Stokes flow near the contact line of an evaporating drop

@article{Gelderblom2012StokesFN,
  title={Stokes flow near the contact line of an evaporating drop},
  author={Hanneke Gelderblom and Oscar Bloemen and Jacco H. Snoeijer},
  journal={Journal of Fluid Mechanics},
  year={2012},
  volume={709},
  pages={69 - 84}
}
Abstract The evaporation of sessile drops in quiescent air is usually governed by vapour diffusion. For contact angles below $9{0}^{\ensuremath{\circ} } $ , the evaporative flux from the droplet tends to diverge in the vicinity of the contact line. Therefore, the description of the flow inside an evaporating drop has remained a challenge. Here, we focus on the asymptotic behaviour near the pinned contact line, by analytically solving the Stokes equations in a wedge geometry of arbitrary contact… Expand
Stokes flow in a drop evaporating from a liquid subphase
The evaporation of a drop from a liquid subphase is investigated. The two liquids are immiscible, and the contact angles between them are given by the Neumann construction. The evaporation of theExpand
Modelling the contact-line dynamics of an evaporating drop
We study the evolution of a thin, axisymmetric, partially wetting drop as it evaporates. The effects of viscous dissipation, capillarity, slip, gravity, surface-tension gradients, and contact-angleExpand
A model for pattern deposition from an evaporating solution subject to contact angle hysteresis and finite solubility.
TLDR
This model takes into account the three-phase contact angle hysteresis and the deposition of the solute whenever its concentration exceeds the solubility limit, and replaces an exact geometric description of the vicinity of the contact line with general insights about the concentration and its flux. Expand
A Mathematical Model of Fluid Flow in Evaporating Droplets Using Wedge Geometry
As a droplet of liquid evaporates, particles within the droplet are often pulled to the edge and deposited in a ring-shaped pattern. This is known as the coffee-ring effect. The coffee-ring effect isExpand
INVESTIGATION OF THERMO-CAPILLARY FLOW INSIDE AN EVAPORATING PINNED WATER DROPLET
Thermo-capillary flow inside an evaporating water drop on heated or non-heated substrate is investigated. The modeling of the internal flow inside the drop takes into account the effects of theExpand
Asymptotic analysis of the evaporation dynamics of partially wetting droplets
We consider the dynamics of an axisymmetric, partially wetting droplet of a one-component volatile liquid. The droplet is supported on a smooth superheated substrate and evaporates into a pure vapourExpand
On thin evaporating drops: When is the $d^{2}$ -law valid?
We study the evolution of a thin, axisymmetric, partially wetting drop as it evaporates. The effects of viscous dissipation, capillarity, slip and diffusion-dominated vapour transport are taken intoExpand
Buoyancy-driven convection of droplets on hot nonwetting surfaces.
TLDR
The global linear stability of a water drop on hot nonwetting surfaces is studied and it is suggested that the experimental observation for a droplet with β=110^{∘} corresponds to the steady toroidal base flow, while for β=160^{ ∘}, the m=1 instability promotes the rigid body rotation motion. Expand
Evaporation at microscopic scale and at high heat flux
This thesis theoretically investigates the transport processes in the vicinity of the triple gas-liquid-solid contact line and its impact on macroscopic evaporation. In the first part of the thesis,Expand
Generalized formulation for evaporation rate and flow pattern prediction inside an evaporating pinned sessile drop
Abstract When a sessile drop is heated from below, it evaporates and it induces a cooling effect in a zone close to the drop surface. The important evaporation rate at the contact line, the surfaceExpand
...
1
2
3
4
5
...

References

SHOWING 1-10 OF 48 REFERENCES
Stokes flow inside an evaporating liquid line for any contact angle.
  • A. J. Petsi, V. Burganos
  • Materials Science, Medicine
  • Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2008
TLDR
The problem of Stokes flow inside a two-dimensional droplet, representing the cross section of an evaporating liquid line lying on a flat surface, is considered, leading to the biharmonic equation in bipolar coordinates that can be used with any type of evaporation mechanism, including diffusion, convection, or kinetically controlled modes. Expand
Analytical solution for Stokes flow inside an evaporating sessile drop: Spherical and cylindrical cap shapes
Exact analytical solutions are derived for the Stokes flows within evaporating sessile drops of spherical and cylindrical cap shapes. The results are valid for all contact angles. Solutions areExpand
Evaporation of a Sessile Droplet on a Substrate
The evaporation of a sessile droplet with a pinned contact line is investigated experimentally, by analytic theory and by computation using the finite element method (FEM). Because of the low valueExpand
Analysis of the microfluid flow in an evaporating sessile droplet.
  • Hua Hu, R. Larson
  • Materials Science, Medicine
  • Langmuir : the ACS journal of surfaces and colloids
  • 2005
TLDR
A finite element algorithm is developed to solve simultaneously the vapor concentration and flow field in the droplet under conditions of slow evaporation and confirms the accuracy of the lubrication solution. Expand
Influence of substrate conductivity on circulation reversal in evaporating drops.
TLDR
It is demonstrated that the Marangoni flow can significantly influence the resulting patterns of particle deposition in the face of nonuniform evaporation. Expand
Evaporation-induced flow near a contact line: Consequences on coating and contact angle
We propose a simple model of the dynamics of a contact line under evaporation and partial wetting conditions, taking into account the divergent nature of evaporation near the contact line, asExpand
The spreading of volatile liquid droplets on heated surfaces
A two‐dimensional volatile liquid droplet on a uniformly heated horizontal surface is considered. Lubrication theory is used to describe the effects of capillarity, thermocapillarity, vapor recoil,Expand
On evaporation of sessile drops with moving contact lines
We consider theoretically, computationally and experimentally spontaneous evaporation of water and isopropanol drops on smooth silicon wafers. In contrast to a number of previous works, the solidExpand
The leading edge of evaporating droplets.
TLDR
A systematic study of the drops dynamics is presented, as a basis for forthcoming theoretical work on polydimethylsiloxane oligomers, which are similar to alkanes as far as evaporation rate is concerned, but have lower surface tensions, and therefore smaller dynamic contact angles. Expand
Particle convection in an evaporating colloidal droplet
An emergent technique of patterning surfaces with solid particles utilizes the evaporation of colloidal droplets from a substrate. Upon complete evaporation of the liquid, the suspended particlesExpand
...
1
2
3
4
5
...