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Mixing of liquids with different viscosities

This PhD aims at understanding how miscible liquids with different viscosities mix.

This PhD aims at understanding how mixing proceeds in a fluid containing heterogeneities in viscosity. This situation is generic to all processes where miscible liquids of different viscosities mix. It differs qualitatively from most conventional mixing problems where the diffusing substance (e.g., heat or diluted solute) does not alter the flow significantly, i.e., where the flow is independent of the degree of homogenization itself. Here, by contrast, a strong and non-trivial feedback coupling is expected: the diffusion of one liquid into the other modifies the viscosity field, hence, changes the kinematic of stretching, which in turn prescribes the diffusion rate.

The PhD will investigate the mixing for various ubiquitous flow configurations, starting with the simplest case of a compact blob of a viscous liquid in a less viscous one that is evenly sheared. We expect to characterize and model the whole mixing problem, i.e., both the kinematics and the evolution of the concentration field, for arbitrary viscosity ratio and deformation rate (Péclet number).

Feel free to contact us if you are scientifically or practically interested in this question.

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Download : PHD Description

Deep ocean mixing by breaking internal waves

Expected Results: Evidence is accumulating that mixing by deep ocean turbulence exerts a leading order control on the global climate system through regulating the oceanic uptake and redistribution through irreversible turbulent mixing of heat, carbon, nutrients and other tracers.

Observations of such turbulent mixing, and our ability to model it numerically, have both been extremely limited historically. However, recently major international field programmes have shed light on deep ocean turbulence through state-of-the-art observations of turbulence generated by deep ocean waves that can have amplitudes measured in the tens to hundreds of metres37.

Computational resources are just now also becoming available to allow us to simulate such flows at adequately high resolution, and in particular to trace the ensuing mixing dynamics in space and time. An exciting opportunity is emerging to use simulations and observations in tandem to understand the physics of such turbulent mixing in detail38, and thus to represent the key effects of this wave-induced mixing in climate models, which inevitably have too coarse a resolution to describe the intricate and fascinating wave-driven dynamics directly.

This project will advance our understanding of deep ocean turbulent mixing mediated by wave-breaking through an iterative combination of observational data analysis and high-resolution numerical simulations. Improving the parameterisation of such turbulence is a key challenge for larger-scale predictive climate modelling, and is central to understanding transport of heat, carbon and nutrients in the oceans.

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Mixing in granular systems

Expected Results: A crucial first step of many industrial processes (pharmaceutical, building materials, industrial beneficiary Saint-Gobain’s activities such as glass forming) is the homogenization of granular raw materials. Although important progresses in the understanding of their rheology have been achieved in the last decade39, the question of grain mixing has received much less attention.

Recent works showed that mixing in granular materials or concentrated suspensions is strongly affected by the shear-induced self-diffusion of the grains40. For simple shear flows, a description was given in terms of an effective diffusivity coefficient. The goal here is to go beyond by providing a description of mixing able to handle complex flows.

This will be achieved by extending the lamellar approach of mixing6 to the case of granular flows. In such case, the key feature is that the diffusion coefficient is not constant, as for molecular diffusion, but depends on the grain size, the local shear rate and the local volume fraction in grains. In the line of CoPeRMix outputs 1 and 2, experiments will be performed to investigate the mixing process of large grains with a focus on the role of the flow field heterogeneities.

To enhance these heterogeneities and broaden the distribution of local shear rates, we will also introduce cohesion between the grains. This project will share experimental techniques and compare stirring protocols with ESRs1,2,5,6.

Supervisor: Pierre Jop,

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Mixing in multiphase, multicomponent fluid systems in confined geometries

Recent advances in high-resolution visualization and pore-scale flow modelling provided by the CoPeRMix network give disruptive tools to understand the fundamental mechanisms controlling flow through porous media and their upscaling to field-scale predictions. A major challenge in pore-scale modeling is the direct simulation of flows involving multicomponent mixtures with complex phase behavior. A key open question is how the interplay between mixing and multiphase flow in the tightly confined pore space of reservoir rocks controls the phase behavior, potentially deviating from the idealized calculations based on thermodynamic equilibrium. To address this question, we will begin by simulating flow of partially miscible two-component two-phase (gas-liquid) mixtures in Hele-Shaw cells. We will characterize the structure of the velocity field induced by interface dynamics and mass transfer. We anticipate that fingering and break- up instabilities may lead to chaotic mixing conditions in the liquid phase. We will also explore the emergence of metastable states of fluid mixtures in porous media systems and propose modified flash calculations to upscale our results to field-scale flow models thereby contributing to CoPeRMix outputs 3 and 5. Strong interactions are expected with ESRs 5, 10, 11, 12 to understand phase transition and drop/supersaturated vapor field interaction.


