Liquid-vapor Phase Change Research Articles

The start-up characteristics of a novel loop heat pipe with stainless steel capillary wick

Loop heat pipe (LHP) is an advanced thermal management technology that utilizes liquid–vapor phase change and capillary action to achieve efficient heat transfer across long distances and in various directions. The start-up of an LHP is crucial for its reliable and stable operation. This study aims to explore the start-up characteristics and temperature variations of various components under different heating conditions by designing a cost-effective flat plate evaporator LHP with a stainless-steel casing and acetone as the working fluid. The experimental analysis examined the performance of the LHP under varying heating powers from 28 to 60 W, positions, and gravity angles. The findings revealed that the LHP successfully started at 28 W, and a temperature overshoot occured when the heating position was near the compensation chamber. Notably, the start-up time was 400 s faster compared to the heating condition near the mean pressure chamber. When the evaporator was tilted such that the compensation chamber was above the evaporator’s pressure equalization chamber, circulation within the LHP could not be established. The thermal resistance of the LHP decreased with increasing heating power, achieving a maximum reduction of 51.51 %. When both the compensation chamber and the mean pressure chamber were heated simultaneously, the impact of the gravity inclination angle on thermal resistance was minimized. This study introduces an innovative capillary wick LHP with high start-up success rates and cost-effectiveness, providing both empirical data and theoretical insights for the refinement and optimization of civilian LHP designs.

Bridging Innovations of Phase Change Heat Transfer to Electrochemical Gas Evolution Reactions.

Bubbles play a ubiquitous role in electrochemical gas evolution reactions. However, a mechanistic understanding of how bubbles affect the energy efficiency of electrochemical processes remains limited to date, impeding effective approaches to further boost the performance of gas evolution systems. From a perspective of the analogy between heat and mass transfer, bubbles in electrochemical gas evolution reactions exhibit highly similar dynamic behaviors to them in the liquid-vapor phase change. Recent developments of liquid-vapor phase change systems have substantially advanced the fundamental knowledge of bubbles, leading to unprecedented enhancement of heat transfer performance. In this Review, we aim to elucidate a promising opportunity of understanding bubble dynamics in electrochemical gas evolution reactions through a lens of phase change heat transfer. We first provide a background about key parallels between electrochemical gas evolution reactions and phase change heat transfer. Then, we discuss bubble dynamics in gas evolution systems across multiple length scales, with an emphasis on exciting research problems inspired by new insights gained from liquid-vapor phase change systems. Lastly, we review advances in engineered surfaces for manipulating bubbles to enhance heat and mass transfer, providing an outlook on the design of high-performance gas evolving electrodes.

Biomimetic bilayer phase change hydrogels with enhanced water adsorption and desorption for evaporative cooling

Hygroscopic hydrogels, reliable carriers for water-based evaporative materials, undergo shrinkage after evaporative cooling, and the consequent reduction in hygroscopic sites can significantly impair their recyclability in cooling period. To realize cyclic evaporative cooling for rapid regeneration and evaporation, bilayer phase change hydrogel (BPH) concept combining an upper layer of hygroscopic polymer film (CaCl2@ carboxymethyl cellulose/konjac glucomannan films, CaCl2@CMC/KGM, MAF) with a lower layer of hygroscopic hydrogel (CaCl2@poly(vinyl alcohol)/sodium tetraborate decahydrate hydrogel, CaCl2@PVA/Borax, PCH), is presented in this paper. The high liquid–vapor phase change enthalpy of BPH (1274 J/g) enables it to continuously and rapidly remove heat. Benefiting from the MAF hygroscopic porous skeleton, the saturated BPH exhibited a faster water evaporation rate (2.15 kg m−2 h−1) and comparable water vapor transmission rate (1.61 kg m−2 h−1) at 50 °C. After being heated at 50 °C for 1 h, BPH requires 9h to regain its initial mass at 25 °C, 90 % RH. Fifteen moisture adsorption–desorption cycles demonstrate the excellent cyclic regeneration capability of BPH. COMSOL Multiphysics simulation results indicate that evaporative cooling in BPH provides excellent heat dissipation (reduced by about 27 °C). BPH reduces the peak temperatures of a mobile phone by 7.8 °C while charging and 6.5 °C while gaming. This design will contribute to the future cooling of heat-related devices and global sustainability.

Superspreading Surface with Hierarchical Porous Structure for Highly Efficient Vapor-Liquid Phase Change Heat Dissipation.

