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The efficient and voidless filling of microcavities is of great importance for Lab-on-a-Chip applications. However, predicting whether microcavities will be filled or not under different circumstances is still difficult due to the local flow effects dominated by surface tension. In this work, a close-up study of the microcavity filling process is presented, shedding light on the mechanisms of the filling process using experimental insights accompanied by 3D numerical simulations. The movement of a fluid interface over a microcavity array is investigated optically under consideration of different fluids, capillary numbers, and cavity depths, revealing a regime map of different filling states. Moreover, the transient interface progression over the cavities is analyzed with attention to small-scale effects such as pinning. Besides the visual analysis of the image series, quantitative data of the dynamic contact angle and the interface progression is derived using an automated evaluation workflow. In addition to the experiments, 3D Volume-of-Fluid simulations are employed to further investigate the interface shape. It is shown that the simulations can not only predict the filling states in most cases, but also the transient movement and shape of the interface. The data and code associated with this work are publicly available at Bosch Research GitHub and at the TUDatalib data repository., Comment: submitted to International Journal of Multiphase Flow

We provide an implementation of the unstructured Finite-Volume Arbitrary Lagrangian / Eulerian (ALE) Interface-Tracking method for simulating incompressible, immiscible two-phase flows as an OpenFOAM module. In addition to interface-tracking capabilities that include tracking of two fluid phases, an implementation of a Subgrid-Scale (SGS) modeling framework for increased accuracy when simulating sharp boundary layers is enclosed. The SGS modeling framework simplifies embedding subgrid-scale profiles into the unstructured Finite Volume discretization. Our design of the SGS model library significantly simplifies adding new SGS models and applying SGS modeling to Partial Differential Equations (PDEs) in OpenFOAM.

Preventing fluid penetration poses a challenging reliability concern in the context of power electronics, which is usually caused by unforeseen microfractures along the sealing joints. A better and more reliable product design heavily depends on the understanding of the dynamic wetting processes happening inside these complex microfractures, i.e. microchannels. A novel automated image processing procedure is proposed in this work for analyzing the moving interface and the dynamic contact angle in microchannels. In particular, the developed method is advantageous for experiments involving non-transparent samples, where extracting the fluid interface geometry poses a significant challenge. The developed method is validated with theoretical values and manual measurements and exhibits high accuracy. The implementation is made publicly available. The developed method is validated and applied to experimental investigations of forced wetting with two working fluids (water and 50 wt% glycerin/water mixture) in four distinct microchannels characterized by different dimensions and curvature. The comparison between the experimental results and molecular kinetic theory (MKT) reveals that the dynamic wetting behavior can be described well by MKT, even in highly curved microchannels. The dynamic wetting behavior shows a strong dependency on the channel geometry and curvature.

Combining machine learning (ML) with computational fluid dynamics (CFD) opens many possibilities for improving simulations of technical and natural systems. However, CFD+ML algorithms require exchange of data, synchronization, and calculation on heterogeneous hardware, making their implementation for large-scale problems exceptionally challenging. We provide an effective and scalable solution to developing CFD+ML algorithms using open source software OpenFOAM and SmartSim. SmartSim provides an Orchestrator that significantly simplifies the programming of CFD+ML algorithms and a Redis database that ensures highly scalable data exchange between ML and CFD clients. We show how to leverage SmartSim to effectively couple different segments of OpenFOAM with ML, including pre/post-processing applications, solvers, function objects, and mesh motion solvers. We additionally provide an OpenFOAM sub-module with examples that can be used as starting points for real-world applications in CFD+ML.

Non-orthogonality errors in unstructured Finite Volume methods for simulating incompressible two-phase flows may break the force-balanced discretization. We show that applying the same explicit non-orthogonality correction for all gradient terms in the context of segregated solution algorithms is not sufficient to achieve force balance. To ensure force balance, we introduce a straightforward and deterministic residual-based control of the non-orthogonality correction, which removes the number of non-orthogonality corrections as a free parameter from the simulation. Our method is directly applicable to different unstructured finite-volume two-phase flow simulation methods as long as they discretize the one-field formulation of incompressible two-phase Navier-Stokes equations. We demonstrate force balance for the surface tension force and the gravity force near linear solver tolerance for an algebraic and a geometric Volume-of-Fluid method using the stationary droplet and stationary water column verification cases on polyhedral unstructured meshes with varying levels of non-orthogonality.

