Development of a central-moment phase-field lattice Boltzmann model for thermocapillary flows: Droplet capture and computational performance

TL;DR

The paper develops a 3D central-moment phase-field lattice Boltzmann model for thermocapillary flows, integrated into the waLBerla framework, and couples it to an energy equation solved via both LBM and Runge–Kutta schemes. It systematically compares lattice stencils (D3Q7, D3Q15, D3Q19, D3Q27) and RK orders, finding negligible accuracy differences but clear performance trends, with D3Q7 and RK2 offering memory- and bandwidth-efficient options. The authors demonstrate 2D and 3D droplet capture under local heating (laser-like sources), revealing nuanced dependence on contact angle and heat-source configuration, including multi-source setups that enable capture in 3D. A comprehensive GPU-focused performance analysis shows near-ideal scaling on NVIDIA and AMD GPUs, highlighting the practicality of large-scale simulations for designing thermocapillary microfluidic devices.

Abstract

This study develops a computationally efficient phase-field lattice Boltzmann model with the capability to simulate thermocapillary flows. The model was implemented into the open-source simulation framework, waLBerla, and extended to conduct the collision stage using central moments. The multiphase model was coupled with both a passive-scalar thermal LB, and a RK solution to the energy equation in order to resolve temperature-dependent surface tension phenomena. Various lattice stencils (D3Q7, D3Q15, D3Q19, D3Q27) were tested for the passive-scalar LB and both the second- and fourth-order RK methods were investigated. There was no significant difference observed in the accuracy of the LB or RK schemes. The passive scalar D3Q7 LB discretisation tended to provide computational benefits, while the second order RK scheme is superior in memory usage. This paper makes contributions relating to the modelling of thermocapillary flows and to understanding the behaviour of droplet capture with thermal sources analogous to thermal tweezers. Four primary contributions to the literature are identified. First, a new 3D thermocapillary, central-moment phase-field LB model is presented and implemented in the open-source software, waLBerla. Second, the accuracy and computational performance of various techniques to resolve the energy equation for multiphase, incompressible fluids is investigated. Third, the dynamic droplet transport behaviour in the presence of thermal sources is studied and insight is provided on the potential ability to manipulate droplets based on local domain heating. Finally, a concise analysis of the computational performance together with near-perfect scaling results on NVIDIA and AMD GPU-clusters is shown. This research enables the detailed study of droplet manipulation and control in thermocapillary devices.

Figures (20)

• Figure 1: Overview of the code generation methodology applied within the waLBerla development framework. The two Python packages lbmpy and pystencils allow the flexible symbolic derivation of LBM kernels which can be executed MPI-parallel for large scale production runs within waLBerla or as standalone application in IPython for rapid model development.
• Figure 2: Schematic of the test domain used to simulate the thermocapillary-driven motion of two-fluids within a heated microchannel.
• Figure 3: Convergence of the temperature and velocity fields using a LBM scheme for all order parameters (LBM-only) with comparison to using RK2 and RK4 scheme to obtain the temperature respectively.
• Figure 4: Temperature contours of fluid systems with heat conduction ratio (a) $k^* = 1$ and (b) $k^* = 1/5$. Analytical solutions are represented using solid lines while the simulation results are shown with dashed lines. The results were conducted with a pure LBM-based method. Similar results could be achieved with a hybrid method, where the energy equation was solved using an RK2 or an RK4 scheme.
• Figure 5: Convergence of the temperature and velocity field for different stencils for the thermal PDFs for the pseudo-3D simulation. The results of all stencils overlap, without any noticeable difference.