Superspreading surfaces with excellent water transport efficiency are highly desirable for addressing thermal failures through the liquid-vapor phase change of water in electronics thermal management applications. However, the trade-off between capillary pressure and viscous resistance in traditional superspreading surfaces with micro/ nanostructures poses a longstanding challenge in the development of superspreading surfaces with high cooling efficiency in confined spaces. Herein, a heat-treated hierarchical porous enhanced superspreading surface (HTHP) for highly efficient electronic cooling is proposed. Compared with the single porous structures in nanograss, nanosheets, and copper foam, HTHP with hierarchical honeycomb pores effectively resolves the trade-off effect by introducing large vertical through-pores to reduce viscous resistance, and connected small pores to provide sufficient capillary pressure synergistically. HTHP exhibits excellent capillary performance in both horizontal spreading and vertical rising. Despite a thickness of only 0.33mm, the as-prepared ultrathin vapor chamber (UTVC) fabricated to exploit the superior capillary performance of HTHP achieved effective heat dissipation with outstanding thermal conductivity (12121 Wm-1K-1), and low thermal resistance (0.1 KW-1) at a power of 5W. This regulation strategy based on hierarchical honeycomb porous structures is expected to promote the development of high-performance superspreading surfaces with a wide range of applications in thermal management.

A Molecular Dynamics Perspective on the Impacts of Random Rough Surface, Film Thickness, and Substrate Temperature on the Adsorbed Film’s Liquid–Vapor Phase Transition Regime

While recent studies have proven an unexpected liquid–vapor phase transition of adsorbed liquid films, a comprehensive description of the mechanisms of different types of phase change regimes over realistic representations of random rough surfaces is absent in the literature. The current comprehensive study investigates the effects of a gold random rough surface, liquid film thickness, and substrate temperature on the liquid–vapor phase change regime of an adsorbed sodium liquid film, considering the evaporator section of a wicked heat pipe (WHP) using a molecular dynamics (MD) simulation. At first, to generate a realistic random rough surface, a new and promising method is proposed that is entirely based on MD simulations. Then, to simulate the evaporator section of a WHP, a unique configuration for eliminating the vapor domain is developed. The simulation results reveal that three distinct regimes, namely, normal evaporation, cluster boiling, and film boiling, could be identified, which are presented on two-dimensional diagrams with the substrate temperature and liquid film thickness as coordinates for the ideally smooth and random rough surfaces. The results also manifest that even though using the random rough surface could lead to different phase transition regimes, the type of regime depends mainly on the substrate temperature and liquid film thickness. Furthermore, this study displays two different modes for normal evaporation. Also, it is shown that the impacts of the liquid film thickness and substrate temperature on the mode of normal evaporation are much more significant than the surface roughness.

Microscopic insights on liquid–vapor phase change phenomena of R1336mzz(Z) nanofilm through molecular dynamics simulations

The ever-growing advances in electronics pose a critical cooling challenge. Two-phase heat transfer technology, with effective heat removal and no extra energy consumption, is emerging as a potential solution for sustainable thermal management. However, questions regarding phase change mechanisms are seemingly not addressed yet due to the limitation in time and space scales. In this work, a series of molecular dynamics simulations are performed where the R1336mzz(Z) liquid film rests over a smooth copper substrate. The molecular system starts with a nanofilm thickness of 4–10 nm and then is subjected to non-equilibrium heating (350, 400, 450, and 500 K) to initiate liquid-to-vapor phase change. Depending on the impacts of film thickness and wall temperature, four distinctive phase change scenarios are identified, i.e., diffusive evaporation, pseudo-diffusive evaporation, explosive boiling, and stable explosive boiling. The characteristics of these phase change modes are explicated from the perspectives of molecular motion, vaporization rate, temperature evolution, heat flux, and interfacial resistance. The phase change mode has a strong dependence on two aspects: improving heat transfer to breakup potential barrier and slowing energy dissipation to support formation of bubble embryos. The insight may deliver better understandings of phase change mechanism and applications of liquid refrigerants.