Geometric flux-based Volume-of-Fluid (VOF) methods are widely considered consistent in handling two-phase flows with high density ratios. However, although the conservation of mass and momentum is consistent for two-phase incompressible single-field Navier-Stokes equations without phase-change, discretization may easily introduce small inconsistencies that result in very large errors or catastrophic failure. We apply the consistency conditions derived for the unstructured Level Set / Front Tracking method to flux-based geometric VOF methods, and implement our discretization into the plicRDF-isoAdvector geometrical VOF method. We find that computing the mass flux by scaling the geometrically computed fluxed phase-specific volume destroys the equivalence between the scaled volume fraction equation and the mass conservation equation, depending on the choice for the temporal and convective term discretization schemes. We propose two solutions. First, based on the analysis of discretization errors, we suggest a consistent combination of the temporal discretization scheme and the interpolation scheme for the momentum convection term. Second, similar to our previous work on the unstructured Level Set / Front Tracking method, we solve an auxiliary mass conservation equation with a geometrical calculation of the face-centered density. We prove the equivalence between these two approaches mathematically and verify and validate their numerical stability for density ratios in the range $[1,10^6]$ and viscosity ratios in the range $[10^2,10^5]$.

Dynamic wetting processes inherently manifest as multiscale phenomena. While the capillary length is typically millimeters, solid-liquid interactions occur at the nanometer scale. These short-range interactions significantly affect macroscopic behaviors like droplet spreading and menisci dynamics. The Navier slip length, determined by liquid viscosity and solid-liquid friction, plays a crucial role in three-phase contact line dynamics. It varies from nanometers (hydrophilic) to microns (hydrophobic). However, resolving it in computational fluid dynamics (CFD) simulations can be computationally expensive. In this study, we propose simplified ordinary differential equation (ODE) models, leveraging local dissipation rates from Stokes flow solutions near the moving contact line, to bridge the nanoscale physics and macroscopic dynamics. Our ODE model accurately predicts the impact of the slip parameter in fully resolved CFD simulations, focusing on capillary rise dynamics., Comment: 10 pages, 2 figures

Since viscoelastic two-phase flows arise in various industrial and natural processes, developing accurate and efficient software for their detailed numerical simulation is a highly relevant and challenging research task. We present a geometrical unstructured Volume-of-Fluid (VOF) method for handling two-phase flows with viscoelastic liquid phase, where the latter is modeled via generic rate-type constitutive equations and a one-field description is derived by conditional volume averaging of the local instantaneous bulk equations and interface jump conditions. The method builds on the plicRDF-isoAdvector geometrical VOF solver that is extended and combined with the modular framework DeboRheo for viscoelastic computational fluid dynamics (CFD). A piecewise-linear geometrical interface reconstruction technique on general unstructured meshes is employed for discretizing the viscoelastic stresses across the fluid interface. DeboRheo facilitates a flexible combination of different rheological models with appropriate stabilization methods to address the high Weissenberg number problem., Comment: 35 pages, 18 figures

We model the Darmstadt Slip Length Tribometer (DSLT), specially designed to measure viscosity and slip length simultaneously for lubrication gaps in the range of approximately 10 micrometres at relevant temperatures and surface roughness. We investigate the inlet effect of the flow on the results by varying the inner radius of the fluid inlet pipe. The outcomes of numerical simulations suggest that variations in the diameter of this inner radius have minimal impact on the results. Specifically, any alterations in the velocity profile near the inlet, brought about by changes in the diameter, quickly revert to the profile predicted by the analytical model. The main conclusion drawn from this study is the validation of the Navier-Slip boundary condition as an effective model for technical surface roughness in CFD simulations and the negligible influence of the inlet effect on the fluid dynamics between the tribometer's plates.

