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# Balestra Gioele

### Professeur HES ordinaire/Co-directeur centre de compétences

#### Hauptkompetenzen

### Professeur HES ordinaire/Co-directeur centre de compétences

Telefon-Nummer: +41 26 429 66 27

Büro: MIC_00_057

Boulevard de Pérolles 80, 1700 Fribourg, CH

Laufend

**Rolle: ** Hauptgesuchsteller/in

**Financement: **
HEIA-FR

**Description du projet : **

Développement d'une nouvelle méthode digitale de dépose de micro-objets.

**Forschungsteam innerhalb von HES-SO:**
Balestra Gioele
, Pirrami Lorenzo
, Maturo Jonas

**Durée du projet:**
14.01.2020

**Statut: ** Laufend

**Rolle: ** Hauptgesuchsteller/in

**Financement: **
HES-SO

**Description du projet : **

Développment d'une nouvelle tête d'impression jet d'encre pour l'impression de fluides complexes.

**Forschungsteam innerhalb von HES-SO:**
Balestra Gioele
, Domae Yoshinori
, Maturo Jonas
, Kämpfer Alexandra
, Laux Edith
, Manimala Ajith

**Durée du projet:**
01.12.2019

**Statut: ** Laufend

Abgeschlossen

**Rolle: ** Mitgesuchsteller/in

**Requérant(e)s: **COMATEC, Cugnoni Joël, COMATEC

**Financement: **
HES-SO Rectorat

**Description du projet : **
Grâce à leur rapport rigidité-masse imbattable, les matériaux composites (p.ex carbone / époxy) sont rapidement
devenus incontournables dans les domaines des transports (aéronautique, automobile, mobilité douce), les
applications biomédicales (fixateurs, prothèses, imagerie) et dans les sports (vélos, skis). La construction de
structures en matériaux composites s'apparente à un mode de fabrication additive qui implique la superposition de
différentes couches de matériaux (plis ou noyaux sandwich) remplissant chacune un rôle spécifique en termes de
fonctionnalités mécanique et thermique mais aussi potentiellement électrique, optique ou électromagnétique. Après
dépose, la résine est réticulée sous pression sur un moule pour obtenir la forme et la résistance finale de la pièce.
Cependant, les fonctionnalités mécaniques et électronique/communication sont généralement réalisées avec deux
sous-systèmes distincts : une structure porteuse et un ensemble de câblage, connecteurs et composants électroniques
(PCB) ce qui augmente le nombre de composants à assembler et le poids.
L'idée principale de ce projet s'inspire de la forte similitude entre la fabrication de PCB et des structures
composites, qui sont tous deux produits par assemblage de couches polymères renforcés de fibres. L'objectif de ce
projet est de combiner les derniers développements de la fabrication composite (composites thin-ply et hybrides par
dépose de plis robotisée) et des technologies de fabrication additive à base d'impression jet d'encres conductrices
pour développer une technologie de fabrication permettant l'intégration de fonctions électriques/électroniques
(capteur, microcontrôleurs, distribution de puissance) et de communication (antennes, bus) au sein même d'une
pièce composite structurelle.
Les défis à relever sont principalement le développement et la fiabilisation de méthodes de fabrication de circuits
sur supports composites 3D par impression directe et/ou par impression et lamination de PCB imprimés sur films
flexibles. L'objectif final est de prototyper une méthode de fabrication digitale et automatisée allant de la dépose de
plis à l'impression du circuit électrique. Des techniques d'interconnexion dans l'épaisseur du laminé compatible
avec la fabrication composite seront également développées, notamment en utilisant des résines époxy conductrices
et/ou des inserts métalliques. Finalement, des méthodes de conception et dimensionnement doivent être mises au
point pour s'assurer de l'intégrité du système. Les technologies nécessaires à la réalisation de ce concept sont
aujourd'hui disponibles, mais l'intégration de ces techniques et surtout leur validation en termes de performance et
fiabilité mécanique et électrique restent à valider en laboratoire et sur un démonstrateur (axe de machine / bras robot
intégré)
Cette technologie de fabrication de composite multifonctionnel a un fort potentiel grâce au gain de poids et donc
d'économie d'énergie (aéronautique, spatial, transports), mais aussi en terme d'augmentation de valeur ajoutée par
pièce (produit à haute valeur ajoutée et automatisable) et comme base pour l'intégration de l'internet des objets
(monitoring, qualité, feedback). Plusieurs projets sont actuellement en phase de lancement en Europe sur ce sujet.
Avec ce financement, notre équipe sera idéalement positionnée pour développer des projets de transfert
technologiques avec l'industrie aérospatiale et des transports, l'industrie des machines mais aussi le biomédical au
niveau Suisse et Européen.