Microscopic insights of phase-transition-induced vapor transport enhancement in porous media

Vapor transport in porous media, often associated with liquid-vapor phase change, is an fundamental process in many emerging underground energy storage and extraction processes (i.e., seasonal solar thermal aquifer storage, geothermal extraction, extraterrestrial in-situ water extraction). By jointly using experimental imaging and numerical modeling at the micro-scale, we conduct mechanistic pore scale investigation of capillarity-dominated phase change dynamics and its influence on vapor transport in partially saturated porous rock micromodel. Strongly linked to surface roughness and wettability condition, the capillarity hinders water vaporization from rock surface micro/nano-structures as observed under the environmental scanning electron microscope. By varying the contact angle of 0°, 60°, and 120°, the lattice Boltzmann simulation shows the wettability-dependent vaporization process of capillary-hold water, where pores with hydrophilic surfaces contains significantly more liquid water than that of the hydrophobic ones under the same temperature. When saturated vapor flows through rock porous patterns, capillarity further induces water condensation on the strongly water-wet surfaces. Water condensation, yet forming water bridges/islands and causing the blockage of vapor diffusion, enhances the vapor diffusion ability counterintuitively. The reduction of diffusion path is revealed as the main reason by assessing the local vapor pressure distribution before and after the pore filling by condensate. The findings support the debatable enhancement mechanisms postulated by Philip and de Vries. This work offers the insightful interfacial hydrodynamics of vapor transport in porous media and potentially provides operational guidance for geothermal applications and beyond.

Simulation of a two-phase loop thermosyphon using a new interface-resolved phase change model

The remarkable progress made in power electronics has been coupled with the miniaturization of systems, requiring high-performance cooling. A solution that has garnered significant interest involves the use of two-phase loops, in which heat transfer is associated with the phase change of the working-fluid. This paper aims at modeling two-phase flow with separated phases in a gravity-driven two-phase loop. The Volume-of-Fluid method is employed to capture the moving interface. Amid the variety of the phase change models available in the literature, we have chosen to employ a hybrid model: a subgrid-scale model to generate phase change at the wall in the absence of an interface, and a interface-resolved model for phase change at pre-existing liquid-vapor interfaces. These models have been implemented in the OpenFOAM computational code. The developed solver makes possible the simulation of compressible laminar two-phase flow with diabatic liquid-vapor phase change. Conjugate heat transfer between the wall and the fluid is also taken into account. Two-dimensional numerical simulations demonstrate that the developed solver is capable of reproducing flow regimes obtained from experiments, including the formation of Taylor bubbles and the propulsion of liquid from the evaporator to the condenser during geyser boiling. Furthermore, this study examines how the filling ratio affects flow regimes and performance.

Nucleation, growth and bubble detachment in liquid-vapor phase change on structured surfaces

Comprehensive grasp of heat and mass transfer, particularly in applications involving liquid-vapor phase change, hinges on management of nucleation, growth, and detachment of vapor bubbles. Various parameters influence the dynamics of phase-change heat and mass transfer and thus dictate the interactions between the surface, the liquid, and the vapor, profoundly impacting the underlying processes. To tailor these phenomena and harness them for technical applications involving high heat flux densities and intense mass transfer, such as boiling and electrolysis, surface functionalization is under intense development. By designing structured surfaces and creating preferential nucleation sites that promote heterogeneous nucleation, it is possible to exert control over the location and density of active nucleation sites on the surface. This, in turn, enables the regulation of bubble growth and detachment from the surface. With the aim of identifying optimal surface treatments for functionalizing surfaces and enhancing their performance in phase-change applications, we evaluated the nucleation, growth and detachment of a single bubble in a liquid-vapor phase change on untextured and laser-textured surfaces during water electrolysis. Platinum was chosen as the preferential material due to its favourable electrochemical properties for the hydrogen evolution reaction in acidic media. Electrolysis was performed at various voltages and the bubble dynamics were evaluated through high-speed imaging to investigate the intricacies of bubble growth and their mutual interactions. At 3.5 V using the laser textured surface, hydrogen bubbles detaching from the electrode surface had on average 40% smaller diameter, while the frequency of their detachment was 2,5-times higher compared to the untextured surface. This opens the possibility for further research that could lead to improving the efficiency of electrolysis.

Multi-scale boiling heat transfer investigation on micro-thin aluminum heaters

Nucleate boiling is a highly efficient heat transfer mode distinguished by the liquid-vapor phase change, which occurs through the formation, growth, and detachment of vapor bubbles from a heated surface. Its crucial role in various industrial applications, such as nuclear power plant operation and effective heat management in small electronic devices, has driven significant research efforts. However, despite extensive research dedicated to boiling investigations, there are still substantial knowledge gaps that hinder our ability to accurately predict heat removal rates. These knowledge gaps arise from the complex nature of small-scale boiling phenomena, which are further complicated by their strong dependence on operating conditions and the interactions between walls and fluids. In an effort to address some of these gaps, we conducted multi-scale investigations during pool boiling of de-ionized water on micro-thin aluminum heaters. We captured bubble dynamics through multiple synchronized diagnostic sources, including high-speed backlit imaging to track bubble growth, synchronized high-speed infrared thermometry to capture the corresponding thermal footprint on the boiling surface, and in-house developed fast-response micro-thermocouples to measure temperature at multiple locations within the fluid. Our study reveals peculiar aspects of heat transfer mechanisms occurring at single bubble level (low heat fluxes) and in fully developed nucleate boiling regimes (high heat fluxes).