University research groups in Computational Science and Engineering (CSE) generally lack dedicated funding and personnel for Research Software Engineering (RSE), which, combined with the pressure to maximize the number of scientific publications, shifts the focus away from sustainable research software development and reproducible results. The neglect of RSE in CSE at University research groups negatively impacts the scientific output: research data - including research software - related to a CSE publication cannot be found, reproduced, or re-used, different ideas are not combined easily into new ideas, and published methods must very often be re-implemented to be investigated further. This slows down CSE research significantly, resulting in considerable losses in time and, consequentially, public funding. We propose a RSE workflow for Computational Science and Engineering (CSE) that addresses these challenges, that improves the quality of research output in CSE. Our workflow applies established software engineering practices adapted for CSE: software testing, result visualization, and periodical cross-linking of software with reports/publications and data, timed by milestones in the scientific publication process. The workflow introduces minimal work overhead, crucial for university research groups, and delivers modular and tested software linked to publications whose results can easily be reproduced. We define research software quality from a perspective of a pragmatic researcher: the ability to quickly find the publication, data, and software related to a published research idea, quickly reproduce results, understand or re-use a CSE method, and finally extend the method with new research ideas., Comment: arXiv admin note: text overlap with arXiv:2208.07460

Parasitic currents still pose a significant challenge for the investigation of two-phase flow in Lab-on-Chip (LoC) applications with Volume-of-Fluid (VoF) simulations. To counter the impact of such spurious velocity fields in the vicinity of the fluid interface, this work presents an implementation of an artificial interface viscosity model in OpenFOAM. The model is introduced as an additional dampening term in the momentum conservation equation. It is implemented as a fvOption, allowing for its simple application to existing VoF solvers. Validation is performed with hydrodynamic and wetting cases, in which constant artificial viscosity values are prescribed to examine the sensitivity of the solution to the artificial dampening. The artificial viscosity model shows promising results in reducing spurious currents for two considered geometrical VoF solvers, namely interIsoFoam and InterFlow. It is found that the influence of the artificial viscosity heavily depends on the fluid properties. Applying the model to simulations of an interface traversing through microcavities relevant in LoC applications, experimental results of the interface progression are predicted well, while spurious currents are effectively reduced by approximately one order of magnitude due to the artificial viscosity model. The code is publicly available on GitHub (https://github.com/boschresearch/sepMultiphaseFoam/tree/publications/ArtificialInterfaceViscosity)., Comment: author manuscript of published article

The numerical simulation of wetting and dewetting of geometrically complex surfaces benefits from unstructured numerical methods because they discretize the domain with second-order accuracy. A recently developed unstructured geometric Volume-of-Fluid (VOF) method, the plicRDF-isoAdvector method, is chosen to investigate wetting processes because of its volume conservation property and high computational efficiency. The present work verifies and validates the plicRDF-isoAdvector method for wetting problems. We present four verification studies. The first study investigates the accuracy of the interface advection near walls. The method is further investigated for the spreading of droplets on a flat and a spherical surface, respectively, for which excellent agreement with the reference solutions is obtained. Furthermore, a 2D capillary rise is considered, and a benchmark comparison based on results from previous work is performed. The benchmark suite, input data, and Jupyter Notebooks used in this study are publicly available to facilitate further research and comparison with other numerical codes.

