2016/04/01 by P. D. Howell, H. Kim, M. G. Popova +1
Engineering · Materials Science · Physics and Astronomy · #Beam (structure) #Deflection (physics) #Fluid Dynamics and Heat Transfer #Fluid Dynamics and Thin Films #Horizontal position representation #Lubrication #Lubrication theory #Surface Modification and Superhydrophobicity #Vertical deflection #physics.flu-dyn
paper · pdf · doi:10.1017/jfm.2016.258
†P. D. Howell and H. Kim contributed equally to this work. *Email address for correspondence: [email protected]
arxiv created 2016/04/01 · openalex publication_date 2016/05/04 · arxiv updated 2016/05/25 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We study theoretically and experimentally how a thin layer of liquid flows along a flexible beam. The flow is modelled using lubrication theory and the substrate is modelled as an elastica which deforms according to the Euler–Bernoulli equation. A constant flux of liquid is supplied at one end of the beam, which is clamped horizontally, while the other end of the beam is free. As the liquid film spreads, its weight causes the beam deflection to increase, which in turn enhances the spreading rate of the liquid. This feedback mechanism causes the front position \itσ(t) and the deflection angle at the front \itφ(t) to go through a number of different power-law behaviours. For early times, the liquid spreads like a horizontal gravity current, with \itσ(t)∝ t4/5 and \itφ(t)∝ t13/5 . For intermediate times, the deflection of the beam leads to rapid acceleration of the liquid layer, with \itσ(t)∝ t4 and \itφ(t)∝ t9 . Finally, when the beam has sagged to become almost vertical, the liquid film flows downward with \itσ(t)∝ t and \itφ(t)∼ \rmπ/2 . We demonstrate good agreement between these theoretical predictions and experimental results.