
Stability Analysis ◽  
Lithium Niobate ◽  
Temperature Stability ◽  
Plate Wave

The influence of a small upstream wire on transition in a rotating cylinder wake

2015 ◽  
Vol 769 ◽  
Author(s):  
Anirudh Rao ◽  
Alexander Radi ◽  
Justin S. Leontini ◽  
Mark C. Thompson ◽  
John Sheridan ◽  
...  
Keyword(s):  
Stability Analysis ◽  
Three Dimensional ◽  
Small Diameter ◽  
Reynolds Numbers ◽  
Rotating Cylinder ◽  
Hydrogen Bubble ◽  
Instability Mode ◽  
Cylinder Wake ◽  
Rotation Rates ◽  
Mode Transitions

Recent experimental research on rotating cylinder wakes has found that a previously numerically predicted subharmonic instability mode, mode C, occurs for considerably lower rotation rates than predicted through stability analysis, yet other mode transitions occur closer to the predicted onset. One difference between the theoretical and experimental set-ups is the use of a small-diameter hydrogen bubble visualisation wire placed upstream of the rotating cylinder. The current paper tests the hypothesis that a wire, of only $1/100$th of the cylinder diameter, placed five diameters upstream of the cylinder, sufficiently perturbs the flow to substantially affect certain wake transitions, including the onset of mode C. This is achieved using stability analysis of a flow that includes the upstream wire. The results indeed show that the wire of a tiny diameter induces a non-negligible asymmetry in the flow, triggering the subharmonic mode at substantially lower rotation rates. Furthermore, at higher rotation rates, the onset of two other three-dimensional modes are delayed to higher Reynolds numbers. These results make the point that even seemingly minute perturbations caused by minimally intrusive methods may result in substantially altered experimental flow behaviour.

Thin-film and curtain flows on the outside of a rotating horizontal cylinder

1999 ◽  
Vol 394 ◽  
pp. 29-49 ◽  
Author(s):  
B. R. DUFFY ◽  
S. K. WILSON
Keyword(s):  
Thin Film ◽  
Finite Thickness ◽  
Surface Profile ◽  
Rotating Cylinder ◽  
Horizontal Cylinder ◽  
Lubrication Approximation ◽  
Coating Flows ◽  
Stagnation Points ◽  
Free Surface Profile ◽  
Two Dimensional Flow

We use the lubrication approximation to investigate the steady two-dimensional flow of a thin film of viscous fluid on the outside of a rigid circular cylinder that is rotating about its (horizontal) axis. Primarily we are concerned with the flow that ensues when fluid is supplied continuously as a ‘curtain’ from above the cylinder, so that it flows round the cylinder and eventually falls off near the bottom. This problem may be thought of as a ‘hybrid’ of the two classical problems studied by Nusselt (1916a, b) and Moffatt (1977), concerning, respectively, flow on a stationary cylinder with a prescribed supply flux, and flow on a rotating cylinder when the supply flux is zero. For all these problems there are indeterminacies in the steady lubrication solution; we present a variety of possible solutions, including both ‘full-film’ and ‘partial-film’ solutions, and solutions that involve smooth ‘jumps’ in the free-surface profile. We show, for example, that stagnation points can occur in the flow, that solutions exist that do not have top-to-bottom symmetry, that in curtain flows the curtain generally takes a characteristic ‘buckled’ shape, and that in full-film curtain flows there is always some fluid that is ‘trapped’ near the rotating cylinder, never escaping as part of the curtain that detaches at the bottom of the cylinder. Also we show that finite-thickness films involving jumps cannot occur in these coating flows (though they are known to occur in rimming flows).

Feedback control of Marangoni convection in a thin film heated from below

2019 ◽  
Vol 876 ◽  
pp. 573-590 ◽  
Author(s):  
Anna E. Samoilova ◽  
Alexander Nepomnyashchy
Keyword(s):  
Thin Film ◽  
Stability Analysis ◽  
Feedback Control ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Control Strategies ◽  
Oscillatory Mode ◽  
Linear Feedback ◽  
Marangoni Instability ◽  
Strategy I

We use linear proportional control for the suppression of the Marangoni instability in a thin film heated from below. Our keen interest is focused on the recently revealed oscillatory mode caused by a coupling of two long-wave monotonic instabilities, the Pearson and deformational ones. Shklyaev et al. (Phys. Rev. E, vol. 85, 2012, 016328) showed that the oscillatory mode is critical in the case of a substrate of very low conductivity. To stabilize the no-motion state of the film, we apply two linear feedback control strategies based on the heat flux variation at the substrate. Strategy (I) uses the interfacial deflection from the mean position as the criterion of instability onset. Within strategy (II) the variable that describes the instability is the deviation of the measured temperatures from the desired, conductive values. We perform two types of calculations. The first one is the linear stability analysis of the nonlinear amplitude equations that are derived within the lubrication approximation. The second one is the linear stability analysis that is carried out within the Bénard–Marangoni problem for arbitrary wavelengths. Comparison of different control strategies reveals feedback control by the deviation of the free surface temperature as the most effective way to suppress the Marangoni instability.

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