Åsmund Ervik

A robust method for calculating interface curvature and normal vectors using an extracted local level set

The level-set method is a popular interface tracking method in two-phase flow simulations. An often-cited reason for using it is that the method naturally handles topological changes in the interface, e.g. merging drops, due to the implicit formulation. It is also said that the interface curvature and normal vectors are easily calculated. This last point is not, however, the case in the moments during a topological change, as several authors have already pointed out. Various methods have been employed to circumvent the problem. In this paper, we present a new such method which retains the implicit level-set representation of the surface and handles general interface configurations. It is demonstrated that the method extends easily to 3D. The method is validated on static interface configurations, and then applied to two-phase flow simulations where the method outperforms the standard method and the results agree well with experiments.

raaSAFT: A framework enabling coarse-grained molecular dynamics simulations based on the SAFT-γ Mie force field

We describe here raaSAFT, a Python code that enables the setup and running of coarse-grained molecular dynamics simulations in a systematic and efficient manner. The code is built on top of the popular HOOMD-blue code, and as such harnesses the computational power of GPUs. The methodology makes use of the SAFT-γ Mie force field, so the resulting coarse grained pair potentials are both closely linked to and consistent with the macroscopic thermodynamic properties of the simulated fluid. In raaSAFT both homonuclear and heteronuclear models are implemented for a wide range of compounds spanning from linear alkanes, to more complicated fluids such as water and alcohols, all the way up to nonionic surfactants and models of asphaltenes and resins. Adding new compounds as well as new features is made straightforward by the modularity of the code. To demonstrate the ease-of-use of raaSAFT, we give a detailed walkthrough of how to simulate liquid–liquid equilibrium of a hydrocarbon with water. We describe in detail how both homonuclear and heteronuclear compounds are implemented. To demonstrate the performance and versatility of raaSAFT, we simulate a large polymer-solvent mixture with 300 polystyrene molecules dissolved in 42 700 molecules of heptane, reproducing the experimentally observed temperature-dependent solubility of polystyrene. For this case we obtain a speedup of more than three orders of magnitude as compared to atomistically-detailed simulations.

Experimental and computational studies of water drops falling through model oil with surfactant and subjected to an electric field

The behaviour of a single sub-millimetre-size water drop falling through a viscous oil while subjected to an electric field is of fundamental importance to industrial applications such as crude oil electrocoalescers. Detailed studies, both experimental and computational, have been performed previously, but an often challenging issue has been the characterization of the fluids. As numerous authors have noted, it is very difficult to have a perfectly clean water-oil system even for very pure model oils, and the presence of trace chemicals may significantly alter the interface behaviour. In this work, we consider a well-characterized water-oil system where controlled amounts of a surface active agent (Span 80) have been added to the oil. This addition dominates any trace contaminants in the oil, such that the interface behaviour can also be well-characterized. We present the results of experiments and corresponding two-phase-flow simulations of a falling water drop covered in surfactant and subjected to a monopolar square voltage pulse. The results are compared and good agreement is found for surfactant concentrations below the critical micelle concentration.

Curvature Calculations for the Level-Set Method

The present work illustrates a difficulty with the level-set method to accurately capture the curvature of interfaces in regions that are of equal distance to two or more interfaces. Such regions are characterized by kinks in the level-set function where the derivative is discontinuous. Thus the standard discretization scheme is not suitable. Three discretization schemes are outlined that are shown to perform better than the standard discretization on two selected test cases.

Influence of surfactants on the electrohydrodynamic stretching of water drops in oil

Abstract In this paper we present experimental and numerical studies of the electrohydrodynamic stretching of a sub-millimetre-sized salt water drop, immersed in oil with added non-ionic surfactant, and subjected to a suddenly applied electric field of magnitude approaching 1  kV/mm. By varying the drop size, electric field strength and surfactant concentration we cover the whole range of electric capillary numbers (CaE) from 0 up to the limit of drop disintegration. The results are compared with the analytical result by Taylor (1964) which predicts the asymptotic deformation as a function of CaE. We find that the addition of surfactant damps the transient oscillations and that the drops may be stretched slightly beyond the stability limit found by Taylor. We proceed to study the damping of the oscillations, and show that increasing the surfactant concentration has a dual effect of first increasing the damping at low concentrations, and then increasing the asymptotic deformation at higher concentrations. We explain this by comparing the Marangoni forces and the interfacial tension as the drops deform. Finally, we have observed in the experiments a significant hysteresis effect when drops in oil with large concentration of surfactant are subjected to repeated deformations with increasing electric field strengths. This effect is not attributable to the flow nor the interfacial surfactant transport.

