# Conference Agenda

Session
Phase-Field, Multiphase and Other Methods for Complex Fluids
 Time: Friday, 01/July/2022: 9:30am - 11:10amSession Chair: François Dubois, CNAM & Univ. Paris-Saclay Location: Michel Crépeau's Lecture Hall, Pôle Communication, La Rochelle UniversityPôle Communication Multimédia Reseaux, La Rochelle University, 44 Avenue Albert Einstein, La Rochelle.

Presentations
9:30am - 10:30am

Three-phase contact implementations to progress towards rough-walled fractures

Mitchell, Travis Ryan1; Sashko, Dmytro1; Laniewski-Wollk, Lukasz1,2; Leonardi, Christopher1

1School of Mechanical and Mining Engineering, The University of Queensland, Brisbane, QLD4072, Australia; 2Institute of Aeronautics and Applied Mechanics, Warsaw University of Technology, Warsaw00-665, Poland

The propagation of two-phase flows through complex geometries are ubiquitous in nature and have numerous application in engineering fields. Of particular interest in this work is the risk of migration of liquid and gas products adjacent to defective oil & gas wells, potentially causing leakage pathways to aquifers and or the surface. In this setting (i.e. defective cement), the flow geometries have a high degree of randomness generally forming complex microannular voids and fractures either through the wellbore cement or between the cement-formation and or cement-pipe boundaries. This work looks to describe these defects as fractures in which the surfaces are correlated self-affine random fields, which allows the random nature of fractures and cracks to be quantified based on a handful of measurable parameters. The aim is to investigate the dependence of relative permeability on these parameters.

In this work, the phase-field lattice Boltzmann model originally proposed by Fakhari et al. [1,2] is extended to account for three-phase contact angles using both the free-energy and geometric approaches for staircase and smoothly defined solid normals. These are often investigated in two-dimensional settings, with non-trivial extensions to complex, three-dimensional geometries. As such, a projection of the phase gradient on the fluid nodes to the plane tangent to the surface is proposed, simplifying the need to determine consistent normal vectors that correspond with the reference frame on every boundary node.

The existing implementations outlined in the literature along with various discretisation methods for the gradients are investigated. This is done through examining the performance and accuracy obtained when studying the Washburn law and interaction of droplets on curved boundaries. Finally, the methods are applied to a stochastically generated, three-dimensional fracture to show the variations in fluid behaviour that can be observed based on the implementation of the three-phase contact.

[1] Fakhari, A., Mitchell, T., Leonardi, C., Bolster, D., Improved locality of the phase-field lattice-Boltzmann model for immiscible fluids at high density ratios, Physical Review E 96, 053301, 2017.

[2] Mitchell, T., Leonardi, C., Fakhari, A., Development of a three-dimensional phase-field lattice Boltzmann method for the study of immiscible fluids at high density ratios, International Journal of Multiphase Flow 107, 1-15, 2018.

10:30am - 10:50am

Engulfment of a drop on solids coated by thin and thick fluid films

Zhao, Chunheng

The City College of New York, United States of America

The short-time evolutions of water droplets propagating on both the thin and the thick oil films are explored by the conservative phase-field Lattice Boltzmann method (LBM). The simulation is conducted to investigate the effect of oil layer thickness on the spreading and the engulfing processes. The simulation and the mathematical derivation are used to demonstrate the scaling analysis of those processes. The simulation findings show that the spreading process on the thin film $H/R<<1$ follows the same scaling rule for both $Oh<<1$ and $Oh>>1$ at the short time: $r/R~ (T/t)^{0.5}$. Besides, 2D simulation produces a similar result comparing to 3D simulation for droplet spreading on thin film. When we increase the film thickness gradually, the effect of the film thickness on the spreading process disappears. This argument is also approved by the viscous dissipation from the flow field. Through the comparison between our simulation results and the experimental results, the short time spreading radius of $Oh<<1$ on a thick film follows the scaling rule: $r/R~(T/t_ \eta)^{0.6}$.

10:50am - 11:10am

Imposing Ratios of Outlet Flow Rates on Large Arterial Networks with Two-Element Windkessel Model: Parametric Analysis

Lo, Sharp Chim Yui1; McCullough, Jon1; Coveney, Peter V.1,2

1University College London, United Kingdom; 2University of Amsterdam, Netherlands

Substantial effort is being invested in the creation of a virtual human --- a model which will improve our understanding of human physiology and diseases and assist clinicians in the design of personalised medical treatments. A central challenge of achieving blood flow simulations at full-human scale is the development of an efficient and accurate approach to imposing boundary conditions on many outlets. A previous study proposed an efficient method for implementing the two-element Windkessel model to control the flow rate ratios at outlets. However, no study to date has examined the conditions for this approach to hold in complex geometries. Here we clarify the general role of the resistance and capacitance in this approach. We show that the error of the flow rate ratios decreases exponentially as the resistance increases. The errors fall below 4\% in a simple five-outlets model and 7\% in a human artery model comprising 10 outlets. Moreover, the flow rate ratios converge faster and suffer from weaker fluctuations as the capacitance decreases. Our findings also establish constraints on the parameters controlling the numerical stability of the simulations. The findings from this work are directly applicable to larger and more complex vascular domains encountered at full-human scale.