2015
DOI: 10.1017/jfm.2015.589
|View full text |Cite
|
Sign up to set email alerts
|

Displacement flows under elastic membranes. Part 2. Analysis of interfacial effects

Abstract: We investigate the injection of inviscid gas into the narrow liquid-filled gap between a rigid base plate and an overlying elastic sheet. After an early-time transient in which the gas deflects the sheet into a large blister, the viscous liquid displaced by the expanding bubble starts to accumulate in a wedge which advances as the elastic sheet peels away from the base. We analyse theoretically the subsequent interaction between viscous forces, elastic (bending or tension) forces and capillary forces. Asymptot… Show more

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...
2
1
1
1

Citation Types

3
65
0

Year Published

2015
2015
2019
2019

Publication Types

Select...
7

Relationship

2
5

Authors

Journals

citations
Cited by 40 publications
(68 citation statements)
references
References 25 publications
3
65
0
Order By: Relevance
“…Scaling by the characteristic dimensions, we define the following normalized quantities: (x, y, z) = (x/l * ,ỹ/l * ,z/h 0 ), (u, v, w) = (ũ/ũ * ,ṽ/ũ * ,w/w * ), p =p/p * , t =t/t * , d =d/d * and h =h/h 0 . As noted by Peng et al (2015), the bending-tension length scalel BT = B /T determines the relative importance of bending and tension forces in the elastic response of the sheet; forl * l BT bending forces dominate, whereas forl * l BT tension forces dominate. A convenient dimensionless number when scaling (2.2) is λ, defined as…”
Section: Scaling Analysis and Non-dimensionalizationmentioning
confidence: 99%
“…Scaling by the characteristic dimensions, we define the following normalized quantities: (x, y, z) = (x/l * ,ỹ/l * ,z/h 0 ), (u, v, w) = (ũ/ũ * ,ṽ/ũ * ,w/w * ), p =p/p * , t =t/t * , d =d/d * and h =h/h 0 . As noted by Peng et al (2015), the bending-tension length scalel BT = B /T determines the relative importance of bending and tension forces in the elastic response of the sheet; forl * l BT bending forces dominate, whereas forl * l BT tension forces dominate. A convenient dimensionless number when scaling (2.2) is λ, defined as…”
Section: Scaling Analysis and Non-dimensionalizationmentioning
confidence: 99%
“…the passage of the finger, which are not accounted for in the lubrication model developed by Thompson et al (2014). Park & Homsy (1984), Reinelt & Saffman (1985) and, more recently, Peng et al (2015) included thin-film effects by modifying the kinematic and dynamic boundary conditions. Consequently, the interface velocity decreases and the cross-sectional curvature increases by a small factor.…”
Section: Comparison Between Experimental and Numerical Modes Of Fingementioning
confidence: 99%
“…and studied a rigid and elastic plates, either pinned or free floating, moving over a viscous film laying on a flat rigid surface. The displacement dynamics of a liquid entrained between an elastic sheet and a rigid surface, due to injection of another fluid, was studied experimentally, numerically and analytically by Peng et al (2015) and Pihler-Puzović et al (2015).…”
Section: Introductionmentioning
confidence: 99%