Øivind Wilhelmsen

Communication: Tolman length and rigidity constants of water and their role in nucleation

A proper understanding of nucleation is crucial in several natural and industrial processes. However, accurate quantitative predictions of this phenomenon have not been possible. The most popular tool for calculating nucleation rates, classical nucleation theory (CNT), deviates by orders of magnitude from experiments for most substances. We investigate whether part of this discrepancy can be accounted for by the curvature-dependence of the surface tension. To that end, we evaluate the leading order corrections for water, the Tolman length and the rigidity constants, using square gradient theory coupled with the accurate cubic plus association equation of state. The Helfrich expansion is then used to incorporate them into the CNT-framework. For water condensation, the modified framework successfully corrects the erroneous temperature dependence of the nucleation rates given by the classical theory and reproduces experimental nucleation rates.

A flexible and robust modelling framework for multi-stream heat exchangers

Abstract Heat exchangers are important units in most industrial processes. They involve physical phenomena such as condensation and evaporation including several boiling regimes. Different types of heat exchangers constructed for different applications may differ much in geometrical design. This work explains and demonstrates a modelling framework which is capable of handling a multitude of geometries and relevant physical phenomena affecting the performance of the heat exchangers. The data structure and governing equations are explained, before the framework is demonstrated for a particular challenging test case with a heat exchanger operating similar to the main heat exchanger in a single mixed refrigerant cycle. In the test case, both evaporation and condensation may happen simultaneously along the length of the heat exchanger. 1000 cases with random changes within predefined intervals in inlet temperatures, mass flows and pressures were used to test the robustness of the model framework. The solution scheme converged in 98.7% of the cases, and in the non-converging cases, the operating conditions exceeded the physical limits of the heat exchanger. The framework demonstrated may thus be used to create flexible and robust heat exchanger models for use in process simulations, optimization, or as a stand-alone model.

Thermodynamic stability of nanosized multicomponent bubbles/droplets: The square gradient theory and the capillary approach

Formation of nanosized droplets/bubbles from a metastable bulk phase is connected to many unresolved scientific questions. We analyze the properties and stability of multicomponent droplets and bubbles in the canonical ensemble, and compare with single-component systems. The bubbles/droplets are described on the mesoscopic level by square gradient theory. Furthermore, we compare the results to a capillary model which gives a macroscopic description. Remarkably, the solutions of the square gradient model, representing bubbles and droplets, are accurately reproduced by the capillary model except in the vicinity of the spinodals. The solutions of the square gradient model form closed loops, which shows the inherent symmetry and connected nature of bubbles and droplets. A thermodynamic stability analysis is carried out, where the second variation of the square gradient description is compared to the eigenvalues of the Hessian matrix in the capillary description. The analysis shows that it is impossible to stabilize arbitrarily small bubbles or droplets in closed systems and gives insight into metastable regions close to the minimum bubble/droplet radii. Despite the large difference in complexity, the square gradient and the capillary model predict the same finite threshold sizes and very similar stability limits for bubbles and droplets, both for single-component and two-component systems.

Coherent description of transport across the water interface: From nanodroplets to climate models.

Transport of mass and energy across the vapor-liquid interface of water is of central importance in a variety of contexts such as climate models, weather forecasts, and power plants. We provide a complete description of the transport properties of the vapor-liquid interface of water with the framework of nonequilibrium thermodynamics. Transport across the planar interface is then described by 3 interface transfer coefficients where 9 more coefficients extend the description to curved interfaces. We obtain all coefficients in the range 260-560 K by taking advantage of water evaporation experiments at low temperatures, nonequilibrium molecular dynamics with the TIP4P/2005 rigid-water-molecule model at high temperatures, and square gradient theory to represent the whole range. Square gradient theory is used to link the region where experiments are possible (low vapor pressures) to the region where nonequilibrium molecular dynamics can be done (high vapor pressures). This enables a description of transport across the planar water interface, interfaces of bubbles, and droplets, as well as interfaces of water structures with complex geometries. The results are likely to improve the description of evaporation and condensation of water at widely different scales; they open a route to improve the understanding of nanodroplets on a small scale and the precision of climate models on a large scale.

Communication: Superstabilization of fluids in nanocontainers

One of the main challenges of thermodynamics is to predict and measure accurately the properties of metastable fluids. Investigation of these fluids is hindered by their spontaneous transformation by nucleation into a more stable phase. We show how small closed containers can be used to completely prevent nucleation, achieving infinitely long-lived metastable states. Using a general thermodynamic framework, we derive simple formulas to predict accurately the conditions (container sizes) at which this superstabilization takes place and it becomes impossible to form a new stable phase. This phenomenon opens the door to control nucleation of deeply metastable fluids at experimentally feasible conditions, having important implications in a wide variety of fields.

