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.


New paper on ensemble invariance in small systems

The paper entitled Small Size Effects in Open and Closed Systems: What Can We Learn from Ideal Gases about Systems with Interacting Particles? has been published in the Journal of Chemical Physics.

Small systems have higher surface area-to-volume ratios than macroscopic systems. One consequence of this is that properties of small systems can be dependent on the system's ensemble. By comparing the properties in grand canonical (open) and canonical (closed) systems, we investigate how a small number of particles can induce an ensemble dependence. The ensemble equivalence of small ideal gas systems is investigated by deriving the properties analytically, while the ensemble equivalence of small systems with particles interacting via the Lennard-Jones or the Weeks-Chandler-Andersen potential is investigated through Monte Carlo simulations.

The system we use to investigate these effects has been illustrated in the figure below. This is a cubic simulation box with surface energy "U" experienced by particles closer than a distance "d" from each wall. Particles close to the sides (light blue regions) experience a potential energy contribution of "U", while particles close to the edges (medium blue regions) experience a potential energy contribution of 2"U", and particles close to the corners (dark blue regions) experience a potential energy contribution of 3"U".

For all investigated small systems, we find clear differences between the properties in open and closed systems. For systems with interacting particles, the difference between the pressure contribution to the internal energy, and the difference between the chemical potential contribution to the internal energy, are increasing with system size and number density. The difference in chemical potential is, with the exception of the density dependence, qualitatively described by the analytic formula derived for an ideal gas system. The difference in pressure, however, is not captured by the ideal gas model. For the difference between the properties in the open and closed systems, the response of increasing the particles' excluded volume is similar to the response of increasing the repulsive forces on the system walls. This indicates that the magnitude of the difference between the properties in open and closed systems is related to the restricted movement of the particles in the system.

The main person behind the work has been PhD candidate Vilde Bråten , with contributions also from Sondre K. Schnell and Dick Bedeaux.


New paper on chocked flow in nozzles

The paper entitled Choked liquid flow in nozzles: Crossover from heterogeneous to homogeneous cavitation and insensitivity to depressurization rate has been published in Chemical Engineering Science.

The critical mass flow rate is the maximum flow rate that can pass through a constrained geometry such as a nozzle. In the paper linked to above, we demonstrate that a delay of the phase transition is necessary to reproduce experiments. Two methodologies are presented: (1) the delayed homogeneous relaxation model (Delayed HRM), and (2) the metastable isentrope model (MIM). Delayed HRM is a relaxation model that can readily be incorporated into a spatially distributed description of the fluid flow, e.g. in ejectors. MIM assumes isentropic flow and instantaneous equilibrium up to the limit of metastability, and yields a geometry-independent critical mass flux as the solution of a set of algebraic equations. We compare the two methodologies to available experimental data on the critical mass flow rates of carbon dioxide and water through nozzles, finding that they give nearly identical predictions. Using the limit of metastability predicted by homogeneous nucleation theory works well at high temperatures, rendering the methodologies completely predictive. They deviate on average 11% from experimental data on CO2, and thus outperform homogeneous relaxation models by a large margin, even when the latter employs several fitted parameters. For water and carbon dioxide, we find a crossover between homogeneous and heterogeneous nucleation at T=590 K and T=285 K respectively. Moreover, the predicted limit of superheat falls on a single curve in the temperature–pressure space of water as shown in the figure below. By combining this expression with the above methodologies, we obtained an average deviation of 3% with available experimental data on critical mass flow rates for water.


I am now working full time as Professor at NTNU

From the 1st of August 2021, I start to work full time as a Professor at the Department of Chemistry at NTNU. The position is within equilibrium and non-equilibrium thermodynamics, and was formally announced more than one year ago. There were many excellent applicants, and I feel very proud to end up on the top of the list. I now look forward both to start new collaborations, and to continue the exciting ongoing research in collaboration with SINTEF Energy Research and with centre of Excellence on Porous media research, Porelab, where I will contribute as one of the Principal Investigators.


Ailo Aasen receives the EFCE Excellence award!

The EFCE Excellence award in Thermodynamics and Transport properties is awarded every second year to an excellent PhD thesis. In 2021, it was awarded to my former PhD student and present collaborator, Dr. Ailo Aasen. The judging committee of EFCE’s Thermodynamics and Transport Properties Working Party was highly complementary of the technical quality of Aasen’s work, which included his innovative approach to include quantum effects into classical Helmholtz energy equations of state and discussion of multicomponent nucleation phenomena. The Excellence Award was received virtually at the 31st European Symposium on Applied Thermodynamics (ESAT 2021), where a picture of Ailo Aasen in his presentation during the coference can be found below.


New paper on the entropy production in shock waves

The paper entitled Theory and simulation of shock waves: Entropy production and energy conversion has been published in Phys. Rev. E.

In the paper, we have investigated shock waves by use of nonequilibrium thermodynamics and nonequilibrium molecular dynamics (NEMD) simulations. We have also considered a shock wave as a surface of discontinuity and computed the entropy production using nonequilibrium thermodynamics for surfaces. The results from this method, which we call the “Gibbs excess method” (GEM), were compared with results from three alternative methods, all based on the entropy balance in the shock-front region, but with different assumptions about local equilibrium. Nonequilibrium molecular dynamics (NEMD) simulations were used to simulate a thermal blast in a one-component gas consisting of particles interacting with the Lennard-Jones/spline potential. This provided data for the theoretical analysis. Two cases were studied, a weak shock with Mach number M≈2 and a strong shock with M≈6. The four theoretical methods gave consistent results for the time-dependent surface excess entropy production for both Mach numbers. The entropy production in the weak and strong shocks were approximately proportional to the square of the Mach number and decayed with time at approximately the same relative rate. In both cases, some 97% of the total entropy production in the gas occurred in the shock wave. The GEM showed that most of the shock's kinetic energy was converted reversibly into enthalpy and entropy, and a small amount was dissipated as produced entropy. The shock waves travelled at almost constant speed, and we found that the overpressure determined from NEMD simulations agreed well with the Rankine-Hugoniot conditions for steady-state shocks.

The main person behind this work was Bjørn Hafskjold, with contributions from Signe Kjelstrup, Dick Bedeaux and myself. The figure below shows the entropy produced at the shock front as computed by some of the methods, where the interested reader is referred to the paper for further details.


New paper on extracting chemical potential differences in the macroscopic limit from fluctuations in small systems

The paper entitled Chemical Potential Differences in the Macroscopic Limit from Fluctuations in Small Systems has been accepted for publication in the Journal of Chemical Information and Modeling.

The paper is the first in the PhD of Vilde Bråten, and written also together with Ass. Prof. S. K. Schnell. The paper presents a new method for computing chemical potential differences of macroscopic systems by sampling fluctuations in small systems. The small system method is used to create small embedded systems from molecular dynamics simulations, in which fluctuations of the number of particles are sampled. The overlapping region of two such distributions, sampled from two different systems, is used to compute their chemical potential difference. Since the thermodynamics of small systems is known to deviate from the classical thermodynamic description, the particle distributions will deviate from the macroscopic behavior as well. We show how this can be utilized to calculate the size dependence of chemical potential differences and eventually extract the chemical potential difference in the thermodynamic limit. The macroscopic chemical potential difference is determined with a relative error of 3% in systems containing particles that interact through the truncated and shifted Lennard-Jones potential. In addition to computing chemical potential differences in the macroscopic limit directly from molecular dynamics simulation, the new method provides insights into the size dependency that is introduced to intensive properties in small systems.

The figure below displays an illustration of the method.