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MiR@W day: Multiscale Modelling Approach to Fluid Flows Involving Phase Change

Friday 20th July 2018

Organisers: Livio Gibelli (School of Engineering), Anirudh Rana (Mathematics Institute, Institute of Advanced Study)

Location: B3.02 Mathematics Institute, Zeeman Building, University of Warwick, Coventry CV4 7AL, UK


Evaporation and condensation processes are both of practical signicance in engineering and of fundamental interest in the pure sciences. These processes span over a wide range of time and length scales, and the challenge of dealing with their multiscale nature is the core motivation of this workshop. Leading experts in the field of phase change processes at different modelling scales, such as, microscopic (e.g., molecular dynamics), mesoscopic (e.g., kinetic theory) and macroscopic (e.g., fluid dynamics) will be brought together to present the state of the art in simulation and modelling and to identify possible new pathways.

This workshop may be of interest to the students/scholars working in area of computational and theoretical fluid dynamics.


Time Event
10:00 – 10:30 Welcome coffee  
10:30 – 11:15 Droplet heating and evaporation: hydrodynamic, kinetic and molecular dynamic modelling Prof. Sergei Sazhin (Thermal Physics, University of Brighton, UK)
11:15 – 12:00 A Numerical Study of Temperature Jumps in Evaporation of Water Prof. Aldo Frezzotti (Politecnico di Milano, Milano, Italy)
12:00 – 12:20 Rarefaction effects in nano-vapour bubbles Michael Negus (Mathematics Institute, University of Warwick, UK)
12:30 – 14:00 Lunch Break
14:00 – 14:45 Developing the Next-Generation of Multiphase Thermal Systems Dr. Ryan Enright (Nokia Bell Labs, Dublin, Ireland)
14:45 – 15:30 Moment equations from the Enskog-Vlasov equation Prof. Henning Struchtrup (University of Victoria, Canada)
15:30 – 15:50 Mass and heat transport effects in molecular simulations of crystal nucleation from fluids Dr. David Quigley (Department of Physics, University of Warwick, UK)
15:50 – 16:10 Phase field modelling with applications in fluids Dr. Björn Stinner (Mathematics Institute, University of Warwick, UK)
16:10– 17:00 Round table  

External speakers

Title: A Numerical Study of Temperature Jumps in Evaporation of Water

Abstract: In 1999, Fang and Ward published a paper reporting measurements of large temperature jumps at the vapor-liquid interface, during the slow evaporation of purified water [1]. Temperature jumps in evaporation flows have also been observed in experiments adopting different setups [2]. The observed temperature jumps appeared as anomalous in that the vapor temperature, in proximity of the interface was found to be a few degrees higher than the liquid surface temperature, whereas it was expected to be slightly lower because of the vapor expansion in the evaporation flow. As pointed out in a few following papers [2], such expectation is not correct, in principle, since the heat flux also contributes to the interfacial temperature jump. The aim of the present work is to benchmark kinetic theory prediction of temperature jumps at the vapor-liquid interface of water, improving previous investigations neglecting molecular internal degrees of freedom and adopting unnecessary approximations on the Knudsen layer structure. The Direct Simulation Monte Carlo (DSMC) is adopted to simulate water vapor in contact with its liquid phase. The companion VSS collision model correctly reproduces water vapor transport properties. A proper setting of kinetic boundary conditions allows reproducing the experimental jumps reported in Refs [1,2].
However, the matching between theory and experiments requires assuming very low values of the evaporation coefficient. Hence, DSMC simulations are also used to estimate the possible corrections to be made on experimental temperature data, based on micro-thermocouples measurements, as pointed out in Ref. [3].
[1] G. Fang , C.A.Ward, Physical Review E, 59, 417-428 (1999)
[2] V. Badam, V. Kumar, F. Durst and K. Danov, Experimental Thermal and Fluid Science, 32, 276-292 (2007)
[3] M.A. Kazemi, D.S. Nobes, and J.A.W. Elliott, Langmuir, 33, 7169-7180 (2017)

Title: Moment equations from the Enskog-Vlasov equation

Abstract: Hydrodynamic models of liquid-vapor flows have to face the difficulty of describing non-equilibrium regions next to interfaces. Depending on the flow regimes and the underlying theoretical models, different answers have been given.

