TY - JOUR
T1 - Coalescence of drops with mobile interfaces in a quiescent fluid
AU - Nemer, M. B.
AU - Santoro, P.
AU - Chen, X.
AU - Bławzdziewicz, J.
AU - Loewenberg, M.
PY - 2013/8/10
Y1 - 2013/8/10
N2 - A study on the axisymmetric near-contact motion of drops with tangentially mobile interfaces under the action of a body force in a quiescent fluid is described. A long-time asymptotic analysis is presented for small-deformation conditions. Under these conditions the drops are nearly spherical, except in the near-contact region, where a flattened thin film forms. According to our analysis, a hydrostatic dome does not form in the near-contact region at long times, in contrast to the assumption underlying all previous analyses of this problem. Instead, the shape of the film in the near-contact region results from the absence of tangential stresses acting on it. As a result, the long-time behaviour of the system is qualitatively different than previously predicted. According to the theory presented herein, the minimum film thickness (rim region) decays with time as hm ~ t-4/5, and the thickness at the centre of the film decays as h0 ~ t- 3/5, which is a faster decay than predicted by prior analyses based on a hydrostatic dome. Numerical thin-film simulations quantitatively confirm the predictions of our small-deformation theory. Boundary-integral simulations of the full two-drop problem suggest that the theory also describes qualitatively the long-time evolution under finite-deformation conditions.
AB - A study on the axisymmetric near-contact motion of drops with tangentially mobile interfaces under the action of a body force in a quiescent fluid is described. A long-time asymptotic analysis is presented for small-deformation conditions. Under these conditions the drops are nearly spherical, except in the near-contact region, where a flattened thin film forms. According to our analysis, a hydrostatic dome does not form in the near-contact region at long times, in contrast to the assumption underlying all previous analyses of this problem. Instead, the shape of the film in the near-contact region results from the absence of tangential stresses acting on it. As a result, the long-time behaviour of the system is qualitatively different than previously predicted. According to the theory presented herein, the minimum film thickness (rim region) decays with time as hm ~ t-4/5, and the thickness at the centre of the film decays as h0 ~ t- 3/5, which is a faster decay than predicted by prior analyses based on a hydrostatic dome. Numerical thin-film simulations quantitatively confirm the predictions of our small-deformation theory. Boundary-integral simulations of the full two-drop problem suggest that the theory also describes qualitatively the long-time evolution under finite-deformation conditions.
KW - Breakup/coalescence
KW - Drops
KW - Emulsions
UR - http://www.scopus.com/inward/record.url?scp=84886301859&partnerID=8YFLogxK
U2 - 10.1017/jfm.2013.288
DO - 10.1017/jfm.2013.288
M3 - Article
AN - SCOPUS:84886301859
SN - 0022-1120
VL - 728
SP - 471
EP - 500
JO - Journal of Fluid Mechanics
JF - Journal of Fluid Mechanics
ER -