Crynodeb
A mathematical analysis is presented of the stability of a soap film with uniform surface tension when stretched between two diameters on the inside of a circular cylinder. The stability boundary is found as a critical twist angle. between the two diameters, as a function of the aspect ratio l of the cylinder. Numerical and asymptotic results agree well with previous numerical simulations and experiments by Cox and Jones (J. Engr. Math., 86 (2014), 17). Their hypothesis that the stability boundary for the multiplevane case is identical to the single film case is confirmed. It is also shown that two distinct instability mechanisms operate. For moderate and small theta/l, the instability is driven by the decrease in area caused by the film moving to an offdiameter position. But for larger theta/l (more twisted films), the decrease in area is dominated by an internal rearrangement of the surface. The latter mechanism is more relevant to Plateau borders in foams, and our results indicate that straight Plateau borders should be stable at any length provided the total twist is less than pi/root 2. Document embargo until 29/01/2016
Iaith wreiddiol  Saesneg 

Tudalennau (oi)  2352 
Nifer y tudalennau  30 
Cyfnodolyn  Quarterly Journal of Mechanics and Applied Mathematics 
Cyfrol  68 
Rhif cyhoeddi  1 
Dyddiad arlein cynnar  29 Ion 2015 
Dynodwyr Gwrthrych Digidol (DOIs)  
Statws  Cyhoeddwyd  Chwef 2015 
Ôl bys
Gweld gwybodaeth am bynciau ymchwil 'Stability of a helicoidal surface inside a cylinder with pinned diameters'. Gyda’i gilydd, maen nhw’n ffurfio ôl bys unigryw.Proffiliau

Simon Cox
 Cyfadran Busnes a’r Gwyddorau Ffisegol, Mathemateg  Professor, Head of Department (Maths)
Unigolyn: Dysgu ac Ymchwil