In particular, diffuse interface models (DIMs) provide, in principle, a unified description of the whole flow field by a set of PDE's, not much more complex than Navier-Stokes-Fourier classical equations. Unfortunately, DIMs fail to provide a proper description of kinetic layers next to interfaces. In order to develop a model incorporating kinetic effects while keeping the relative simplicity of DIMs, macroscopic transport equations-moment equations- are derived from the Enskog-Vlasov equation. The Enskog-Vlasov equation extends the Enskog equation by accounting for the attractive forces between the gas molecules. Hence, it gives a van-der-Waals-like description of a non-ideal gas, including liquid-vapor phase change. Specifically, the equation describes the liquid phase, the vapor phase, and a diffusive transition region connecting both phases. While not the most accurate model, solutions of the Enskog-Vlasov equation exhibits all relevant phenomena occurring in the evaporation and condensation of rarefied or dense vapors.

In this work, Grad's moment method is used to derive a closed set of 26 moment equations. In the appropriate limits, these reduce to the Navier-Stokes-Fourier system for liquid and vapor. Our main interest is to study non-hydrodynamic effects, in particular transport in and across the transition region, and the interplay between the transition region and Knudsen layers. We will present first results of this program, including the closed transport equations for 26 moments, discussion of the limits, and solutions in simple geometries.

Title: Droplet heating and evaporation: hydrodynamic, kinetic and molecular dynamic modelling

Abstract: Some recently developed approaches to the hydrodynamic, kinetic and molecular dynamic modelling of mono and multi-component droplet heating and evaporation are discussed. New approaches to taking into account the effect of the moving interface during droplet evaporation on droplet heating for mono- and multi-component droplets are summarised. Simplified models for multi-component droplet heating and evaporation, based on the analytical solutions to the species diffusion equation inside droplets, are described. A multi-dimensional quasi-discrete model for heating and evaporation of complex multi-component hydrocarbon fuel droplets, and its application to modelling the heating and evaporation of realistic Diesel and gasoline fuel droplets are described. Recent developments of kinetic algorithms, including those taking into account the effect of inelastic collisions between molecules, are reviewed. The results of applications of molecular dynamics and quantum-chemical simulations to study the evaporation of n-dodecane droplets are described.

Title: Developing the Next-Generation of Multiphase Thermal Systems

Abstract: In the last two decades, substantial efforts have been focused on understanding how surface micro- and nanostructuring can modify the behaviour of wetting liquids to produce interesting and, potentially, very useful effects. One well-known example of surface engineering is the “Lotus-effect”, whereby the combination of intrinsic hydrophobicity and surface structuring results in superhydrophobic droplet behaviour characterized by water droplet contact angles approaching 180° and negligible contact angle hysteresis. In the thermal engineering community, surface engineering has emerged as a new paradigm in the push towards higher performance in multi-phase thermofluid systems. However, while a good deal of work has been done to show how fundamental understanding of these types of wetting interactions can be exploited for thermal applications, for researchers applying surface engineering techniques to unlock further performance enhancements and new functionalities in phase-change heat and mass transfer, the availability of accessible multiscale, multiphase modeling techniques remains a key challenge.

In this talk, I will present an overview of two thermal systems we have been investigating where wetting interactions dominate and that have the potential to make great gains in thermal management systems for 5G wireless, power electronics, 3D optoelectronics and space-based systems applications. Special attention will be given to the challenges associated with modeling these systems which are characterised by multiple phases and length scales. In the first example, I will describe a high-performance nanoporous evaporator design that operates in a new thermal regime where the solid and liquid conduction resistances are similar or smaller in comparison to that of the interphase region between the liquid and vapour. In the second example, I will discuss our recent work focused on understanding the role of surface forces in controlling the heat and mass transfer performance of jumping droplet water condensation.


There is no registration required for the workshop. However, if you want to attend this event please write us an email ( or so that we can have accurate numbers for lunch and coffee.

Aerial photograph of Maths Houses

See also:
Mathematics Research Centre
Mathematical Interdisciplinary Research at Warwick (MIR@W)
Past Events 
Past Symposia 

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