Supervisor: Luis Cueto-Felgueroso,

Impact of pore structures on mixing dynamics

The large diversity of subsurface porous media (sedimentary layers, soils, rocks) that host water and energy resources is inherited from long-term geological processes. These heterogeneities and anisotropies in the pore structure drive macroscale solute dispersion, mixing and reaction8. Recent experimental breakthroughs obtained by the CoPeRMix teams14,18 have enabled the first quantification of mixing dynamics in random monodisperse bead packs rendered transparent by optical index matching (Fig. 1.2a), providing an experimental proof of the chaotic behaviour of fluid stirring in porous media. The key question to address now is whether these results apply to a larger class of porous media. To investigate these questions, fundamental to key applications involving solute mixing (e.g., contaminant transport, CO2 sequestration, biogeo- chemical reactions), the PhD candidate will extend the optical techniques developed in the CoPeRMix network to a range of multiscale porous media including: polydisperse bead packs, packs of crushed materials and upscaled transparent models of real rocks in order to derive their scale dependent stirring laws. The expected results will contribute directly to CoPeRMix output 2 by documenting the impact of the complexity in pore structure of real rock and sedimentary morphologies on the dynamics of solute mixing. It will also contribute to CoPeRMix output 4.

Supervisor: Tanguy Le Borgne,  

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A new geo-inspired mixer

Large output growing of biological cells is difficult because cells need a large supply of oxygen (hence large mixing rates) but they are killed by large shear strains. Thus, bioreactors require efficient mixing yet very smooth stirring. Such a “soft mixer”, inspired by the precession of the Earth, has recently been proposed in a patent, which is currently tested for algae growth by a local start-up company. The bioreactor consists of a cylindrical container rotating slowly around its axis. The flow is forced by the motion of the free surface with respect to the cylinder due to the small angle between the axis and the vertical. This generates a strong resonance of the flow leading to a large increase of scalar transport, while decreasing the small-scale shear. The goal of the project is to improve the fundamental knowledge on mixing in this simple configuration which can be tuned to generate a 3D laminar or a turbulent flow. The mixing characteristics (stirring law, mixing times, concentration distributions) of the “soft mixer” will be investigated using Laser Induced Fluorescence measurements. In parallel, the flow will be characterized through PIV measurements (mean velocities and shear, PDF of velocity and shear) and described analytically using the eigen modes of rotating fluids. The mixing properties will then be recovered using a new numerical technique based on diffusive Lagrangian tracers.


Download : PHD Description

Impact of Structure on Mixing and Dispersion Dynamics in Heterogeneous Porous Media

This position is open : PhD_IDAEA2

While the local Darcy scale flow and transport processes are based on Fourier’s law (Darcy equation, advection-dispersion equation) and extensions thereof, large-scale mixing and transport processes are a result of the synergetic action of local scale mass transfer processes and the spatial heterogeneity inherent to natural and engineered media8. Despite its importance, little is known on the impact of realistic medium Darcy scale architecture and heterogeneity distribution as well as (velocity-dependent) local scale dispersion on large (regional) scale mixing dynamics. The combination of geostatis- tical and stratigraphic information with novel stochastic approaches to large scale transport, and an original lamellar frame- work (DSM17), will lead to a new understanding of mixing and dispersion processes in geological media. The interaction with ESR5 will feed into the development of a novel three-dimensional dispersive mixing approach, which will be integrated into a predictive model for memory-dependent transport in geological media. Interactions with ESR11 will explore these new concepts in the context of biogeochemical reactions.

