VOF Surface Tension & Continuum Surface Force (CSF) Model Spurious Currents

1. Definition & Mathematical Engineering Foundations

Simulating free-surface multiphase flows—such as fuel tank sloshing, liquid droplet breakup, microfluidic lab-on-a-chip devices, and casting mold filling—relies on the Volume of Fluid (VOF) interface capturing method. To incorporate surface tension forces across the gas-liquid interface, Brackbill's Continuum Surface Force (CSF) model converts the macroscopic interface pressure jump into an equivalent continuous volumetric body force added to the Navier-Stokes momentum equations. However, numerical truncation errors in calculating interface curvature frequently trigger notorious unphysical parasitic velocity vortexes, known as Spurious Currents.

2. Technical Architecture & Key Formulations

• Brackbill CSF Formulation ($F_{\text{vol}}$):
  F_vol = σ · κ · (∇α) · [2ρ / (ρ₁ + ρ₂)]
  where $\sigma$ is surface tension coefficient, $\kappa = -\nabla \cdot (\nabla \alpha / |\nabla \alpha|)$ is interface curvature, and $\alpha$ is liquid volume fraction.
• Root Cause of Spurious Currents: Slight numerical errors in evaluating normal vectors and curvature $\kappa$ from the discrete $\alpha$ field generate unphysical unbalanced momentum forces, creating artificial circulating velocity vortices at the interface even in a perfectly static droplet.
• Capillary Number ($Ca$) & Ohnesorge ($Oh$) Criteria: Spurious currents become catastrophic in surface-tension-dominated flows where capillary forces exceed viscous and inertial forces ($We < 1$, $Oh > 0.1$).
• Remedy: Height Function (HF) Curvature Calculation: Modern VOF solvers (OpenFOAM interFoam, ANSYS Fluent) compute interface curvature using the Height Function method rather than direct gradient convolution, reducing spurious velocities by orders of magnitude.

3. Industry Failure Modes & Risk Mitigation

In inkjet printhead or microfluidic bubble simulations, unmitigated spurious currents can reach speeds of several meters per second, artificially ripping static micro-droplets apart before physical jetting even occurs.

4. Production Governance & Metrological Standards

CFD engineers suppress parasitic currents by coupling Height Function curvature evaluation with balanced-force pressure-velocity algorithms and local adaptive mesh refinement (AMR) along the interface.

Cross-Disciplinary Resources

Enterprise Production Implementation & GstarCAD 2027 Workflow

• Database Serialization & Binary Fidelity: Ensure all entities and symbol table records associated with VOF Surface Tension & Continuum Surface Force (CSF) Model Spurious Currents are authored on standardized ISO 13567 layers rather than Layer 0 or Defpoints, and verify lossless round-trip persistence in native DWG (AC1032) format.