This page contains news about my research such as new publications, new project grants, happenings, collaborations, or other topics of significance which I think could be of interest to others.


Tolman lengths and rigidities from full DFT

Our article entitled Tolman lengths and rigidity constants from free-energy functionals—General expressions and comparison of theories has been published in the Journal of Chemical Physics.

The leading order terms in a curvature expansion of surface tension, the Tolman length (first order), and rigidities (second order) have been shown to play an important role in the description of nucleation processes. In the work, we present general and rigorous expressions to compute these quantities for any nonlocal density functional theory (DFT). The expressions hold for pure fluids and mixtures and reduce to the known expressions from density gradient theory (DGT). The framework is applied to a Helmholtz energy functional based on the perturbed chain polar statistical associating fluid theory (PCP-SAFT) and is used in an extensive investigation of curvature corrections for pure fluids and mixtures. Predictions from the full DFT are compared to two simpler theories: predictive DGT, which has a density and temperature dependent influence matrix derived from DFT, and DGT, where the influence parameter reproduces the surface tension predicted from DFT. All models are based on the same equation of state and predict similar Tolman lengths and spherical rigidities for small molecules, but the deviations between DFT and DGT increase with chain length for alkanes. For all components except water, we find that DGT underpredicts the value of the Tolman length but overpredicts the value of the spherical rigidity. An important basis for the calculation is an accurate prediction of the planar surface tension. Therefore, we show in our paper that further work is required to accurately extract Tolman lengths and rigidities of alkanols because DFT with PCP-SAFT does not accurately predict surface tensions of these fluids.

The main person behind the work is Philipp Rehner, a visiting PhD student from the group of Joachim Gross at the University of Stuttgart. He visited the group and the team at Porelab, autumn 2019. A picture of Philipp Rehner is shown below.


Consistent effective one-layer models for spreading of fluids

Our article entitled A consistent reduction of the two-layer shallow-water equations to an accurate one-layer spreading model has been accepted for publication in Physics of Fluids.

The gravity-driven spreading of one fluid in contact with another fluid is of key importance to a range of topics. To describe these phenomena, the two-layer shallow-water equations is commonly employed. When one layer is significantly deeper than the other, it is common to approximate the system with the much simpler one-layer shallow water equations. So far, it has been assumed that this approximation is invalid near shocks, and one has applied additional front conditions for the shock speed. In this paper, we prove mathematically that an effective one-layer model can be derived from the two-layer equations that correctly captures the behaviour of shocks and contact discontinuities without any additional closure relations. The proof yields a novel formulation of an effective one-layer shallow water model. The result shows that simplification to an effective one-layer model is well justified mathematically and can be made without additional knowledge of the shock behaviour. The shock speed in the proposed model is consistent with empirical models and identical to the front conditions that have been found theoretically by e.g. von Kármán and by Benjamin. This suggests that the breakdown of the shallow-water equations in the vicinity of shocks is less severe than previously thought. We further investigate the applicability of the shallow water framework to shocks by studying shocks in one-dimensional lock-exchange/lock-release. We derive expressions for the Froude number that are in good agreement with the widely employed expression by Benjamin. We then solve the equations numerically to illustrate how quickly the proposed model converges to solutions of the full two-layer shallow-water equations. We also compare numerical results using our model with results from dam break experiments. Predictions from the one-layer model are found to be in good agreement with experiments.

The work was done in collaboration with E. Fyhn from the Department of Physics at NTNU, Åsmund Ervik and Karl Yngve Lervåk from SINTEF Energy Research.


In our latest article, we disucss thermodynamic stability in pores

Our article entitled Thermodynamic stability of droplets, bubbles and thick films in open and closed pores has been published in Fluid Phase Equilibria.

