SP-C1: Micro and macro drop impact dynamics with miscible liquids
The impact dynamics of droplets on wetted solid substrates has traditionally received considerable attention due to its relevance to inkjet printing, aerosol coating technologies, food processing, pesticide and paint spraying. The fluid dynamic analyses have typically focused on the maximum spreading diameter, and on the splashing behaviour, as these aspects determine the quality of printing in inkjets and the coverage efficiency of the impinging droplet.
Although the impact dynamics is very similar to that of single component drop-collisions, new phenomena have been observed. A common explanation is that miscibility-gaps and strong differences in surface tension may lead to a local unbalance of surface forces and hence to a premature rupture of the thin lamella.
However, holes und web-like structures in the lamella can be found also in unary systems, where no inhomogeneities in surface tension or viscous force can be present. Thus, observed collisional phenomena are strongly dominated by liquid motion and mixing in very thin liquid films.
These preliminary considerations show clearly the need of developing new models for predicting the outcome of drop impact with miscible liquids. Therefore, to gain a better understanding of collisional dynamics with miscible and immiscible fluids, it is necessary to adopt a unified approach that couples the micro-scale flow in such thin regions to the overall macroscopic flow features (e.g. crown shape). The coupling of fluid dynamic processes at different scales is exactly the focus of this sub-project through a combined experimental and theoretical approach.
The objectives of SP-C1 are threefold. First, in cooperation with SP-C5, we will further extend the micro-flow analysis by enabling time-resolved micro-PIV and defocused micro-PTV with different fluorescent dyes to distinguish between the evolution of the droplet and wall-film velocities. This will enable out of plane measurements of velocities and allow to obtain for the first time the velocity profile in the wall film both in the radial and vertical direction. Second, we plan to extend the metastability analysis of the lamella rupture to miscible fluids by introducing also the effects of unbalanced surface tension forces. Third, a systematic study of miscibility and wettability effects by varying systematically the interfacial tension 𝜎𝑑𝑓 and the spreading parameter 𝛽 = 𝜎𝑓 − (𝜎𝑑 + 𝜎𝑑𝑓) will be carried out. These unresolved issues require a joint experimental and theoretical study that combines macroscopic investigations of the crown dynamics and morphology with microscopic investigations of the wall film dynamics. The research activities in SP-C1 are organised in three main tasks:
- Parametric study of binary droplet impact on wetted walls by varying systematically the interfcial tension 𝜎𝑑𝑓 and the spreading parameter 𝛽. The primary objective is to understand how the development of the two embedded crowns correlates with the wall film dynamics.
- In cooperation with SP-C5, extension of the micro-PIV and micro-PTV techniques to enable time resolved defocused velocity measurements both in the wall film and in the upper liquid layer, originating from the impinging droplet.
- Extension of our theoretical model to include surface tension and interfacial tension effects. The main objective is to understand how surface tension non-homogeneities affect the metastability of the lamella
SP-C2: Oblique drop impact onto a wetted surface
Impacts of liquid drops on wetted surfaces are involved in a large range of engineering applications, e.g., in spray cooling, during spreading of plant protection agents and fuel injection in combustion engines. The impact of a single droplet can be regarded as an elementary process. There exists a large number of studies on normal impact of a drop on a liquid film in literature. However, only little research has been done so far for oblique drop impact on a liquid film, although its characterisation is fundamental for spray applications.
The outcome of the oblique drop impact is not only determined by the thermo-physical properties of the liquid, the impact speed, the size of the droplet and the film thickness, but also by the impact angle. The understanding of the fundamental fluid dynamics during oblique drop impact and the characterisation of the outcome is the focus of this sub-project.
Within SP-C2, we will carry out 3D Direct Numerical Simulations (DNS) of oblique droplet impacts on thin and thick liquid films in order to give a comprehensive picture of the oblique impact event and to characterise the splashing process and formation of secondary droplets. Different impact conditions, fluid properties and film thicknesses will be considered. The resulting regime maps will be compared with those of a normal impact, and the corresponding splashing threshold will be identified considering the film thickness.
We will use the in-house DNS program FS3D, which solves the Navier-Stokes equations for incompressible flows with arbitrary free surfaces. In addition to the numerical study, experiments on oblique drop impact are envisioned. The experiments will focus on impacts of drops with inclined trajectory on walls covered with liquid films of various thicknesses. The experimental results will be used to validate the numerical simulations since no known reference can be referred at present. The investigation of the formation and evolution of the crown, and consequently the secondary atomisation remains experimentally unexplained for inclined droplet impacts. The research activities in SP-C2 are organized as follows:
- Systematic study on oblique drop impact onto thin and thick wall films of different heights for the creation of regime maps and comparison with normal impact conditions. The numerical results will be validated by experiments.
- Characterisation of splashing and formation of secondary droplets after oblique drop impact based on numerical and experimental results.
- Reduction of film thickness towards very thin wall films with influence of surface structure (numerically).
SP-C3: High-order numerical methods for multi-component in-compressible flows in pools
The main goal of this sub-project is the development of a robust and accurate tool for the numerical simulation of interface problems. The nature of the physical processes considered within this sub-project is complex and involves different spatial and temporal scales. An efficient simulation tool, based on a flow model studied to correctly predict the interface evolution, and which is able to accurately solve the evolving flow structures without spoiling all the smaller scales resolution, is then mandatory.