Convective mixing in heterogeneous porous media

The dynamics of convective mixing are controlled by the medium and fluid properties42. Determining how the heterogeneity of the porous medium affects convective instabilities is important to understand the behavior of geo- physical fluids systems (e.g., geothermal groundwater systems, CO2 storage) and industrial applications (e.g., heat conduction in metallic foams). High resolution numerical simulations will be performed to assess the relation between heterogeneous permeability fields and scalar distribution patterns, fluid deformation, convective velocity structure, and mixing efficiency. The simulations will be complemented with experiments in Hele-Shaw cells of EAWAG and data from reactive experiments from ULB (ESRs 11, 12, 15). Mixing diagnostics as the scalar dissipation rate and the concentration probability density function will be related to the variance and correlation length of the permeability field to extract the convective stirring and mixing dynamics under heterogeneity. This will allow developing a theoretical framework to assess the performance of the systems in terms of upscaled parameters, and the feedback between reactions and instabilities.

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Mixing and precipitation patterns linked to groundwater evaporation in arid environments

Evaporation in arid environments leads to the salinization of soils, which is one of the processes of soil degradation contributing to land desertification. Physically, the evaporated groundwater becomes denser and generates den- sity-driven convective flow fields. Chemically, the evaporated water becomes saturated in carbonate minerals, gypsum and, eventually, halite. Precipitated calcium carbonate forms a hard, calcareous cement known as caliche, which changes the hy- draulic properties of the soil. The precipitation patterns of these minerals can only be understood by the interplay between evaporation, convective flow, mixing and reactions. An experimental and numerical approach is proposed. First, numerical models to simulate groundwater flow and mixing in highly evaporative environments will be performed. The simulations will be used to design experiments in 2D tank experiments or Hele-Shaw cells to be performed in EAWAG (EAWAG-Zurich) and at ULB (Brussels). A reactive transport model will be developed in collaboration with ESRs 11, 12 to replicate the flow and reactivity patterns observed in the experiments. The temporal dynamics and spatial patterns of flow and reactivity will be investigated to predict the formation of mineral crusts, define desertification indicators and the critical time under which the process becomes irreversible and to design mitigation strategies.

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Supervisor: Elena Abarca,

Entrainment and turbulent mixing at the interface of atmospheric clouds

The entrainment of clear unsaturated air via the interface of a cloud and the subsequent turbulent mixing are fundamental processes that determine the lifetime of a cloud43. Particularly relevant for a fast broadening of the droplet size distribution are inhomogeneous mixing events, typically caused by larger turbulent vortices. The project investigates the role of the chemical composition of the cloud condensation nuclei, droplet surface tension and Ostwald ripening, as present in poly-disperse droplet ensembles, on the broadening of droplet size distribution in an inhomogeneous turbulent mixing process. We want to understand which of these mechanisms is the most important one to grow droplets by condensation to radii of about 25 microns for which collisional growth takes over all the way to mature rain droplets. The results will help to improve cloud microphysics parametrizations in larger numerical models, e.g. in form of stochastic condensation schemes. This project mainly contributes to WP3 with interactions with ESR 6 for the lamellar description of mixing process (DSM) and with ESRs 4, 5, 11, and 12 for phase transition and drop/supersaturated vapour field interaction.

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Reactive mixing in porous media

Our objective is to understand by combined experimental and theoretical analysis how flow conditions can influence the mixing of reactive species in simple bimolecular A+B->C fronts44. The ESR will first study in Brussels how the properties of A+B->C fronts can be modulated in a radial flow in empty horizontal Hele-Shaw (HS) cells. In particular, experiments and modelling will analyze the influence of dispersion and possible buoyancy- or viscosity-driven mixing ef- fects45 within the gap of the cell on scalings for the location and width of the front as well as for the reaction rate. In a second step, the situation of quasi-2D porous media will be considered by filling the Hele-Shaw cell with obstacles in order to see how geometric constraints affect the mixing scaling laws obtained in an empty cell. The more complicated 3D porous medium case will finally be tackled by studying the properties for A+B->C fronts in 3D packing of beads with index matching tech- niques. The study interacts with ESRs 7, 8, 9 for mixing and reaction in complex geometries.