A fluid in a pore can form diverse heterogeneous structures. In our latest work on thermodynamic stability analysis, we combine a capillary description with the cubic-plus-association equation of state to study the thermodynamic stability of droplets, bubbles and films of water at 358 K in a cylindrically symmetric pore. The equilibrium structure depends strongly on the size of the pore and whether the pore is closed (canonical ensemble) or connected to a particle reservoir (grand canonical ensemble). A new methodology is presented to analyze the thermodynamic stability of films, where the integral that describes the total energy of the system is approximated by a quadrature rule. We show that, for large pores, the thermodynamic stability limit of adsorbed droplets and bubbles in both open and closed pores is governed by their mechanical stability, which is closely linked to the pore shape. This is also the case for a film in a closed pore. In open pores, the film is chemically unstable except for very low film-phase contact angles and for a limited range in external pressure. This result emphasizes the need to invoke a complete thermodynamic stability analysis, and not restrict the discussion to mechanical stability. A common feature for most of the heterogeneous structures examined is the appearance of regions where the structure is metastable with respect to a pore filled with a homogeneous fluid. In the closed pores, these regions grow considerably in size when the pores become smaller. This can be understood from the larger energy cost of the interfaces relative to the energy gained from having two phases. Complete phase diagrams are presented that compare all the investigated structures. In open pores at equilibrium, the most stable structure is either the homogeneous phase or adsorbed droplets and bubbles, depending on the type of phase in the external reservoir. Smaller pores allow for droplets and bubbles to adsorb for a larger span in pressure. In closed pores, most of the investigated configurations can occur depending on the total density, the contact angle, the pore shape and the pore size. Phase diagrams for closed pores of different sizes are shown below.

The analysis presented in the work is a step towards developing a thermodynamic framework to map the rich heterogeneous phase diagrams of porous media and other confined systems. The work was done in collaboration with Magnus Aa. Gjennestad from the Department of Physics at NTNU.


New paper on Fabricating of Fiber Optic Interferometers

Our article entitled Addressing Challenges in Fabricating Reflection-Based Fiber Optic Interferometers has been published in the journal Sensors.

In our work to study phase-transitions by use of fiber optic sensors, we found that their fabrication requires accurate control to obtain reproducible results. In the paper, we evaluate the consequences of practical challenges in fabricating reflection-based, fiber optic interferometers by the use of theory and experiments. A guided-mode propagation approach is used to investigate the effect of the end-face cleave angle and the accuracy of the splice in core-mismatched fiber optic sensors. Cleave angles from high-end fiber cleavers were found to give differences in optical path lengths approaching the wavelength close to the circumference of the fiber, and the core-mismatched splice decided the ensemble of cladding modes excited. In the paper, we show that the cleave angle may significantly alter the spectrum, whereas the splice is more robust. We found that the interferometric visibility can be decreased by up to 70% for cleave angles typically obtained. An offset splice may reduce the visibility, but for offsets experienced experimentally the effect is negligible. We found that an angled splice did not affect the visibility but caused a lower overall intensity in the spectrum. The insight presented in this work has helped us to improve the phase transition studies.

The work was done in collaboration with Markus Wahl and Dag Roar Hjelme from the Department of Electronic Systems at NTNU.


New paper on the Lennard-Jones spline potential

Our article entitled Thermodynamic properties of the 3D Lennard-Jones/spline model has been published in the journal Molecular Physics.

The Lennard-Jones spline potential is a truncated LJ potential so that both the pair potential and the force continuously approach zero at rc≈1.74 sigma. The advantage is then that the computational time is very short, even though it behaves very similarly as the full Lennard-Jones potential when plotted in reduced units. In the paper, we present a systematic map of the thermodynamic properties of the LJ spline model from molecular dynamics and Gibbs ensemble Monte Carlo simulations. Results are presented for gas/liquid, liquid/solid and gas/solid coexistence curves, the Joule-Thomson inversion curve, and several other thermodynamic properties. A main conclusion is that we at the moment do not have a theory or model that adequately represents the thermodynamic properties of the LJ spline system. This represents an interesting challenge for future work.

