TY - JOUR
T1 - Interfacial elastic fingering in Hele-Shaw cells
T2 - A weakly nonlinear study
AU - Carvalho, Gabriel D.
AU - Miranda, José A.
AU - Gadelha, Hermes
PY - 2013/11/11
Y1 - 2013/11/11
N2 - We study a variant of the classic viscous fingering instability in Hele-Shaw cells where the interface separating the fluids is elastic, and presents a curvature-dependent bending rigidity. By employing a second-order mode-coupling approach we investigate how the elastic nature of the interface influences the morphology of emerging interfacial patterns. This is done by focusing our attention on a conventionally stable situation in which the fluids involved have the same viscosity. In this framework, we show that the inclusion of nonlinear effects plays a crucial role in inducing sizable interfacial instabilities, as well as in determining the ultimate shape of the pattern-forming structures. Particularly, we have found that the emergence of either narrow or wide fingers can be regulated by tuning a rigidity fraction parameter. Our weakly nonlinear findings reinforce the importance of the so-called curvature weakening effect, which favors the development of fingers in regions of lower rigidity.
AB - We study a variant of the classic viscous fingering instability in Hele-Shaw cells where the interface separating the fluids is elastic, and presents a curvature-dependent bending rigidity. By employing a second-order mode-coupling approach we investigate how the elastic nature of the interface influences the morphology of emerging interfacial patterns. This is done by focusing our attention on a conventionally stable situation in which the fluids involved have the same viscosity. In this framework, we show that the inclusion of nonlinear effects plays a crucial role in inducing sizable interfacial instabilities, as well as in determining the ultimate shape of the pattern-forming structures. Particularly, we have found that the emergence of either narrow or wide fingers can be regulated by tuning a rigidity fraction parameter. Our weakly nonlinear findings reinforce the importance of the so-called curvature weakening effect, which favors the development of fingers in regions of lower rigidity.
UR - http://www.scopus.com/inward/record.url?scp=84888141451&partnerID=8YFLogxK
U2 - 10.1103/PhysRevE.88.053006
DO - 10.1103/PhysRevE.88.053006
M3 - Article
AN - SCOPUS:84888141451
SN - 1539-3755
VL - 88
JO - Physical Review E
JF - Physical Review E
IS - 5
M1 - 053006
ER -