The model involves a system of four equations, obtained from the conservation principles applied to each phase, and closed by an equation for the evolution of the volume fraction. The coupling between these classes of two-phase flow models with a high-order discretization technique such as the Discontinuous Galerkin (DG) method, known for its favourable dissipation properties, is then very appealing and will be the subject of this sub-project.
The purpose of this sub-project is the development of a new highly-accurate and efficient simulation tool for the thorough investigation of two-phase incompressible flow problems. The implementation of a diffuse interface approach in the existing code MIGALE will aim at exploiting, as much as possible, the unified and high-order, both in space and time, numerical framework currently used for compressible and incompressible flow simulations. The following workplan is foreseen during the sub-project:
- Extension to the multi-phase case of the local incompressible Riemann problem formulation and thorough validation on simple one-dimensional flow problems.
- High-order DG implementation within the DG code MIGALE of a five equation two-phase model inspired by the works on incompressible flows of Drew and on compressible flows of Saurel and Abgrall. Possible simplifications of the model that could lead to a set of governing equations for a sole "averaged phase" will be also considered.
- Development of a stabilization approach, able to provide a sharp sub-cell resolution, to control numerical oscillations when volume fraction discontinuities occur inside cells.
- Validation of the developed two-phase solver by addressing benchmark test cases and comparing the solutions with experimental and numerical results available in the literature.
- Assessment of the solver against the theoretical and experimental findings obtained within the IRTG project.
SP-C4: Visualization of droplet-liquid interaction
Droplet-liquid interaction processes are highly complex because the interface dynamics yield intricate interface formations and the mixing of the liquid phases leads to complex phase structures. Other scenarios describe the interplay between droplets and solid surfaces or within porous media. Therefore, advanced visual data analysis methods are required to help to understand these phenomena. To this end, we will develop visualization techniques and integrate data analysis methods into interactive visual analysis tools.
For the second funding period, we continue the work from the first period, but also add new directions. The visualization challenge is to capture the complexity and dynamics of drop impacts, incorporate data uncertainty, consider multi-scale and multi-physics representations, and understand the interplay of fluid and solids, e.g., for flow in porous media or droplet impact on surfaces. We will extend topology techniques so that they can be applied to multi-scale or highly dynamic scenarios, for example, by including scale-space and persistence computations, time- dependent topology for feature tracking or the concept of Jacobi sets to combine several types of fields.
In this context we will develop and integrate new topological analysis techniques to identify the relevant features of the data and to facilitate the combination of the different kinds of data sources. Our goal is to provide interactive and high-performance visual analysis methods for simulation and experimental data alike.
SP-C5: Development of novel optical techniques for microfluid dynamics (Postdoc-Project)
Drop-liquid interactions described in SP-C1 and SP-C2 feature macroscopic flow characteristics that are governed by fluid dynamics on the micro-scale. In particular, as shown in SP-C1 during the first funding period, the wall film dynamics governs both the decay in local flow rate and wall-film thickness. If both parameters decrease below a minimum critical value, a web-like structure is created within the lamella, leading to its premature rupture. The latter affects both the coverage efficiency of the impinging droplet in coating processes as well as the distribution and composition of secondary droplets. The objective of SP-C5 is to provide a reliable database on the temporal evolution of the wall-film thickness and crown propagation speed, required for the validation of theoretical models developed in SP-C1 and SP-C2. Commercially available micro-PIV systems are capable of providing a high spatial resolution for measurements in micro-channels, albeit limited to a single shot analysis for unsteady flow applications. This limitation is unacceptable for droplet impact problems due to the exponential decay of wall-film height and speed of crown propagation. Therefore, the focus of this sub-project is to extend the application of current microscale measurement techniques to droplet impact processes by enabling simultaneously a high temporal and spatial resolution. In addition, different fluorescent dyes will be employed for the liquid droplet and wall film, in order to distinguish the different velocity of propagation of the two embedded crowns in impact problems with immiscible fluids. Finally, in SP-C5 macro- and microscale techniques will be unified with the aim of creating a joined multi-scale tool for the experimental characterization of droplet impact problems onto solid substrates. In this context, the experimental methods developed in SP-C5 can be also applied to the characterization of wall-film dynamics on structured interfaces (SP-B1, SP-B2).
The main objective of this project is the extension of the micro-scale measurement approaches micro-PTV and LPSM, and their implementation as complementary techniques to the already established equipment of the respective sub-projects. A joined multi-scale tool is envisioned to ensure high temporal and spatial resolution, aimed at capturing instabilities and flow motions on small scales. The research activities in SP-C5 can be structured in four main tasks:
- Extension of micro-PTV by employing a defocused optical arrangement with a high-speed laser and fluorescent dye for particle tracking. This allows to strongly reduce the size of seeding particles and to increase the accuracy of the measurements. Special attention will be devoted to: (a) optical distortion correction, (b) choice of tracer particles (type and concentration) and its effect on the flow dynamics.
- Together with SP-B1, the LPSM shall be extended further to be used for binary mixtures with similar refractive indexes and textured wall structures.
- Infrared techniques for the observation of temperature distributions for drop impact onto smooth and structured walls will be investigated in cooperation with SP-B1.
- Development of analytical models for splashing dynamics, e.g. for splashing thresholds and flow field description in the film.