The work was done in collaboration with Prof. B. Hafskjold from the Department of Chemistry at NTNU, Karl Travis and Amanda B. Hass from the University of Sheffield, Ailo Aasen from NTNU/SINTEF and Morten Hammer from SINTEF Energy Research.


Pauline Zimmermann will make progress on electrodialysis

Pauline Zimmermann shown below, started her PhD this autumn. In her PhD, she will investigate to what extent undesired ions in wastewater from industrial processes can be removed by use of electrodialysis by combining cation and anion exchange membranes. She will do this by combining theory and experimental work. In fact, she has already contributed to a review on the topic that has been accepted for publication in the conference proceedings titled Rare Metal Technology 2020. Nonequilibrium thermodynamics and coupling of mass and charge transfer will be of key importance in her PhD. Together with Prof. O. S. Burheim and Prof. L. Deng, I am part of her team of supervisors.


New equation of state and force fields for hydrogen, helium, neon and deuterium

Our article entitled Equation of state and force fields for Feynman–Hibbs-corrected Mie fluids. I. Application to pure helium, neon, hydrogen, and deuterium has just been published in the Journal of Chemical Physics.

Liquefaction of hydrogen is a promising method for large-scale transport and distribution of hydrogen across long distances. Mixtures between helium-hydrogen and neon may have the potential to significantly improve the energy efficiency of the hydrogen liquefaction process when used as refrigerant. These fluids can be liquids at temperatures below 50~K. However, at sufficiently low temperatures, they exhibit strong quantum effects, in particular helium. Because of these quantum effects, there is currently no accurate equation of state available for mixtures between helium, neon and hydrogen.

One way to emulate the influence of the wave-particle duality on classical interaction potentials is by using Feynman-Hibbs corrections. In the paper above, we use Mie potentials to represent the classical part of the interaction potential and investigate to which extent Mie-Fluids with first and second order Feynman-Hibbs correction can represent the thermodynamic properties of hydrogen, helium, neon and deuterium. The good thing with these quantum corrections is that they introduce no new fitting parameters in comparison to classical Mie fluids. We find that the quantum corrections improve significantly the accuracy for all fluids, where a comparison between the force field/interaction potential, the perturbation theory/EoS and the most accurate equation of state available for hydrogen (solid line) is shown below. The figure displays excellent agreement between the equation of state, the underlying potential and the properties of hydrogen and a vast improvement in comparison to the cubic equation of state, SRK. We are currently working to finalize force fields for mixtures between these fluids as well.

This work has indeed been a team effort and would not have been possible without the excellent contributions from Ailo Aasen, Morten Hammer, Åsmund Ervik and Erich A. Müller from Imperial Collegue in London.


Magnus Aa. Gjennestad joins the team

Magnus Aa. Gjennestad, shown in the picture below, wants to understand how to more accurately describe multi-phase flow in porous media as well as their thermodynamic properties. Fluids in porous media can exist in a diverse set of heterogeneous structures such as adsorbed droplets, free droplets, films or bubbles. Thermodynamics can give answer to what configurations that are most likely to find, i.e. those that result in the lowest energy of the respective ensemble.

Magnus is also my colleague at SINTEF who is now on leave to pursue his PhD. We already have two articles together from our work at SINTEF, on the spinodals and present challenges with modern equations of state. Together with Prof. A. Hansen and Prof. S. Kjelstrup, I have now become part of his team of supervisors at the Porelab center of excellence in Trondheim. We are currently working hard to complete a first article that gives new and valuable insight into the rich heterogeneous phase state of pores.


Visitor from the University of Lorraine in France

The 24th of April, we were so fortunate to have visitors from the University of Lorraine in France, Prof. Jean Noël Jaubert and Ass. Prof. Silvia Lasala. In a seminar, they shared with us new insight on their recent research and progress on consistent alpha-correlations for cubic equations of state, classification of binary mixtures with the scheme of van Konynenburg and Scott, comparison of PC-SAFT and cubic equations of state and a consistent derivation of residual excess Helmholtz energy based mixing rules. Altogether, a very insightful and interesting seminar. A well deserved beer at Heidis Bier Bar at the "sunny-side" of Trondheim afterwards (see picture below). From the left, the picture shows Morten Hammer, myself, Jean Noël and Silvia.


