[Paper Review] Achieving tunable surface tension in the pseudopotential lattice Boltzmann modeling of interface dynamics

Q. Li, Kai Luo|arXiv (Cornell University)|Jun 27, 2013

Lattice Boltzmann Simulation Studies3 references4 citations

TL;DR

This paper proposes a novel source term addition to the pseudopotential lattice Boltzmann model that enables independent tuning of surface tension without altering the density ratio, preserving mechanical stability and computational efficiency. Numerical tests confirm wide tunability of surface tension while maintaining constant density ratio across droplet, capillary wave, and splashing flows.

ABSTRACT

In this paper, we aim to address an important issue about the pseudopotential lattice Boltzmann (LB) model, which has attracted much attention as a mesoscopic model for simulating interfacial dynamics of complex fluids, but suffers from the problem that the surface tension cannot be tuned independently of the density ratio. In the literature, a multi-range potential was devised to adjust the surface tension [Sbragaglia et al., Phys. Rev. E, 2007, 75, 026702; Sbragaglia et al. Soft Matter, 2012, 8, 10773]. However, this approach was found to be unable to keep the density ratio unchanged when the surface tension is adjusted. An alternative approach is therefore proposed in the present work. The basic strategy is to add a new source term to the LB equation so as to tune the surface tension of the pseudopotential LB model. The proposed approach can guarantee that the adjustment of the surface tension does not affect the mechanical stability condition of the pseudopotential LB model, and thus provides a separate control of the surface tension and the density ratio. Meanwhile, it still retains the mesoscopic feature and the computational simplicity of the pseudopotential LB model. Numerical simulations are carried out for stationary droplets, capillary waves, and droplet splashing on a thin liquid film. The original Shan-Chen pseudopotential and the pseudopotential with a piecewise linear equation of state [Colosqui et al., Soft Matter, 2012, 8, 3798] are both considered. The numerical results demonstrate that the proposed approach is capable of achieving a tunable surface tension over a wide range and can keep the density ratio unchanged when adjusting the surface tension.

Motivation & Objective

• Address the long-standing limitation in pseudopotential lattice Boltzmann models where surface tension and density ratio are inherently coupled.
• Overcome the shortcomings of multi-range potentials, which fail to decouple surface tension from density ratio during adjustment.
• Preserve the mesoscopic nature and computational simplicity of the pseudopotential LB model while enabling independent control of surface tension.
• Ensure mechanical stability is maintained during surface tension tuning to guarantee reliable simulation of interfacial dynamics.
• Demonstrate the method’s robustness across diverse interfacial flow scenarios, including stationary droplets, capillary waves, and droplet splashing.

Proposed method

• Introduce a new source term into the lattice Boltzmann equation to directly manipulate surface tension in the pseudopotential model.
• Design the source term such that it affects intermolecular forces without altering the equation of state or fluid density distribution.
• Ensure the added source term satisfies the mechanical stability condition of the pseudopotential LB model by preserving the consistency of the hydrodynamic limit.
• Apply the method to both the original Shan-Chen pseudopotential model and a piecewise linear equation of state variant for broad validation.
• Use standard lattice Boltzmann schemes with BGK collision and multiple relaxation time (MRT) for numerical stability and accuracy.
• Validate the method through simulations of stationary droplets, capillary waves, and droplet splashing on thin liquid films under varying surface tension settings.

Experimental results

Research questions

• RQ1 Can surface tension be tuned independently of the density ratio in the pseudopotential lattice Boltzmann model without compromising mechanical stability?
• RQ2 Does the proposed source term method preserve the mesoscopic advantages and computational efficiency of the original pseudopotential LB model?
• RQ3 How does the method perform across different interfacial flow configurations, such as stationary droplets and dynamic splashing events?
• RQ4 Can the method maintain a constant density ratio while achieving a wide range of surface tension values in numerical simulations?
• RQ5 What is the impact of the source term on the accuracy of capillary wave and droplet deformation dynamics?

Key findings

• The proposed source term enables independent tuning of surface tension over a wide range without altering the density ratio.
• The mechanical stability condition of the pseudopotential LB model is preserved under all tested surface tension adjustments.
• Stationary droplet simulations show accurate equilibrium shapes and consistent surface tension values across different parameter settings.
• Capillary wave simulations confirm the correct dispersion relation and surface tension dependence, validating dynamic accuracy.
• Droplet splashing simulations demonstrate consistent behavior across varying surface tension, with no unphysical deformation or instability.
• The method remains effective for both the original Shan-Chen model and the piecewise linear equation of state variant, confirming broad applicability.