A computational framework for modelling micro-scale fluids in the presence of surface tension

Mackenzie, Ross J.D. (2015) A computational framework for modelling micro-scale fluids in the presence of surface tension. PhD thesis, University of Glasgow.

Abstract

Immunisation, pioneered by Edward Jenner (1749-1823), has saved millions of lives and has helped the human race survive several disease pandemics. Today, the immunisation industry conducts vast amounts of research, not only developing new vaccinations, but also new methods of diagnosis. Currently, blood samples are taken manually using a syringe, loaded into a centrifuge and spun for several hours to separate out the different parts of the blood sample. These parts can then be tested manually for a range of ailments. In some areas of the world, access to such a device is unavailable and even if it was, this can be a long, energy intensive and costly process. Hence, new faster methods involving the use of microchips and surface acoustic waves and are an inviting possibility.
Utilising the field of fluid dynamics, notably the work of Newton, Euler, Cauchy, Navier and Stokes, combined with modern computational methods allows for an engineering perspective to be taken on this problem. This thesis combines many novel contributions to create a computational modelling framework to model external excitation of axisymmetric micro-scale fluid droplets. In the present work fluid motion is governed by an axisymmetric form of the Navier-Stokes equations, with focus on incompressible Newtonian fluids, and this is presented in full. At the micro-scale, surface tension is the most dominant force, hence additional contributions are derived and included due to surface tension and contact line forces. Additionally, to reduce spurious oscillations within the pressure field, the pressure Laplacian stabilisation (PLS) technique is implemented. A derivation of the technique as well as an investigation into the effect of the stabilisation parameter is presented.
The kinematics of the system are of great importance. At the micro-scale, tracking of the surface of the fluid is highly desirable and most advantageous, and the choice of kinematic description must reflect this. Unlike more traditional computational methods adopting an Eulerian description or a Lagrangian description of the governing equations, the presented computational framework makes use of the Arbitrary Lagrangian Eulerian (ALE) description. The ALE formulation avoids many of the drawbacks of traditional methods whilst allowing for accurate tracking of the fluid surface and minimising the requirement for frequent remeshing. Taking the current, deformed, configuration as the reference configuration in an Updated Lagrangian (UL) manner, combines into a kinematic description termed the Updated Arbitrary Lagrangian Eulerian (UALE) formulation. The physics underlying this formulation are presented in detail within this thesis.
Several problems, examining a range of droplet volume, contact angle and experimental configuration are presented to validate the computational framework against analytical solutions. Of the various problems examined, all show a very good correlation to analytical solutions. Differences, if any, are attributed to the density of the mesh, which is shown to alter the amplitude but not the frequency of oscillation, or over-simplification made in the analytical solutions.
Lastly, a new hypothesis is tested which until recently was extremely difficult to verify. The current hypothesis in the literature proposes that upon reaching the fluid-solid inter- face, surface acoustic waves propagate through the fluid causing motion. Conversely, the new hypothesis proposes that upon reaching the fluid-solid interface, surface acoustic waves propagate capillary waves up the surface of the droplet, changing the apparent wetting angle and inducing motion. This is implemented by changing the contact angle in time to simulate the action of surface acoustic waves and the resulting analysis recorded the occurrence of jetting thereby confirming the hypothesis. Further testing can be conducted and this technology utilised in the development of new disease diagnosis devices.
The computational framework has been very successful in modelling a range of micro-scale problems. Further development of this framework will allow for a greater understanding of the effect of surface acoustic waves on a fluid droplet. In turn, this will allow for the improved design of surface acoustic wave devices.

• Item Type: Thesis (PhD)
• Qualification Level: Doctoral
• Keywords: finite element method, computational fluid dynamics, surface tension, ALE, pressure stabilisation, surface acoustic waves
• Subjects: T Technology > TA Engineering (General). Civil engineering (General)
• Colleges/Schools: College of Science and Engineering > School of Engineering > Infrastructure and Environment
• Supervisor's Name: Kacamarczyk, Dr. Lukasz and Pearce, Prof. Chris
• Date of Award: 2015
• Depositing User: Ross James Donald Mackenzie
• Unique ID: glathesis:2015-5925
• Copyright: Copyright of this thesis is held by the author.
• Date Deposited: 20 Jan 2015 14:22
• Last Modified: 20 Jan 2015 14:34
• URI: https://theses.gla.ac.uk/id/eprint/5925