The Volume-of-Fluid (VoF) method for simulating incompressible two-phase flows is widespread in academic and commercial simulation software because of its many advantages: a high degree of volume conservation, applicability to unstructured domain discretization (relevant for engineering applications), straightforward parallel implementation with the domain-decomposition and message-passing approach (important for large-scale simulations), and intrinsic handling of strong deformations and topological changes of the fluid interface. However, stable and accurate handling of small-scale capillary flows (dominated by surface tension forces) is still challenging for VoF methods. With many different VoF methods making their way into commercial and open-source software, it becomes increasingly important to compare them quantitatively and directly. For this purpose, we propose a set of simulation benchmarks and use them to directly compare VoF methods available in OpenFOAM, Basilisk, and Ansys Fluent. We use Jupyter notebooks to document and process the benchmark results, making a direct comparison of our results with other two-phase simulation methods very straightforward. The publicly available input data, secondary benchmark data, and post-processing Jupyter notebooks can be re-used by any two-phase flow simulation method that discretizes two-phase Navier-Stokes equations in a one-fluid formulation, which can save a significant amount of person-hours.

University research groups in Computational Science and Engineering (CSE) generally lack dedicated funding and personnel for Research Software Engineering (RSE), which, combined with the pressure to maximize the number of scientific publications, shifts the focus away from sustainable research software development and reproducible results. The neglect of RSE in CSE at University research groups negatively impacts the scientific output: research data - including research software - related to a CSE publication cannot be found, reproduced, or re-used, different ideas are not combined easily into new ideas, and published methods must very often be re-implemented to be investigated further. This slows down CSE research significantly, resulting in considerable losses in time and, consequentially, public funding. We propose a RSE workflow for Computational Science and Engineering (CSE) that addresses these challenges, that improves the quality of research output in CSE. Our workflow applies established software engineering practices adapted for CSE: software testing, result visualization, and periodical cross-linking of software with reports/publications and data, timed by milestones in the scientific publication process. The workflow introduces minimal work overhead, crucial for university research groups, and delivers modular and tested software linked to publications whose results can easily be reproduced. We define research software quality from a perspective of a pragmatic researcher: the ability to quickly find the publication, data, and software related to a published research idea, quickly reproduce results, understand or re-use a CSE method, and finally extend the method with new research ideas.

It is well-known that the standard level set advection equation does not preserve the signed distance property, which is a desirable property for the level set function representing a moving interface. Therefore, reinitialization or redistancing methods are frequently applied to restore the signed distance property while keeping the zero-contour fixed. As an alternative approach to these methods, we introduce a modified level set advection equation that intrinsically preserves the norm of the gradient at the interface, i.e. the local signed distance property. Mathematically, this is achieved by introducing a carefully chosen source term being proportional to the local rate of interfacial area generation. The introduction of the source term turns the problem into a non-linear one. However, we show that by discretizing the source term explicitly in time, it is sufficient to solve a linear equation in each time step. Notably, without further adjustment, the method works in the case of a moving contact line. This is a major advantage since redistancing is known to be an issue when contact lines are involved. We provide a first implementation of the method in a simple first-order upwind scheme in both two and three spatial dimensions., Comment: 22 pages, 10 figures

We extend the unstructured LEvel set / froNT tracking (LENT) method for handling two-phase flows with strongly different densities (high-density ratios) by providing the theoretical basis for the numerical consistency between the mass and momentum conservation in the collocated Finite Volume discretization of the single-field two-phase Navier-Stokes equations. Our analysis provides the theoretical basis for the mass conservation equation introduced by Ghods and Herrmann [3] and used in [4, 5, 6, 7, 8]. We use a mass flux that is consistent with mass conservation in the implicit Finite Volume discretization of the two-phase momentum convection term, and solve the single-field Navier-Stokes equations with our SAAMPLE segregated solution algorithm [2]. The proposed $\rho$LENT method recovers exact numerical stability for the two-phase momentum advection of a spherical droplet with density ratios ranging in $[1, 10^4]$. Numerical stability is demonstrated for in terms of the relative $L_\infty$ velocity error norm, for density-ratios in the range of $[1, 10^4]$, dynamic viscosity-ratios in the range of $[1, 10^4]$ and very strong surface tension forces, for challenging mercury/air and water/air fluid pairings. In addition, the solver performs well in cases characterized by strong interaction between two phases, i.e., oscillating droplets and rising bubbles. The proposed $\rho$LENT method is applicable to any other two-phase flow simulation method that discretizes the single-field two-phase Navier-Stokes Equations using the collocated unstructured Finite Volume Method but does not solve an advection equation for the phase indicator using a flux-based approach, by adding the proposed geometrical approximation of the mass flux and the auxiliary mass conservation equation to the solution algorithm.