Study on dynamic characteristics of cavitation in underwater explosion with large charge

Underwater explosions (UNDEX) generate shock waves that interact with the air–water interface and structures, leading to the occurrence of rarefaction waves and inducing cavitation phenomena. In deep-water explosions, complex coupling relationships exist between shock wave propagation, bubble motion, and cavitation evolution. The shock wave initiates the formation of cavitation, and their growth and collapse are influenced by the pressure field. The collapsing bubbles generate additional shock waves and fluid motion, affecting subsequent shock wave propagation and bubble behavior. This intricate interaction significantly impacts the hydrodynamic characteristics of deep-water explosions, including pressure distribution, density, and phase changes in the surrounding fluid. In this paper, we utilize a two-fluid phase transition model to capture the evolution of cavitation in deep-water explosions. Our numerical results demonstrate that the introduction of a two-phase vapor–liquid phase change model is necessary to accurately capture scenarios involving prominent evaporation or condensation phenomena. Furthermore, we find that the cavitation produced by the same charge under different explosion depths exhibits significant differences, as does the peak value of cavitation collapse pressure. Similarly, the cavitation produced by different charge quantities under the same explosion depth varies, and the relationship between cavitation volume and charge quantity is not a simple linear increase. The research methods and results presented in this paper provide an important reference for studying the dynamic characteristics of deep-water explosions.

Turbulent flow boiling simulation based on pseudopotential lattice boltzmann method with developed wall boundary treatments and unit conversion

The lattice Boltzmann method (LBM) is widely studied for complex flow simulations, including liquid–vapor phase change phenomena. Although previous studies extended the LBM simulation capability from single-phase to two-phase boiling simulations, most of them are restricted to no-flow (pool boiling) or low-flow-rate (laminar flow) boiling conditions owing to the stability problem in collision at low viscosity, representing high Reynolds numbers. However, a high Reynolds number flow is essential for investigating the effects of turbulence on bubble dynamics. Recently, the central moment-based collision method is used to enable high Reynolds numbers for bulk flow; however, extending the method for multiphase-flow simulation with high Reynolds numbers is limited owing to the boundary treatment near the wall. In this study, we augment the previous boundary treatment in LBM simulation with a forcing term, which increases the stability of the simulation even under two-phase conditions. With the improved boundary treatment, the flow boiling phenomena at high Reynolds numbers (up to Re = 107,000) are successfully reproduced. Moreover, in this study, unit conversion is reconsidered with the relationship between conversion factors because the poor outcomes of bubble dynamics are attributed to misinterpreted unit conversion. The new unit conversion method satisfies the necessary conditions for mapping the physical bubble behavior to lattice frame, reproducing bubble dynamics effectively following the Reynolds number, with reasonable spatial and temporal resolution. Consequently, the flow boiling simulation can accurately predict the bubble departure diameter from the real experimental results and the heat transfer trend as a function of the Reynolds number.

Data-driven diagnostics of boiling heat transfer on flat heaters from non-intrusive visualization

Rankine-based power generation cycles require the use of boiling heat exchangers for liquid–vapor phase change. However, operating boilers at too high heat fluxes can lead to heater meltdown due to onset of the boiling crisis. Despite recent advances in increasing this critical heat flux, the lack of fast and accurate diagnostics hinders boiling heat transfer safety at high heat fluxes. Here we show that neural networks fed on direct observation of bubble dynamics can be used to measure heat flux during nucleate boiling. The boiling heat transfer data was obtained with a horizontally oriented, circular flat heater with saturated water as the heat transfer fluid. A deep convolutional neural network (CNN) was trained using frames from videos acquired from 15 different heat dissipation values on the boiling curve to learn how these images correlate to the underlying heat flux. The CNN predicted heat fluxes with a mean square error of 14.6 W/cm2. Furthermore, the CNN presented high sensitivity to pixel intensity in image regions relevant to boiling heat transfer physics (e.g. bubble boundaries, contextual clues about bubble image distortion). Understanding this approach may allow future studies in unstable and critical boiling regimes that require fast transient heat flux diagnostics and cannot rely on slower thermohydraulic measurements.

