Physiochemical Hydrodynamics of Droplets and Bubbles Far from Equilibrium
Summary
Classical hydrodynamics focuses on pure liquids in a single phase. However, in most cases in nature and technology, liquid systems are multicomponent and multiphase, with phase transitions between the phases, and thus far from equilibrium. The objective of Detlef Lohse’s Balzan research project is to explore well-defined examples of systems involving droplets and bubbles. A successful quantitative description and one-to-one comparison between well-controlled experiments and theory and numerics can potentially be achieved for such systems, making it possible to identify the underlying principles, and to place these examples in the context of relevant applications of multicomponent and multiphase liquid systems. In particular, on a small scale, focus will be on solvent exchange and multicomponent droplet nucleation and dissolution, while on large scales multiphase and multicomponent turbulent Taylor-Couette flow will be emphasized.
Background
Classical hydrodynamics focuses on pure liquids. In nature and technology, in systems far from equilibrium, fluid dynamical systems are, however, multicomponent, with gradients in concentration, and they often even change in time. These concentration gradients, whether smoother or sharper, can induce a flow. Moreover, phase transitions can occur, with either evaporation, dissolution, or nucleation of a phase. The liquids can be binary, ternary, or they may contain even more components, with several in different phases. The state of non-equilibrium can be driven by flow, mixture, phase transitions, chemical reactions, electrical current, or heat, to name some of the driving factors.
In the 1950s, to deal with such systems theoretically, Veniamin G. Levich wrote Physicochemical Hydrodynamics [1], the central theme of which is the «elucidation of mechanisms of transport phenomena and the conversion of understanding so gained into plain, useful tools for applications», as stated by L. E. Scriven in the foreword of the 1962 English translation. Levich can be seen as both a physical chemist and a theoretical physicist at the same time, or as Scriven puts it, as an «engineering scientist» with a distinguishable «blend of applied chemistry, applied physics, and fluid mechanics». In fact, in his foreword to the first Russian edition of 1952, Levich describes the scope of physiochemical hydrodynamics as the «aggregate of problems dealing with the effect of fluid flow on chemical or physicochemical transformations as well as the effect of physiochemical factors of the flow».
In the first place, Physicochemical Hydrodynamics describes theoretical and mathematical concepts. It should be noted that in those days, the experimental tools to actually measure the flow on the microscale were very limited, and it was impossible to perform direct numerical simulations of the underlying partial differential equations. Today, more than sixty years later, the scientific and, in particular, the hydrodynamical and physiochemical community have developed tremendously, and in the meantime the experimental, instrumental, and numerical means to actually deal with the problems Levich defined in his book have become available and are being used to do so.
These developments are more than timely, as the relevance of physiochemical hydrodynamics of multicomponent and multiphase liquids has become increasingly important in facing challenges to mankind in the twenty-first century. These challenges include energy, namely: storage and batteries, hydrogen production by electrolysis, CO2 capture, polymeric solar cell manufacturing, and biofuel production and catalysis. They also include health and medical issues, like diagnostics or the production and purification of drugs; environmental issues like flotation, water cleaning, membrane management, and separation technology; or food processing and food safety. Yet other challenges are presented by modern production technologies like additive manufacturing on ever-decreasing length scales and inkjet printing, and for the paint and coating industry.
These challenges have traditionally been approached from a pure engineering point of view, and less in the spirit of Levich, that is, as an engineering scientist. On the other hand, as stated above, classical hydrodynamics has focused on pure- and single-phase liquids. However, in recent years the scientific community has begun to bridge the gap from fluid dynamics to chemical engineering and colloidal and interfacial science. The objective of this effort is to come to a quantitative understanding of multicomponent and multiphase fluid dynamics systems far from equilibrium in order to master and better control them. To achieve this objective, controlled experiments and numerical simulations for idealized setups must be performed, thus allowing for a one-to-one comparison between experiments and numerics/theory in order to test theoretical understanding. Indeed, this effort is in the spirit of Levich’s Physicochemical Hydrodynamics, but now builds on and benefits from the developments of modern microfluidics, microfabrication, digital (high-speed) imaging technology, confocal microscopy, atomic force microscopy, and various computational techniques and opportunities for high-performance computing – in a nutshell, the blessings from what can be considered as the golden age of fluid dynamics, which builds on the digital revolution, both on the experimental and the numerical side. Given these developments, and given the necessity in chemical engineering to move towards higher precision and enhanced control, this effort is indeed very timely.
A large amount of physical phenomena and effects comes into play in multicomponent and multiphase liquids far from equilibrium, including gradients in the concentration, either in the bulk of the liquid or on the surface, leading to solutal Marangoni flow and diffusiophoresis. They include (selective) dissolution of (multicomponent) droplets and bubbles in host liquids, or vice versa, their nucleation and growth. They also include the coalescence of droplets consisting of different liquids, possibly with chemical reactions and/or solidification and other transitions from one phase to another. The material parameters which become important are the various diffusivities and viscosities of the liquids, their surface tensions and how they depend on the concentrations, the volatilities and mutual solubilities, latent heats, reaction rates, etc.
