InterPore2026

Accurate Curvature and Surface-Tension Modeling for Pinned and Moving Contact Lines in Pore-Scale Wetting Simulations

19 May 2026, 12:05

15m

Oral Presentation (MS09) Pore-Scale Physics and Modeling MS09

Speaker

David Gösele (University of Stuttgart)

Description

Wetting of a single pore by a liquid phase is a fundamental process in multiphase flow through porous media, and is relevant for many natural and industrial processes. While static wetting is well understood, the dynamic wetting behavior in pores still poses challenges for both experiments and numerical simulations. One major difficulty arises at the contact line, where the fluid interface meets the solid boundary and the contact angle $\theta$ is imposed. Despite its microscopic scale, the contact angle critically influences macroscopic interface shape, overall wetting behavior, and capillary response in a pore. Moreover, contact line pinning can occur due to contact angle hysteresis or complex pore geometries. For Volume-of-Fluid (VoF)-based multiphase-flow Direct Numerical Simulations (DNS), accurate curvature computation is crucial, as surface tension forces, which dictate capillary effects, are directly derived from it. Standard methods such as the Continuous Surface Force (CSF) exhibit limitations, including divergence with mesh refinement (Patel, Kuipers, and Peters 2018).

We present a novel numerical method for VoF-based multiphase-flow DNS, which accurately captures moving and pinned contact lines. Our method enhances a height-function approach for curvature calculation (Afkhami and Bussmann 2007) by incorporating wall-adjacent height functions (Figure 1). This innovation enables precise curvature computation even at dynamic or pinned contact lines, significantly improving the robustness of surface tension modeling.

To demonstrate the capabilities of the new method, we present DNS results for wetting in a single two-dimensional pore geometry, considering both forced wetting and spontaneous imbibition. The simulations capture the dynamics of the contact line, including pinning and depinning events at the sharp corner of the pore geometry. Figure 2 illustrates a forced wetting case from the left boundary, showing snapshots of the fluid interface at different saturations. For low capillary number, $Ca=1\times10^{-5}$ (black lines), the interface has an approximately constant curvature, as expected from static theory. In contrast, for $Ca=4\times10{-3}$ (red lines), significant interface deformation and deviations from static pressure predictions (see Fig. 3) are observed, quantifying the increasing influence of viscous and inertial forces. Figure 3 presents the measured inlet pressure as a function of saturation for different capillary numbers. For low $Ca$, excellent agreement with static theory is obtained, whereas for higher $Ca$ the pressure deviates significantly from the static prediction due to increasing viscous and inertial contributions. These findings underscore the critical importance of robust curvature evaluation at wall-bounded interfaces and provide crucial insights into how dynamic wetting in pores departs from quasi-static behavior with increasing $Ca$.