Thermopneumatic Liquid Metal Radiofrequency Switch Actuated by Low‐Boiling‐Point Fluid

Existing radiofrequency (RF) switches used in reconfigurable antennas often encounter performance issues such as high insertion loss, low isolation, and nonlinear effects of the switch. To address these issues, this article presents a liquid metal RF switch that utilizes a heated low‐boiling‐point fluid (LBPF) to drive the movement of a eutectic gallium‐indium alloy (EGaIn) plunger to turn the switch on/off. The operating principle of the switch is to use the pressure difference generated by the liquid–vapor phase change of the LBPF to make the EGaIn plunger to contact with, or disconnect from the copper electrodes of the switch. The performances of the RF switches actuated by different LBPFs are respectively investigated, and the results show that all RF switches have millisecond response times, and the contact resistances are as low as 0.14 mΩ. In addition, good RF performances are achieved, with an insertion loss of less than 3 dB and isolation of more than 17 dB in the frequency band from 0 to 2 GHz, and no nonlinear effects. This study also validates the performance of the proposed switch for frequency reconfiguration of a folded monopole antenna.

A thermal lattice Boltzmann model for evaporating multiphase flows

Modeling thermal multiphase flows has become a widely sought methodology due to its scientific relevance and broad industrial applications. Much progress has been achieved using different approaches, and the lattice Boltzmann method is one of the most popular methods for modeling liquid–vapor phase change. In this paper, we present a novel thermal lattice Boltzmann model for accurately simulating liquid–vapor phase change. The proposed model is built based on the equivalent variant of the temperature governing equation derived from the entropy balance law, in which the heat capacitance is absorbed into transient and convective terms. Then a modified equilibrium distribution function and a proper source term are elaborately designed in order to recover the targeting equation in the incompressible limit. The most striking feature of the present model is that the calculations of the Laplacian term of temperature, the gradient term of temperature, and the gradient term of density can be simultaneously avoided, which makes the formulation of the present model is more concise in contrast to all existing lattice Boltzmann models. Several benchmark examples, including droplet evaporation in open space, droplet evaporation on a heated wall, and nucleate boiling phenomenon, are carried out to assess numerical performance of the present model. It is found that the present model effectively improves the numerical accuracy in solving the interfacial behavior of liquid–vapor phase change within the lattice Boltzmann method framework.

Liquid evaporation from nanochannel in the presence of non-condensable gas by direct simulation Monte Carlo

Liquid-vapor phase change in the form of evaporation and with the confinement of nanostructures is of vast importance in many engineering applications. The direct simulation Monte Carlo (DSMC) approach was employed to simulate the liquid evaporation from two-dimensional nanochannels in the presence of non-condensable (NC) gases. The thermodynamic properties of vapor and NC gas flow fields as well as the evaporation rate of liquid were calculated. Factors such as channel opening ratio, meniscus receding depth and the NC gas density were examined to reveal their impacts on the liquid evaporation rates. The results showed that the gas mixture flow field transforms to one-dimensional away from the channel exit. The overall vapor pressure drop can be divided into that across the liquid–vapor interface, that within the channel, outside the channel, as well as that caused by the binary diffusion. The effect of NC gas on the evaporation rate was found to be the most outstanding with pinned meniscus and with a wide channel opening, in which case the normalized evaporation rate drops to 0.43. Moreover, the Maxwell-Stefan equation could capture the evaporation data with modified diffusion lengths. For receded meniscus (250 nm deep) and small opening ratio (0.417), the effective diffusion length was as large as 1.6 times that in the one-dimensional case.

An immersion flow boiling heat dissipation strategy for efficient battery thermal management in non-steady conditions

Aiming at the heat dissipation requirements of future high-power batteries under complex operating conditions, this paper adopts immersion flow boiling as the strategy to investigate battery thermal management performance under Nürburgring circuit condition of Porsche Taycan. A multi-filed coupled model is proposed to investigate its flow and heat transfer performance. The results show that batteries have a higher heat generation in non-steady conditions, which means that it is more crucial to investigate the battery thermal management performance under non-steady state. Immersion flow boiling can meet the thermal management requirements of batteries with high heat generation rate, which has significant advantages over single-phase liquid cooling, and the temperature uniformity can be further improved by means of roughing surface. Besides, flow velocity will completely change the heat transfer and flow mechanism of immersion flow boiling. The optimum flow regime can both exchange heat by liquid–vapor phase change and replenish the vaporized working medium by convection, achieving the lower temperature rise and better temperature uniformity in battery. Moreover, the boiling heat transfer in battery thermal management is in the partial nuclear boiling state, which is much lower than the critical heat flux, and thus can effectively inhibit high heat flux conditions such as thermal runaway.

