Drops

Droplets are fundamental to fluid transport on solids. The sessile drop is the canonical problem upon which many modern fluid transport applications are based. Typical examples include 3D printing with relevance to rapid prototyping, self-cleansing surfaces for enhanced solar cell efficiency, microfluidics, spray cooling for high heat flux applications, drop atomization for drug delivery (aerosol) methods, and energy harvesting technologies, all of which involve the motion of droplets on scales where surface tension dominates.

We develop models to describe the hydrodynamics and compare with related experiments. For the sessile drop, the spectrum depends upon both the wetting properties of the solid substrate and the mobility of the three-phase contact-line (spreading). Modal shapes can be distingushed by a polar k and azimuthal l wavenumber pair (k,l) (see figure). In experiment, we find that the sequence of modes observed during a frequency sweep can become distorted; i.e. the (8,8) mode has a lower resonance frequency than the (7,3) mode. This stands in contrast to the free drop (Rayleigh 1879), which preserves spectral ordering. The distorted spectrum can be understood by recasting the system in a symmetry-breaking framework organized by a `periodic table of mode shapes'. 

Among other motions, we have discovered a new fluid instability deemed the 'walking instability' that is fundamental to fluid transport on solids. Here, under certain circumstances, the potential energy stored in the liquid shape can be converted into fluid motion (kinetic energy).
 
Previous studies have focused on drops in constrained geometries. Current studies focus on sessile droplets with mobile contact-lines, subject to various types of excitation.   
mode table
Modal classification of sessile drops by (polar,azimuthal) wavenumber pair (k,l) into zonal, sectoral and tesseral shapes.


PUBLICATIONS
  1. C.T. Chang, J.B. Bostwick, S. Daniel and P.H. Steen. "Dynamics of sessile drops. Part 2. Experiment". Journal of Fluid Mechanics. 768, 442-467, (2015). [Link]
  2. J.B. Bostwick and P.H. Steen. "Dynamics of sessile drops. Part 1. Inviscid theory." Journal of Fluid Mechanics. 760, 5-38, (2014). [Link]
  3. C.T. Chang, J.B. Bostwick, P.H. Steen and S. Daniel. "Substrate constraint modifies the Rayleigh spectrum of vibrating sessile drops". Physical Review E. 88, 023015, (2013). [Link]
  4. J.B. Bostwick and P.H. Steen. "Coupled oscillations of deformable spherical-cap droplets. Part 2. Viscous motions". Journal of Fluid Mechanics. 714, 336-360, (2013). [Link]
  5. J.B. Bostwick and P.H. Steen. "Coupled oscillations of deformable spherical-cap droplets. Part 1. Inviscid motions". Journal of Fluid Mechanics. 714, 312-335, (2013). [Link]
  6. J.B. Bostwick and P.H. Steen. "Constrained capillary oscillations of a spherical fluid drop". Physics of Fluids. 21, 032108, (2009). [Link]