New article gives insight about the highway

Our article entitled Minimum entropy generation in a heat exchanger in the cryogenic part of the hydrogen liquefaction process: On the validity of equipartition and disappearance of the highway has just been accepted for publication in the International Journal of Hydrogen Energy.

In the paper, we use optimal control theory to minimize the total entropy production of a heat exchanger in the cryogenic part of the hydrogen liquefaction process. The heat exchanger is also a reactor, as catalyst is placed in some of the layers to speed up to conversion between the two spin-isomers of hydrogen, ortho- and para-hydrogen.

In recent literature, there has been a discussion about whether it is beneficial to invoke a higher operation pressure than 20 bar in the hydrogen liquefaction process. Inspired by this discussion, we investigate two reference cases; one where the feed stream enters at 20 bar, and one where it enters at 80 bar. The optimal refrigeration strategies give a reduction of the total entropy production of 8.7% in the 20-bar case and 4.3% in the 80-bar case. The overall heat transfer coefficient and duty is higher in the 20~bar case, which compensates for the increase in entropy production due to a thermal mismatch that is avoided in the 80-bar case. This leads the second law efficiency of the 20-bar case (91%) to be similar to the 80 bar case (89%).

We demonstrate in the article that equipartition of the entropy production and equipartition of the thermal driving force are both excellent design principles for the process unit considered, with total entropy productions deviating only 0.2% and 0.5% from the state of minimum entropy production. We find that both heat transfer and the spin-isomer reaction contribute significantly to the entropy production throughout the length of the process unit. Unlike previous examples in the literature, the process unit considered in this work is not characterized by a ``reaction mode'' at the inlet followed by a ``heat transfer mode''. Therefore, it does not follow a highway in state space, i.e. a band that is particularly dense with energy efficient solutions. By artificially increasing the spin-isomer conversion rate, the highway appears when the conversion rate becomes sufficiently high (see figure below).

The work is an outcome of the thesis work of my previous Msc. student, Ragnhild Hånde from the Department of Physics (see picture below), who delivered her thesis last year. She is now working as a software developer.


Presenting about hydrogen liquefaction at the Cryogenics conference in Prague

This week, I was travelling to Prague in the Check Republic to the 15th Cryogenics conference together with two of my colleagues from SINTEF, Stian Trædal and David Berstad. Me and David were both presenting recent progress on technology related to liquefaction of hydrogen. David presented recent research from dynamic modelling of a liquid hydrogen loading cycle from onshore storage to a seaborne tanker (see picture below). The insight gained from this research will be very important to realize large-scale transport of liquid hydrogen, as the transport between tanks represents a critical part of the value-chain, with large potential for exergy losses if not done properly. I presented research performed together with my colleague, Geir Skaugen, on design and evaluation of novel, catalyst-filled spiral wound heat exchangers which hold the potential to further improve the efficiency in the bottom part of the hydrogen liquefaction process. A paper is under development on this topic.


Vilde Bråten will improve the understanding of thermodynamic for nano-systems in her PhD

Vilde Bråten started her PhD in the autumn of 2018. In her PhD, she will bring new insight on the thermodynamics of nano-systems. It is well known that the thermodynamics of nano-systems differs from bulk-behavior, and this is often referred to as finite-size effects. Thus far, the finite-size effects have been undesired e.g. in molecular simulations. However, with the introduction of nanotechnology comes the need to understand the behavior of small systems and these finite-size effects. In her PhD, Vilde will build on the work by T. Hill on the thermodynamics of small systems, and the ultimate aim is to develop thermodynamic methodology and understanding of molecular machines in order to explore the potential of these devices in technological and scientific applications.