The Twente Physics of Fluids group started to work in the direction of the physiochemical hydrodynamics of multicomponent systems only a few years ago, so the subject is quite new for us. The work was initiated by our research on surface nanobubbles and nanodroplets [2], which served as the base for our investigations into droplet nucleation in solvent exchange processes [3-7], including purely theoretical and numerical studies [8, 9]. We also looked into the evaporation of multicomponent droplets [10, 11]. In references 12 and 13, we studied the diffusive and inertial dynamics of so-called plasmonic bubbles, for which phase transitions are crucial.
To give a more visual illustration for physicochemical phenomena and effects in multicomponent and multiphase liquids far from equilibrium, two examples are illustrated below, one on small scales, and one on large scales.
On small scales, the impact of droplets on superheated surfaces [14, 15] has been known for centuries: droplets gently deposited on sufficiently hot surfaces will float – the so-called Leidenfrost effect [16]. The very rich dynamics of the impacting process is illustrated in Fig. I. The temperature beyond which direct contact between liquid and substrate is lost will increase as droplet impact velocity increases. However, it is not known – nor understood – what heat exchange mechanisms determine the so-called Leidenfrost temperature. Our studies have shown that this temperature – and in fact the whole of droplet dynamics – strongly depends on the thermal properties of the substrate. The example in Fig. I shows a substrate (sapphire) that conducts very well thermally. For substrates with poor heat conduction, the dynamics is very different, and so is the Leidenfrost temperature, but the field is very far from being able to predict the Leidenfrost temperature.
On large scales, the example for multiphase hydrodynamics chosen for this introduction is thermal convection around the boiling point of a liquid. Ahlers and co-workers [18] have performed measurements of the Nusselt number (dimensionless heat transfer) of turbulent Rayleigh-Bénard convection in boiling liquids (Fig. II). These measurements were highly reproducible from run to run in the parameter range where liquid droplets form from vapour. In the multiphase regime around boiling temperature, heat transfer is dramatically enhanced, but we are still far from any quantitative understanding of the phenomenon. We tried to model Ahlers’ experiments numerically, but with limited quantitative success up to the present [19], although various features can be qualitatively reproduced.
Objectives
Obviously, the field of multicomponent and multiphase hydrodynamics is far too vast to address exhaustively, even for an entire research group or research community. Therefore, we focus on the physiochemical hydrodynamics of (multicomponent) droplets and bubbles far from equilibrium. The examples in Figures 1 and 2 above were already taken from this subset of problems, and even then our research is of necessity restricted to certain systems. Thus the objective of the proposed project is to explore examples of such systems for which a successful quantitative description and one-to-one comparison of well-controlled experiments and theory and numerics can potentially be achieved in order to identify the underlying principles and to place these examples in the context of relevant applications of multicomponent and multiphase liquid systems.
A postdoctoral fellow supported by Balzan funds will work on these types of problems. In order to have a greater impact and benefit from the intellectual and technological infrastructure, the fellow must be embedded in the Twente Physics of Fluids research group.
Research Platforms and Programme
The following introduces the two main experimental platforms with which the physiochemical hydrodynamics of multicomponent droplet and bubbles far from equilibrium – one on small scales and one on large scales. A sketch of planned experiments for the project will also be included. On small scales, a solvent-exchange microchannel is involved (Fig. III); on large scales, the Twente Taylor-Couette facility is sketched out in Fig. IV.
Small Scales: Multicomponent Droplets with Phase Transitions
Controlled drop nucleation and growth experiments can be performed through the so-called solvent exchange process, as illustrated in Fig. IIIa, c, which show how an oil-saturated ethanol solution (with relatively high oil solubility) is pushed away by an oil-saturated water solution (with relatively low oil solubility). In the mixing zone, a temporal oil oversaturation will emerge (Fig. IIIb), leading to droplet nucleation and growth on the substrate (Fig. IIId). The Twente group would like to study how this growth process depends on flow velocity, channel geometry and scale, oil types (allowing for multiple oils in one experiment), oil saturations, surface properties, and neighbouring droplets. This appears to be an ideal platform to quantitatively understand the physiochemical hydrodynamics of multicomponent droplets.
In particular, plans are underway to work on multicomponent systems, employing several oils with different solubilities dissolved in the aqueous phase. A multicomponent droplet will then nucleate and grow, but clearly the fraction of the oils in the droplet will be different than in the aqueous solution. It will be determined by the relative solubilities, but how? Can one calculate this a priori?
There are also plans to sequentially push different solutions through the microchannel, so that concentration gradients evolve in the emerging droplets. In general, this will lead to flow within the droplet, which may interact with the outside flow. When pushing clean water through the channel, the multicomponent droplets will selectively dissolve, opening even more methods for concentrating or diluting certain components.
The experimental methods to be used are high-speed imaging, particle image velocimetry, confocal microscopy and diagnostics techniques to measure the composition of the droplets. The substrate can be chemically patterned, similarly as in references 20 and 21, to fix the positions of the droplet nucleation.
