Catenoid Stability with a Free Contact Line

We analytically study the stability of catenoids pinned at one contact line, with the other free to move on a substrate subject to axisymmetric and nonaxisymmetric perturbations. A variational formulation is applied to derive the corresponding stability criteria. The maximal stability region and the stability region are represented in the favorable and canonical phase diagrams, providing a complete description of catenoid equilibrium and stability. All catenoids are stable with respect to nonaxisymmetric perturbations. For a fixed contact angle, there exists a critical volume below which catenoids are unstable to axisymmetric perturbations. Equilibrium solution multiplicity is discussed in detail, and we elucidate how geometrical symmetry is reflected in the maximal stability and stability regions.

[1]  K. Breuer,et al.  The motion, stability and breakup of a stretching liquid bridge with a receding contact line , 2010, Journal of Fluid Mechanics.

[2]  David Neff,et al.  NTA directed protein nanopatterning on DNA Origami nanoconstructs. , 2009, Journal of the American Chemical Society.

[3]  C. Wilkinson,et al.  Applications of nano-patterning to tissue engineering , 2006 .

[4]  Paul H. Steen,et al.  Capillary surfaces: stability from families of equilibria with application to the liquid bridge , 1993, Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences.

[5]  H. Stone,et al.  Wetting of flexible fibre arrays , 2012, Nature.

[6]  R. Bellman.  Calculus of Variations (L. E. Elsgolc) , 1963 .

[7]  R. Hill,et al.  An elastocapillary model of wood-fibre collapse , 2015, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[8]  Gijsbertus J.M. Krijnen,et al.  Micromachined fountain pen for atomic force microscope-based nanopatterning , 2004 .

[9]  L. E. Scriven,et al.  Pendular rings between solids: meniscus properties and capillary force , 1975, Journal of Fluid Mechanics.

[10]  D. Strube.  Stability of a Spherical and a Catenoidal Liquid Bridge Between Two Parallel Plates in the Absence of Gravity , 1992 .

[11]  L. Rayleigh.  On the Capillary Phenomena of Jets , 1879 .

[12]  Lian Zhou.  ON STABILITY OF A CATENOIDAL LIQUID BRIDGE , 1997 .

[13]  E. Bayramlı,et al.  An experimental study of liquid bridges between spheres in a gravitational field , 1987 .

[14]  José Manuel Perales Perales,et al.  Stability of an isorotating liquid bridge between equal disks under zero‐gravity conditions , 1996 .

[15]  S. Tomotika.  On the Instability of a Cylindrical Thread of a Viscous Liquid Surrounded by Another Viscous Fluid , 1935 .

[16]  L. Mahadevan,et al.  Equilibrium of an elastically confined liquid drop , 2008 .

[17]  K. Breuer,et al.  Micron-scale droplet deposition on a hydrophobic surface using a retreating syringe. , 2009, Physical review letters.

[18]  C. Hsu,et al.  Mechanical stability and adhesion of microstructures under capillary forces. II. Experiments , 1993 .

[19]  R. Wadhwa,et al.  Low-Gravity Fluid Mechanics , 1987 .

[20]  A. Tejado,et al.  Why does paper get stronger as it dries , 2010 .

[21]  P. Steen,et al.  Stability of Constrained Capillary Surfaces , 2015 .

[22]  C. Hsu,et al.  Mechanical stability and adhesion of microstructures under capillary forces. I. Basic theory , 1993 .

[23]  G. Jung,et al.  Fabrication of Nanopattern by Nanoimprint Lithography for the Application to Protein Chip , 2009 .

[24]  Satish Kumar,et al.  Stretching and slipping of liquid bridges near plates and cavities , 2009 .

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

[26]  P. Smith,et al.  The separation of a liquid drop from a stationary solid sphere in a gravitational field , 1985 .

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

[28]  J. CLERK MAXWELL,et al.  Statique expérimentale et théorique des Liquides soumis aux seules Forces moléculaires, , 1874, Nature.

[29]  D Langbein,et al.  Capillary Surfaces: Shape, Stability, Dynamics, in Particular Under Weightlessness. Tracts in Modern Physics, Vol 178 , 2002 .

[30]  D. Langbein.  Stability of liquid bridges between parallel plates , 1992 .

[31]  J. Eggers.  Nonlinear dynamics and breakup of free-surface flows , 1997 .

[32]  Manuel G. Velarde,et al.  Physicochemical hydrodynamics : interfacial phenomena , 1988 .

[33]  J. M. Perales,et al.  Liquid bridge stability data , 1986 .

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

[35]  D. Vella,et al.  Multiple equilibria in a simple elastocapillary system , 2012, Journal of Fluid Mechanics.

[36]  Song Xu,et al.  Nanofabrication of self-assembled monolayers using scanning probe lithography. , 2000, Accounts of chemical research.

[37]  John H. Maddocks,et al.  Stability and folds , 1987 .