Heat transport through a solid-solid junction: the interface as an autonomous thermodynamic system

We perform computational experiments using nonequilibrium molecular dynamics simulations, showing that the interface between two solid materials can be described as an autonomous thermodynamic system. We verify the local equilibrium and give support to the Gibbs description of the interface also away from the global equilibrium. In doing so, we reconcile the common formulation of the thermal boundary resistance as the ratio between the temperature discontinuity at the interface and the heat flux with a more rigorous derivation from nonequilibrium thermodynamics. We also show that thermal boundary resistance of a junction between two pure solid materials can be regarded as an interface property, depending solely on the interface temperature, as implicitly assumed in some widely used continuum models, such as the acoustic mismatch model. Thermal rectification can be understood on the basis of different interface temperatures for the two flow directions.

Constrained non-linear optimisation of a process for liquefaction of natural gas including a geometrical and thermo-hydraulic model of a compact heat exchanger

Abstract A great deal of effort has been put into improving natural gas liquefaction processes, and a number of new process configurations have been described. Recent literature has identified a need for more realistic heat exchanger models to obtain optimum design and operating conditions that do not compromise safety, or that are unrealistic. Here we describe a concept for finding the design and operating conditions of a single mixed-refrigerant process which gives minimum power consumption under given space or weight constraints. We use a sophisticated heat exchanger modelling framework that takes into account system geometry and resolves the details of the heat exchanger through conservation equations coupled with accurate models of thermo-physical properties. First, we find the feasible region which does not compromise safety with Ledinegg instabilities. We then identify the optimal operating conditions for a specific design within this region, before identifying the process design that requires least power consumption. We illustrate how this differs from a purely thermodynamic optimisation, and discuss our key results.

Finite-size and truncation effects for microscopic expressions for the temperature at equilibrium and nonequilibrium

Several expressions have been proposed for the temperature in molecular simulations, where some of them have configurational contributions. We investigate how their accuracy is influenced by the number of particles in the simulation and the discontinuity in the derivatives of the interaction potential introduced by truncation. For equilibrium molecular dynamics with fixed total volume and fixed average total energy per particle, all the evaluated expressions including that for the kinetic temperature give a dependence on the total number of particles in the simulation. However, in a partitioned simulation volume under the same conditions, the mean temperature of each bin is independent of the number of bins. This finding is important for consistently defining a local temperature for use in nonequilibrium simulations. We identify the configurational temperature expressions which agree most with the kinetic temperature and find that they give close to identical results in nonequilibrium molecular dynamics (NEMD) simulations with a temperature gradient, for high and low density bulk-systems (both for transient and steady-state conditions), and across vapor-liquid interfaces, both at equilibrium and during NEMD simulations. The work shows that the configurational temperature is equivalent to the kinetic temperature in steady-state molecular dynamics simulations if the discontinuity in the derivatives of the interaction potential is handled properly, by using a sufficiently long truncation-distance or tail-corrections.

Evaluation of finite-size effects in cavitation and droplet formation

Nucleation of bubbles and droplets is of fundamental interest in science and technology and has been widely investigated through experiments, theory, and simulations. Giving the rare event nature of these phenomena, nucleation simulations are computationally costly and require the use of a limited number of particles. Moreover, they are often performed in the canonical ensemble, i.e., by fixing the total volume and number of particles, to avoid the additional complexities of implementing a barostat. However, cavitation and droplet formation take place differently depending on the ensemble. Here, we analyze the importance of finite-size effects in cavitation and droplet formation. We present simple formulas which predict the finite-size corrections to the critical size, the nucleation barrier, and the nucleation rates in the canonical ensemble very accurately. These results can be used to select an appropriate system-size for simulations and to get a more precise evaluation of nucleation in complex substances, by using a small number of molecules and correcting for finite-size effects.

Multi-Scale modelling of a membrane reforming power cycle with CO2 capture

Abstract This work presents the initial investigations of an Integrated Reforming Combined Cycle (IRCC) process with CO2 capture using a membrane reformer. A geometrically generic 1-dimensional model of a membrane reformer has been implemented in Matlab 7.9. This model includes detailed balance equations for energy, momentum and mass in all three sections of the membrane reformer. Widely accepted empirical relations have been used to take into account the mass and energy transport across the membrane as functions of the conditions inside the chemical reactor. The reactor model has been integrated into an overall steady state IRCC process simulation model developed in HYSYS and GTPro. The work shows that multi-scale modelling is necessary to capture the behaviour of the process. The overall cycle efficiency of the process was 46.83 % with 85 % CO2 capture.