A multiscale method for simulating fluid interfaces covered with large molecules such as asphaltenes

Abstract The interface between two liquids is fully described by the interfacial tension only for very pure liquids. In most cases the system also contains surfactant molecules which modify the interfacial tension according to their concentration at the interface. This has been widely studied over the years, and interesting phenomena arise, e.g. the Marangoni effect. An even more complicated situation arises for complex fluids like crude oil, where large molecules such as asphaltenes migrate to the interface and give rise to further phenomena not seen in surfactant-contaminated systems. An example of this is the “crumpling drop” experiments, where the interface of a drop being deflated becomes non-smooth at some point. In this paper we report on the development of a multiscale method for simulating such complex liquid–liquid systems. We consider simulations where water drops covered with asphaltenes are deflated, and reproduce the crumpling observed in experiments. The method on the nanoscale is based on using coarse-grained molecular dynamics simulations of the interface, with an accurate model for the asphaltene molecules. This enables the calculation of interfacial properties. These properties are then used in the macroscale simulation, which is performed with a two-phase incompressible flow solver using a novel hybrid level-set/ghost-fluid/immersed-boundary method for taking the complex interface behaviour into account. We validate both the nano- and macroscale methods. Results are presented from nano- and macroscale simulations which showcase some of the interesting behaviour caused by asphaltenes affecting the interface. The molecular simulations presented here are the first in the literature to obtain the correct interfacial orientation of asphaltenes. Results from the macroscale simulations present a new physical explanation of the crumpled drop phenomenon, while highlighting shortcomings in previous hypotheses.

Computation of three-dimensional three-phase flow of carbon dioxide using a high-order WENO scheme

Abstract We have developed a high-order numerical method for the 3D simulation of viscous and inviscid multiphase flow described by a homogeneous equilibrium model and a general equation of state. Here we focus on single-phase, two-phase (gas–liquid or gas–solid) and three-phase (gas–liquid–solid) flow of CO 2 whose thermodynamic properties are calculated using the Span–Wagner reference equation of state. The governing equations are spatially discretized on a uniform Cartesian grid using the finite-volume method with a fifth-order weighted essentially non-oscillatory (WENO) scheme and the robust first-order centered (FORCE) flux. The solution is integrated in time using a third-order strong-stability-preserving Runge–Kutta method. We demonstrate close to fifth-order convergence for advection–diffusion and for smooth single- and two-phase flows. Quantitative agreement with experimental data is obtained for a direct numerical simulation of an air jet flowing from a rectangular nozzle. Quantitative agreement is also obtained for the shape and dimensions of the barrel shock in two highly underexpanded CO 2 jets.

A review on wetting and water condensation - Perspectives for CO 2 condensation

Liquefaction of vapor is a necessary, but energy intensive step in several important process industries. This review identifies possible materials and surface structures for promoting dropwise condensation, known to increase efficiency of condensation heat transfer. Research on superhydrophobic and superomniphobic surfaces promoting dropwise condensation constitutes the basis of the review. In extension of this, knowledge is extrapolated to condensation of CO2. Global emissions of CO2 need to be minimized in order to reduce global warming, and liquefaction of CO2 is a necessary step in some carbon capture, transport and storage (CCS) technologies. The review is divided into three main parts: 1) An overview of recent research on superhydrophobicity and promotion of dropwise condensation of water, 2) An overview of recent research on superomniphobicity and dropwise condensation of low surface tension substances, and 3) Suggested materials and surface structures for dropwise CO2 condensation based on the two first parts.

The transition in settling velocity of surfactant-covered droplets from the Stokes to the Hadamard–Rybczynski solution

Abstract The exact solution for a small falling drop is a classical result by Hadamard and Rybczynski. But experiments show that small drops fall slower than predicted, giving closer agreement with Stokes’ result for a falling hard sphere. Increasing the drop size, a transition between these two extremes is found. This is due to surfactants present in the system, and previous work has led to the stagnant-cap model. We present here an alternative approach which we call the continuous-interface model. In contrast to the stagnant-cap model, we do not consider a surfactant advection–diffusionequation at the interface. Taking instead the normal and tangential interfacial stresses into account, we solve the Stokes equation analytically for the falling drop with varying interfacial tension. Some of the solutions thus obtained, e.g. the hovering drop, violate conservation of energy unless energy is provided directly to the interface. Considering the energy budget of the drop, we show that the terminal velocity is bounded by the Stokes and the Hadamard–Rybczynski results. The continuous-interface model is then obtained from the force balance for surfactants at the interface. The resulting expressions gives the transition between the two extremes, and also predicts that the critical radius, below which drops fall like hard spheres, is proportional to the interfacial surfactant concentration. By analysing experimental results from the literature, we confirm this prediction, thus providing strong arguments for the validity of the proposed model.

Comment on the level-set method used in ‘Numerical study on mobilization of oil slugs in capillary model with level set approach’

ABSTRACT This is a comment on a 2014 paper by Dai and Wang. It is argued that the validation in Dai and Wangs paper is an artifact caused by the boundary conditions of the level-set function, meaning that the effects reported in their paper have little physical relevance. Simulations are presented using Dai and Wangs methods to illustrate this claim. Remarks are made on the choice of boundary conditions for the level-set function, as well as the frequency of reinitialization, both of which are important topics that are sometimes overlooked. A simple criterion is proposed for determining the appropriate reinitialization frequency in simulations of highly viscous flows.