Next to the experiments and analytical calculations for the diffusive processes around single surface bubbles and droplets, numerical simulations for controlled populations of nanobubbles/nanodroplets will also be performed, by numerically solving the advection-diffusion equations with the respective boundary conditions. The methods will be direct finite difference simulations of the continuum equations with immersed boundary methods (IBM) and MD simulations. We are very optimistic that at least for the controlled conditions of chemically or geometrically pre-patterned surfaces, a favourable one-to-one comparison between experiment, theory, and numerical simulations will be achieved. Initial success in this direction has been achieved [21].
Large Scales: Multiphase and Multicomponent Turbulence
For turbulent flows with phase transitions the complexity seems overwhelming: turbulence, several phases with transitions between them, and nucleation and condensation. For these experiments on large scales, the platform will be the Taylor-Couette system, i.e. two coaxial co- or counter-rotating cylinders with a fluid in between [22]. Up to now at Twente, the Taylor-Couette system has been used only for single phase flow [23-27] and for bubbly flow [28], but in spite of the complexity of turbulent multiphase flow with phase transitions, we are optimistic about being able to perform controlled experiments, namely in our new Twente turbulent Taylor-Couette setup [29], which has excellent temperature control (up to 0.03K over time and up to 0.1K over space) and with which the overall drag can be measured very precisely. Moreover, it can be operated with low-temperature boiling point liquids. At phase transition close to the boiling point, the vapour bubbles are expected to emerge in the low pressure regions, namely within the so-called Taylor vortices. This will have major consequences for the local velocity and temperature fields, and the overall flow organization and the drag laws.
Next to the Reynolds numbers of the inner and outer cylinder, crucial control parameters are the liquid temperature and its thermal properties. For strong turbulence, vapour bubbles will form in the Taylor vortices, affecting the overall drag, which can be measured by adjusting the required torque to rotate the cylinders at fixed velocity. To our knowledge, these would be the first controlled drag measurements in a turbulent boiling liquid.
Correlated with the global measurements of the drag, local optical high-speed observations of vapour bubble dynamics and densities (to be measured with 3D particle tracking velocimetry (PTV)) and of the velocity field (to be measured with 3D particle image velocimetry (PIV)) will also be performed.
A second case to be analysed is the strongly turbulent flow of (multicomponent) oil and water, also in the Taylor-Couette geometry. The easiest case in this class of problems would be the turbulence in an oil-water mixture, with the oil concentration as the central control parameter. Clearly, for low oil fraction, one would have oil droplets in water, but with increasing oil fraction, at some point there must be a phase inversion, leading to water droplets in the oil. In the strongly turbulent regime (i.e. far from equilibrium) and without surfactants (e.g. used to stabilize mayonnaise), the dynamics of this oil-water mixture is totally unexplored. Is this inversion hysteretic? How does the overall viscosity depend on the oil concentration? What is the typical droplet size in both cases and what about the size distribution?
This project, however, wants to go beyond two-component mixtures: first, by analysing a ternary system with three components, e.g. the famous ouzo system (oil, ethanol, and water), and second, just as on the microscale in the previous subsection, by performing a solvent exchange, but instead in the turbulent Taylor Couette system, e.g., slowly introducing water into the Taylor-Couette device initially filled with fully miscible oil-ethanol mixtures. By adding water, the oil solubility will go down and oil droplets will nucleate, similar to the vapour bubbles in the boiling case. How exactly will this happen in this strongly stirred system? What will the consequences for the overall drag be? What is the droplet size distribution, depending on the concentration and the degree of turbulence?
The backbone of the numerical simulations in this part of the project will be a finite difference code with which we will simulate the advection-diffusion equations for the temperature and the gas concentrations of the various reactants and reaction products fully coupled to the Navier-Stokes equation. This massively parallel central-finite-difference code has been developed and optimized within the Twente group and applied to highly turbulent Taylor-Couette and Rayleigh Bénard flows [30–35]. Thanks to the combination of openMP and MPI parallelization directives, the method can efficiently run on tens of thousands of processors, thus tackling unprecedented high Reynolds number turbulent flows. Recently, we further improved our scheme [36] through a multiple resolution strategy, in order to be able to take care of potentially different time scales sets by the scalar field and the velocity field. This is absolutely essential at this point, due to the very large Schmidt number (which is the ratio between kinematic viscosity and diffusivity, in this case, about 1000) characteristic for the (slow) mass diffusion.
The emerging and growing or shrinking droplets and bubbles will be represented with the immersed boundary (IB) method [37–40], with a boundary which is moving due to growth or shrinkage (i.e. due to the diffusive flux) of the bubbles or droplets, and fully resolved concentration boundary layers around them, which can deform thanks to the surrounding flow. With the IB method, the effect of the diffusive interaction of bubbles and droplets in general and in particular of Ostwald ripening can thus be implemented [8], by adjusting the surface concentration at the bubble-liquid or drop-liquid interface according to Henry’s law. It should be emphasized not only that we are able to employ these methods for multicomponent systems, but also that the coupling of IB and FD for bubbles or droplets and strongly turbulent flow is a major new development. Moreover, we intend to push further ahead with this project.