Available algorithms for the initialization of volume fractions typically utilize exact functions to model fluid interfaces, or they rely on computationally costly intersections between volume meshes. Here, a new algorithm is proposed that computes signed distances and volume fractions on unstructured meshes from arbitrarily shaped surfaces, e.g. originating from experimental data. The proposed algorithm calculates signed distances geometrically near the fluid interface, approximated as a triangle surface mesh, and propagates the inside/outside information by an approximate solution of a Laplace equation. Volume fractions are computed based on signed distances, using either geometrical intersections between cells of the unstructured mesh and a sub-set of the surface mesh that represents the interface, or using a polynomial approximation and adaptive mesh refinement. Although primarily developed for multiphase flow simulations, the proposed algorithm can potentially be used for other problems that require a phase-indicator: inside/outside information with respect to an arbitrarily shaped surface on arbitrarily unstructured meshes.

A straightforward and computationally efficient Consecutive Cubic Spline (CCS) iterative algorithm is proposed for positioning the planar interface of the unstructured geometrical Volume-of-Fluid method in arbitrarily-shaped cells. The CCS algorithm is a two-point root-finding algorithm specifically designed for the VOF interface positioning problem, where the volume fraction function has diminishing derivatives at the ends of the search interval. As a two-point iterative algorithm, CCS re-uses function values and derivatives from previous iterations and does not rely on interval bracketing. The CCS algorithm only requires only two iterations on average to position the interface with a tolerance of $10^{-12}$, even with numerically very challenging volume fraction values, e.g. near $10^{-9}$ or $1-10^{-9}$. The proposed CCS algorithm is very straightforward to implement because its input is already calculated by every geometrical VOF method. It builds upon and significantly improves the predictive Newton method and is independent of the cell's geometrical model and related intersection algorithm. Geometrical parametrizations of truncated volumes used by other contemporary methods are completely avoided. The computational efficiency is comparable in terms of the number of iterations to the fastest methods reported so far. References are provided in the results section to the open-source implementation of the CCS algorithm and the performance measurement data.

Geometrical Volume-of-Fluid (VoF) methods mainly support structured meshes, and only a small number of contributions in the scientific literature report results with unstructured meshes and three spatial dimensions. Unstructured meshes are traditionally used for handling geometrically complex solution domains that are prevalent when simulating problems of industrial relevance. However, three-dimensional geometrical operations are significantly more complex than their two-dimensional counterparts, which is confirmed by the ratio of publications with three-dimensional results on unstructured meshes to publications with two-dimensional results or support for structured meshes. Additionally, unstructured meshes present challenges in serial and parallel computational efficiency, accuracy, implementation complexity, and robustness. Ongoing research is still very active, focusing on different issues: interface positioning in general polyhedra, estimation of interface normal vectors, advection accuracy, and parallel and serial computational efficiency. This survey tries to give a complete and critical overview of classical, as well as contemporary geometrical VOF methods with concise explanations of the underlying ideas and sub-algorithms, focusing primarily on unstructured meshes and three dimensional calculations. Reviewed methods are listed in historical order and compared in terms of accuracy and computational efficiency.

Existing hybrid Level Set / Front Tracking methods have been developed for structured meshes and successfully used for efficient and accurate simulations of complex multiphase flows. This contribution extends the capability of hybrid Level Set / Front Tracking methods towards handling surface tension driven multiphase flows using unstructured meshes. Unstructured meshes are traditionally used in Computational Fluid Dynamics to handle geometrically complex problems. In order to simulate surface-tension driven multiphase flows on unstructured meshes, a new SAAMPLE Segregated Accuracy-driven Algorithm for Multiphase Pressure-Linked Equations is proposed, that increases the robustness of the unstructured Level Set / Front Tracking (LENT) method. The LENT method is implemented in the Open- FOAM open source code for Computational Fluid Dynamics.

