Svend Tollak Munkejord

Influence of surfactant on drop deformation in an electric field

The deformation of a surfactant-covered, viscous drop suspended in a viscous fluid under the influence of an electric field is investigated using numerical simulations. The full Navier–Stokes equations are solved in both fluid phases, and the motion of the interface and the interfacial discontinuities are handled using the level-set method. The leaky-dielectric model is used to take into account the effect of an electric field. The surfactant is assumed to be insoluble, and an evolution equation for the motion of surfactant is solved along the drop surface. The surfactant concentration and the interfacial tension are coupled through a nonlinear equation of state. The numerical results show that the effect of surfactant strongly depends on the relative permittivity and conductivity between the fluids. The presence of surfactant can both increase and reduce the deformation, depending on the shape of the deformation and the direction of the electrically induced circulation.

Micro technology in heat pumping systems

Abstract Micro heat pumps, with dimensions in the order of centimetres, may in the future be utilised for the heating and/or cooling of buildings, vehicles, clothing, and other products or applications. A number of issues have yet to be solved, including the construction of a microscale compressor, and determination of micro heat exchanger heat transfer capacities. Test samples of micro heat exchangers and a corresponding test apparatus have been built. Some two-phase experiments with propane (R-290) as refrigerant have been conducted. Preliminary results for a micro condenser with 0.5 mm wide trapezoidal channels of 25 mm length showed that a heat flux of up to 135 kW/m 2 , based on the refrigerant-side area, was attainable. The corresponding overall heat transfer coefficient was 10 kW/(m 2 K), with a refrigerant mass flux of 165 kg/(m 2 s) and a refrigerant-side pressure drop of 180 kPa/m.

Wave Propagation in Multicomponent Flow Models

We consider systems of hyperbolic balance laws governing flows of an arbitrary number of components equipped with general equations of state. The components are assumed to be immiscible. We compare two such models: one in which thermal equilibrium is attained through a relaxation procedure, and a fully relaxed model in which equal temperatures are instantaneously imposed. We describe how the relaxation procedure may be made consistent with the second law of thermodynamics. Exact wave velocities for both models are obtained and compared. In particular, our formulation directly proves a general subcharacteristic condition: For an arbitrary number of components and thermodynamically stable equations of state, the mixture sonic velocity of the relaxed system can never exceed the sonic velocity of the relaxation system.

On Solutions to Equilibrium Problems for Systems of Stiffened Gases

We consider an isolated system of N immiscible fluids, each following a stiffened-gas equation of state. We consider the problem of calculating equilibrium states from the conserved fluid-mechanical properties, i.e., the partial densities and internal energies. We consider two cases; in each case mechanical equilibrium is assumed, but the fluids may or may not be in thermal equilibrium. For both cases, we address the issues of existence, uniqueness, and physical validity of equilibrium solutions. We derive necessary and sufficient conditions for physically valid solutions to exist, and prove that such solutions are unique. We show that for both cases, physically valid solutions can be expressed as the root of a monotonic function in one variable. We then formulate efficient algorithms which unconditionally guarantee global and quadratic convergence toward the physically valid solution.

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.

Sharp-interface simulations of drop deformation in electric fields

This paper describes numerical simulations of two-phase electrohydrodynamics using a sharp-interface method. Simulations are performed on typical test cases from the literature, and the results are compared to methods that use a smeared interface. The results show that the sharp-interface method gives significant improvements in accuracy.

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.

Numerical investigation of electrostatically enhanced coalescence of two drops in a flow field

When an electric field is applied to an emulsion where a conductive fluid is dispersed in an insulating fluid, attractive forces will arise between the drops due to polarization. The drops then tend to coalesce more readily than when no electric field is applied. This phenomenon, often denoted electrocoalescence, is employed for instance to enhance the separation of water from oil extracted from offshore wells. In this work, we employ detailed numerical simulations to study the influence of external flow and electric field on the head-on collision between two drops.

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.