An efficient thermal lattice Boltzmann method for simulating three-dimensional liquid–vapor phase change

In this paper, a multiple-relaxation-time lattice Boltzmann (LB) approach is developed for the simulation of three-dimensional (3D) liquid–vapor phase change based on the pseudopotential model. In contrast to some existing 3D thermal LB models for liquid–vapor phase change, the present approach has two advantages: for one thing, some gradient terms, such as the gradient of volumetric heat capacity and the Laplacian term of temperature, that must be computed with finite-difference scheme in previous works is not needed for the present thermal model. For another, the current model is constructed based on the seven discrete velocities in three dimensions (D3Q7), making it more efficient and much easier to be implemented. Also, based on the scheme proposed by Zhou and He (1997), a pressure boundary condition for the D3Q19 lattice is proposed to model the multiphase flow in open systems. This model is then validated by considering the temperature distribution in a 3D saturated liquid–vapor system, the d2 law, the droplet evaporation on a heated surface and the nucleate boiling. It is observed that the numerical results fit well with the analytical solutions, and the results of the finite difference method or the experimental data. Our numerical results indicate that the present approach is reliable and efficient in dealing with the 3D liquid–vapor phase change.

Acoustofluidic bubble-driven assisted functionalized nano-array coated micro pin-fins surface for efficient liquid-vapor phase change chip cooling

Embedded phase change boiling heat transfer is crucial for addressing the energy saving posed by high-power compact electronic devices. However, the endeavor to fabricate improved heat transfer structures in confined and constricted spaces remains a formidable challenge. Herein, we present a simple and straightforward acoustofluidics strategy to create stable, controllable, and efficient functional Zinc oxide (ZnO) nanoarray coatings in narrow micro-pin-fins chip surfaces with excellent phase change cooling performance. A robust acoustic micromixer combining bubble acoustic streaming and hydrodynamic effect provided by spiral microchannels is proposed to facilitate microscale fluid mixing across a broad flow rate range. The ZnO nanoarray-coated micro pin-fins chip, which allows for customizable lengths, densities, diameter, and morphology, is fabricated through straightforward adjustment of acoustofluidics micromixer parameters. Excellent phase change cooling performance is obtained on this surface, giving priority to nucleation (superheat≈ 4 °C, reduced by 50.2 %), low wall temperature (≤70.7 ℃) under the limit CHF, negligible pumping energy (≤3.5 kPa), and simultaneously enhancing the critical heat flux (CHF, from 45.1 to 77.2 W·cm−2) and heat transfer coefficient (HTC, from 5955 to 15552 W·m−2·K−1) by up to 71.3 % and 161.1 %, respectively, compared with the smooth chip surface. In situ observation and analysis of the dynamic wetting behavior and boiling bubble dynamics indicated ZnO nanoarray coated micro pin-fins chip promotes the phase change heat exchange process by massive nucleation sites, effective control of boiling bubbles, and ultra-fast two-stage liquid rewetting capability. These findings not only provide important guidelines for the precise control and rational design of functional nanomaterials, but also provide new insights for embedded cooling and significant energy savings on power devices.

Mixtures of phase transforming fluids and gases: Phase field model and stabilized isogeometric discretization

Liquid–vapor phase change in the presence of non-condensable gases is a classical problem, which continues to challenge continuum modeling. Here, we propose a new model based on the phase field method, which describes the dynamics of the non-condensable gas, phase change and flow simultaneously. The model is built by extending van der Waals and Korteweg’s theory for phase-transforming mixtures. The model equations have fourth order partial differential operators which presents significant challenges to standard spatial discretization methods. In addition, the isentropic form of the model equations is not hyperbolic at the liquid–gas interface, which inhibits the direct application of most algorithms for systems of hyperbolic equations. We propose a novel numerical scheme based on Isogeometric Analysis and the Taylor–Galerkin method, and also implement a residual based discontinuity capturing scheme. We show numerical results, at micron length scales, to study the accuracy and stability of our algorithm. We study the flow of a shock wave past a liquid droplet to test our numerical algorithm when steep gradients are present in the solution. Finally, we use the model to study the problem of gas–vapor bubble collapse near a solid wall.