The breakup dynamics of a capillary bridge on a hydrophobic stripe between two hydrophilic stripes is studied experimentally and numerically using direct numerical simulations. The capillary bridge is formed from an evaporating water droplet wetting three neighboring stripes of a chemically patterned surface. By considering the breakup process in a phase space representation, the breakup dynamics can be evaluated without the uncertainty in determining the precise breakup time. The simulations are based on the Volume-of-Fluid (VOF) method implemented in Free Surface 3D (FS3D). In order to construct physically realistic initial data for the VOF simulation, Surface Evolver is employed to calculate an initial configuration consistent with experiments. Numerical instabilities at the contact line are reduced by a novel discretization of the Navier-slip boundary condition on staggered grids. The breakup of the capillary bridge cannot be characterized by a unique scaling relationship. Instead, at different stages of the breakup process different scaling exponents apply, and the structure of the bridge undergoes a qualitative change. In the final stage of breakup, the capillary bridge forms a liquid thread that breaks up consistently with the Rayleigh-Plateau instability., Comment: accepted manuscript, 28 pages, 19 figures

We consider the interface advection problem by a prescribed velocity field in the special case when the interface intersects the domain boundary, i.e. in the presence of a contact line. This problem emerges from the discretization of continuum models for dynamic wetting. The kinematic evolution equation for the dynamic contact angle (Fricke et al., 2019) expresses the fundamental relationship between the rate of change of the contact angle and the structure of the transporting velocity field. The goal of the present work is to develop an interface advection method that is consistent with the fundamental kinematics and transports the contact angle correctly with respect to a prescribed velocity field. In order to verify the advection method, the kinematic evolution equation is solved numerically and analytically (for special cases). We employ the geometrical Volume-of-Fluid (VOF) method on a structured Cartesian grid to solve the hyperbolic transport equation for the interface in two spatial dimensions. We introduce generalizations of the Youngs and ELVIRA methods to reconstruct the interface close to the domain boundary. Both methods deliver first-order convergent results for the motion of the contact line. However, the Boundary Youngs method shows strong oscillations in the numerical contact angle that do not converge with mesh refinement. In contrast to that, the Boundary ELVIRA method provides linear convergence of the numerical contact angle transport., Comment: 22 pages, 20 figures, accepted manuscript

A new parallelized unsplit geometrical Volume of Fluid (VoF) algorithm with support for arbitrary unstructured meshes and dynamic local Adaptive Mesh Refinement (AMR), as well as for two and three dimensional computation is developed. The geometrical VoF algorithm supports arbitrary unstructured meshes in order to enable computations involving flow domains of arbitrary geometrical complexity. The implementation of the method is done within the framework of the OpenFOAM library for Computational Continuum Mechanics (CCM) using the C++ programming language with modern policy based design for high program code modularity. The development of the geometrical VoF algorithm significantly extends the method base of the OpenFOAM library by geometrical volumetric flux computation for two-phase flow simulations. For the volume fraction advection, a novel unsplit geometrical algorithm is developed, which inherently sustains volume conservation utilizing unique Lagrangian discrete trajectories located in the mesh points. This practice completely eliminates the possibility of an overlap between the flux polyhedra and hence significantly increases volume conservation. A new efficient (quadratic convergent) and accurate iterative flux correction algorithm is developed, which avoids topological changes of the flux polyhedra. Our geometrical VoF algorithm is dimension agnostic, providing automatic support for both 2D and 3D computations, following the established practice in OpenFOAM. The geometrical algorithm used for the volume fraction transport has been extended to support dynamic local AMR available in OpenFOAM. Furthermore, the existing dynamic mesh capability of OpenFOAM has been modified to support the geometrical mapping algorithm executed as a part of the dynamic local AMR cycle. The method implementation is fully parallelized using the domain decomposition approach., Comment: voFoam - geometrical unsplit VoF algorithm on unstructered meshes