Extensional deformation of Newtonian liquid bridges

A numerical investigation is presented of axisymmetric, static and elongating, viscous Newtonian liquid bridges confined between identical circular disks. The time‐dependent interface shapes and applied forces on the end plates, which separate at a constant prescribed velocity, are calculated as functions of the capillary number, the viscosity ratio between the inner and outer fluids, and an initial bridge configuration characterized by the aspect ratio. The numerical simulations are in excellent agreement with available experimental data and provide useful insight into the different dynamical responses of extending liquid bridge configurations. In particular, liquid bridges surrounded by fluids of a relatively small viscosity deform in a fore‐aft symmetrical manner and undergo breakup sooner than in the case of relatively viscous outer fluids, which also require a greater applied force on the end plates to maintain the desired motion. Decreasing the capillary number (increasing interfacial tension) and t...

[1]  A. Laverón-Simavilla,et al.  Equilibrium shapes of nonaxisymmetric liquid bridges of arbitrary volume in gravitational fields and their potential energy , 1995 .

[2]  Fluid physics : lecture notes of summer schools , 1995 .

[3]  J. Eggers.  Theory of drop formation , 1995, physics/0111003.

[4]  H. Rath,et al.  Measurement of extensional viscosity by stretching large liquid bridges in microgravity , 1994 .

[5]  Christopher W. Macosko,et al.  Rheology: Principles, Measurements, and Applications , 1994 .

[6]  P. Steen,et al.  Stabilization of an axisymmetric liquid bridge by viscous flow , 1994 .

[7]  J. Tsamopoulos,et al.  Nonlinear dynamics of capillary bridges: theory , 1993, Journal of Fluid Mechanics.

[8]  José Manuel Perales Perales,et al.  Stability of liquid bridges between equal disks in an axial gravity field , 1993 .

[9]  H. Dijkstra.  On the shear stabilization of capillary break-up of finite liquid bridges , 1993 .

[10]  A. Delgado,et al.  Stretching behaviour of large polymeric and Newtonian liquid bridges in plateau simulation , 1992 .

[11]  J. A. Nicolás.  Hydrodynamic stability of high‐viscosity cylindrical liquid bridges , 1992 .

[12]  Anthony M. J. Davis,et al.  Cylindrical liquid bridges squeezed between parallel plates: Exact Stokes flow solutions and hydrodynamic forces , 1992 .

[13]  C. Pozrikidis.  Boundary Integral and Singularity Methods for Linearized Viscous Flow: Index , 1992 .

[14]  J. Tsamopoulos,et al.  Viscous oscillations of capillary bridges , 1992, Journal of Fluid Mechanics.

[15]  H. Stone,et al.  Boundary Integral Methods for Viscous Free-Boundary Problems: Deformation of Single and Multiple Fluid-Fluid Interfaces , 1992 .

[16]  J. Meseguer,et al.  Non-steady Phenomena in the Vibration of Viscous Cylindrical Long Liquid Bridges , 1992 .

[17]  J. Tsamopoulos,et al.  Boundary‐layer analysis of the dynamics of axisymmetric capillary bridges , 1991 .

[18]  R. Keunings,et al.  Mechanics of the “falling plate” extensional rheometer , 1991 .

[19]  R. Gupta,et al.  Measurement of extensional viscosity of polymer solutions , 1991 .

[20]  A. Delgado.  Non-Newtonian effects under microgravity conditions , 1991 .

[21]  J. Meseguer,et al.  Stability limits of minimum volume and breaking of axisymmetric liquid bridges between unequal disks , 1991 .

[22]  W. Barnes,et al.  Adhesion and Detachment of the Toe Pads of Tree Frogs , 1991 .

[23]  A. F. G. Dixon,et al.  The Mechanism by Which Aphids Adhere to Smooth Surfaces , 1990 .

[24]  J. Matta,et al.  Liquid stretching using a falling cylinder , 1990 .

[25]  Howard A. Stone,et al.  Relaxation and breakup of an initially extended drop in an otherwise quiescent fluid , 1989, Journal of Fluid Mechanics.

[26]  A. Sanz.  The influence of the outer bath in the dynamics of axisymmetric liquid bridges , 1985, Journal of Fluid Mechanics.

[27]  J. Meseguer,et al.  Numerical and experimental study of the dynamics of axisymmetric slender liquid bridges , 1985 .

[28]  J. Meseguer,et al.  One-dimensional self-similar solution of the dynamics of axisymmetric slender liquid bridges , 1984, Journal of Fluid Mechanics.

[29]  I. Martínez,et al.  Minimum volume for a liquid bridge between equal disks , 1983 .

[30]  Motion of a sphere in the presence of a deformable interface , 1982 .

[31]  L. G. Leal,et al.  The motion of a sphere in the presence of a deformable interface: II. A numerical study of the translation of a sphere normal to an interface , 1982 .

[32]  A. Acrivos,et al.  A numerical study of the deformation and burst of a viscous drop in an extensional flow , 1978, Journal of Fluid Mechanics.

[33]  Sam R. Coriell,et al.  Stability of liquid zones , 1977 .

[34]  R. Bird.  Dynamics of Polymeric Liquids , 1977 .

[35]  D. Dyson,et al.  Stability of fluid interfaces of revolution between equal solid circular plates , 1971 .

[36]  D. Dyson,et al.  Stability of interfaces of revolution with constant surface tension—the case of the catenoid , 1970 .

[37]  S. Gupta.  Slow broad side motion of a flat plate in a viscous liquid , 1957 .

[38]  M. Ray.  XLVI. Application of Bessel functions to the solution of problem of motion of a circular disk in viscous liquid , 1936 .

[39]  F. T. Trouton,et al.  On the coefficient of viscous traction and its relation to that of viscosity , 1906 .