Supervisor: Anne De Wit,

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Chemical control of interfacial hydrodynamic instabilities

ESR12 will investigate numerically and theoretically the conditions in which a simple bimolecular A+B- >C reaction can actively tune mixing by changing the spatio-temporal properties of hydrodynamic convective instabilities45 triggered by changes in density, in viscosity or in permeability. She/he will compare control methods in reactive and non- reactive cases by performing a theoretical analysis of the stabilizing or destabilizing effects of the reaction on the spatial profile of the physical property (density, viscosity, permeability) at the origin of the hydrodynamic instability considered. The objective is to obtain the general common denominator in the form of this profile needed to target the flow mixing control strategy to be devised. On the basis of this general control strategy, numerical simulations of (i) CO2 convective dissolution triggered by density changes, (ii) viscous fingering induced by viscosity gradientsand (iii) precipitation patterns controlled by spatial variations of permeability will be devised to check the validity of the general approach. An overall unifying theory will ultimately be developed. Naturally interacts with ESR7, and with ESRs 4, 5, 10, 11.

Supervisor: Anne De Wit,

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Learning to navigate in complex odor landscapes

Odor-guided navigation is inherently difficult because turbulent air flow mixes the relevant chemical signal with clean air and with other background signals, resulting in a highly dynamic and complex odor landscape48. Besides the immediate interest in animal behavior, understanding the principles of olfactory search and navigation stands at the basis of applications ranging from the localization of the source of dangerous substances to ecological control of vector-borne diseases27. In the first stage, the problem of locating an odor source will be framed as a Reinforcement Learning problem49 and optimal solutions will be sought. This will also require answering the question about which is the most efficient repre- sentation of the olfactory landscape that the searcher must adopt for a given goal. Then we will turn to the problem of telling apart and reaching several distant sources which emit different odor blends, and we will also address the problem of cooper- ative olfactory search by many interacting agents.

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Bacterial growth and competition in scalar mixtures

In natural environments, bacteria play a major role in triggering chemical reactions, producing catalysts or degrading contaminants. The vast majority of bacteria live in complex fluid environments, such as porous media or turbulent flows51, where heterogeneous nutrients and redox landscapes are shaped by flows and transport processes. Bacterial growth laws generally describe bacterial development in well mixed and homogeneous environment. Yet, bacterial activity in soils is known to occur at well identified biogeochemical hot spots and mixing interfaces. It consequently depends on the joint probability of concentrations of nutrients that mix across interfaces. Recent theoretical breakthroughs have allowed the quantification of the joint probability of concentration in complex scalar fields31. Based on these new insights, the ESR will develop microfluidics measurements of bacterial growth in concentration gradients representative of porous media and turbulent flows to investigate the spatial patterns and temporal dynamics of bacteria populations in scalar mixtures. Results will be integrated into a mechanistic model linking mixing dynamics, chemical gradients and microbial growth and competi- tion. Expected results will contribute to CoPeRMix outputs 2 and 5 by establishing the consequences of stirring and mixing laws on biogeochemical processes in porous media. They will also contribute to CoPeRMix output 6 (ESRs 13, 15) by providing experimental observations of how bacteria sense information and develop growth strategies in complex chemical gradient environments where their growth rate depends on intermingled scalar fields.

Supervisor: Tanguy Le Borgne,

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Chemotactic strategies in heterogeneous concentration fields

Chemotactic bacteria51, which often develop in complex environments such as soils, move and develop according to the local concentration field of nutrient. To better understand chemotactic strategies within heterogeneous chem- ical landscapes, we propose an experiment allowing simultaneous visualization of nutrient concentration and bacterial trajec- tories. The goals are (1) to characterize bacterial search strategies under sporadic nutrient signals and (2) understand the contribution of motility to bacterial residence times in complex environments. To this end different fluorescent labels for bacteria and nutrient will allow tracking of individual bacteria and the concentration field. We will also develop a theoretical model which will greatly improve our ability to predict mixing in these complex systems by accounting both for the spatial bacterial distributions and the residence times. The comparison between chemotactic and non-chemotactic strains will high- light the impact of chemotaxis on residence time distribution of bacteria. Segmentation of the concentration field will be used to identify the chemotactic strategies above and below the bacterial nutrient detection limit.

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Supervisor: Joaquin Jimenez-Martinez,