A Caltech Library Service

A Novel Methodology for Simulating Contact-Line Behavior in Capillary-Driven Flows


Della Rocca, Gerry V. (2014) A Novel Methodology for Simulating Contact-Line Behavior in Capillary-Driven Flows. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/Z9CN71WW.


Despite the wide swath of applications where multiphase fluid contact lines exist, there is still no consensus on an accurate and general simulation methodology. Most prior numerical work has imposed one of the many dynamic contact-angle theories at solid walls. Such approaches are inherently limited by the theory accuracy. In fact, when inertial effects are important, the contact angle may be history dependent and, thus, any single mathematical function is inappropriate. Given these limitations, the present work has two primary goals: 1) create a numerical framework that allows the contact angle to evolve naturally with appropriate contact-line physics and 2) develop equations and numerical methods such that contact-line simulations may be performed on coarse computational meshes.

Fluid flows affected by contact lines are dominated by capillary stresses and require accurate curvature calculations. The level set method was chosen to track the fluid interfaces because it is easy to calculate interface curvature accurately. Unfortunately, the level set reinitialization suffers from an ill-posed mathematical problem at contact lines: a ``blind spot'' exists. Standard techniques to handle this deficiency are shown to introduce parasitic velocity currents that artificially deform freely floating (non-prescribed) contact angles. As an alternative, a new relaxation equation reinitialization is proposed to remove these spurious velocity currents and its concept is further explored with level-set extension velocities.

To capture contact-line physics, two classical boundary conditions, the Navier-slip velocity boundary condition and a fixed contact angle, are implemented in direct numerical simulations (DNS). DNS are found to converge only if the slip length is well resolved by the computational mesh. Unfortunately, since the slip length is often very small compared to fluid structures, these simulations are not computationally feasible for large systems. To address the second goal, a new methodology is proposed which relies on the volumetric-filtered Navier-Stokes equations. Two unclosed terms, an average curvature and a viscous shear VS, are proposed to represent the missing microscale physics on a coarse mesh.

All of these components are then combined into a single framework and tested for a water droplet impacting a partially-wetting substrate. Very good agreement is found for the evolution of the contact diameter in time between the experimental measurements and the numerical simulation. Such comparison would not be possible with prior methods, since the Reynolds number Re and capillary number Ca are large. Furthermore, the experimentally approximated slip length ratio is well outside of the range currently achievable by DNS. This framework is a promising first step towards simulating complex physics in capillary-dominated flows at a reasonable computational expense.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:Contact-line dynamics, Multiphase fluid flow, Level set methods, Slip length modeling
Degree Grantor:California Institute of Technology
Division:Engineering and Applied Science
Major Option:Mechanical Engineering
Awards:Centennial Prize for the Best Thesis in Mechanical and Civil Engineering, 2014
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Blanquart, Guillaume
Thesis Committee:
  • Hunt, Melany L. (chair)
  • Colonius, Tim
  • Brady, John F.
  • Blanquart, Guillaume
Defense Date:20 May 2014
Funding AgencyGrant Number
Record Number:CaltechTHESIS:05262014-160059300
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:8394
Deposited By: Gerry Della Rocca
Deposited On:07 Oct 2016 23:46
Last Modified:25 Oct 2023 21:11

Thesis Files

PDF (Thesis) - Final Version
See Usage Policy.

[img] Video (MPEG) (Video of Drop impact with final parameters) - Supplemental Material
See Usage Policy.

[img] Video (MPEG) (Drop impact movie with no viscous shear) - Supplemental Material
See Usage Policy.


Repository Staff Only: item control page