**Forschungsteam innerhalb von HES-SO:**
Maturo Jonas
, Bircher Fritz
, Bürgy Olivier
, Huber Benjamin
, Renner Johannes
, Mauron Muriel
, Perritaz Bastien
, Compagnon Dimitri
, Schneuwly Vincent
, Bovay Justine
, Brügger Luca
, Schaad Nicolas
, Carrie Natalia
, Cugnoni Joël
, Nardin Raphaël
, Balestra Gioele
, Brodard Patricia
, Stefanucci Alfonso
, Lapaire Clovis
, Blum Remo
, Chandran Rajasundar
, Giuntoli Bruno

**Partenaires académiques: **COMATEC; FR - EIA - Institut IPRINT; Cugnoni Joël, COMATEC

**Durée du projet:**
01.09.2019 - 10.01.2022

**Montant global du projet: **144'925 CHF

**Statut: ** Abgeschlossen

2021

**Zusammenfassung:**

We study the role of hydrodynamic instabilities in the morphogenesis of some typical karst draperies structures encountered in limestone caves. The problem is tackled using the long wave approximation for the fluid film that flows under an inclined substrate, in the presence of substrate variations that grow according to a deposition law. We numerically study the linear and nonlinear evolution of a localized initial perturbation both in the fluid film and on the substrate, i.e. the Green function. A novel approach for the spatio-temporal analysis of two-dimensional signals resulting from linear simulations is introduced, based on the concepts of the Riesz transform and the monogenic signal, the multidimensional complex continuation of a real signal. This method allows for a deeper understanding of the pattern formation. The linear evolution of an initial localized perturbation in the presence of deposition is studied. The deposition linearly selects substrate structures aligned along the streamwise direction, as the spatio-temporal response is advected away. Furthermore, the growth of the initial defect produces a quasi-steady region also characterized by streamwise structures both on the substrate and the fluid film, which is in good agreement with the Green function for a steady defect on the substrate, in the absence of deposition.

2020

*Journal of Fluid Mechanics*,
2020, vol. 904

**Zusammenfassung:**

We study the pattern formation of a thin film flowing under an inclined planar substrate. The phenomenon is studied in the context of the Rayleigh–Taylor instability using the lubrication equation. Inspired by experimental observations, we numerically study the thin film response to a streamwise-invariant sinusoidal initial condition. The numerical response shows the emergence of predominant streamwise-aligned structures, modulated along the direction perpendicular to the flow, called rivulets. Oscillations of the thickness profile along the streamwise direction do not grow significantly when the inclination is very large or the liquid layer very thin. However, for small inclinations or thick films, streamwise perturbations grow on rivulets. A secondary stability analysis of one-dimensional and steady rivulets reveals a strong stabilization mechanism for large inclinations or very thin films. The theoretical results are compared with experimental measurements of the streamwise oscillations of the rivulet profile, showing a good agreement. The emergence of rivulets is investigated by studying the impulse response. Both the experimental observation and the numerical simulation show a marked anisotropy favouring streamwise-aligned structures. A weakly nonlinear model is proposed to rationalize the levelling of all but streamwise-aligned structures.

**Zusammenfassung:**

The flow of a thin film coating the underside of an inclined substrate is studied. We measure experimentally spatial growth rates and compare them to the linear stability analysis of a flat film modelled by the lubrication equation. When forced by a stationary localized perturbation, a front develops that we predict with the group velocity of the unstable wave packet. We compare our experimental measurements with numerical solutions of the nonlinear lubrication equation with complete curvature. Streamwise structures dominate and saturate after some distance. We recover their profile with a one-dimensional lubrication equation suitably modified to ensure an invariant profile along the streamwise direction and compare them with the solution of a purely two-dimensional pendent drop, showing overall a very good agreement. Finally, those different profiles agree also with a two-dimensional simulation of the Stokes equations.

2019

**Zusammenfassung:**

This paper is associated with a video winner of a 2018 American Physical Society's Division of Fluid Dynamics (DFD) Milton van Dyke Award for work presented at the DFD Gallery of Fluid Motion. The original video is available online at the Gallery of Fluid Motion, https://doi.org/10.1103/APS.DFD.2018.GFM.V0070.

**Zusammenfassung:**

We study here experimentally, numerically and using a lubrication approach, the shape, velocity and lubrication film thickness distribution of a droplet rising in a vertical Hele-Shaw cell. The droplet is surrounded by a stationary immiscible fluid and moves purely due to buoyancy. A low density difference between the two media helps to operate in a regime with capillary number

**Zusammenfassung:**

We investigate the stability of a thin Newtonian fluid spreading on a horizontal cylinder under the action of gravity. The capillary ridge forming at the advancing front is known to be unstable with respect to spanwise perturbations, resulting in the formation of fingers. In contrast to the classic case of a flow over an inclined plane, the gravity components along a cylindrical substrate vary in space and the draining flow is time-dependent, making a modal stability analysis inappropriate. A linear optimal transient growth analysis is instead performed to find the optimal spanwise wavenumber. We not only consider the optimal perturbations of the initial film thickness, as commonly done in the literature, but also the optimal topographical perturbations of the substrate, which are of significant practical relevance. We found that, in both cases, the optimal gains are obtained when the perturbation structures are the least affected by the time horizon. The optimal spanwise wavenumber is found to be dependent on the front location, due to the dependence of the characteristic length of the capillary ridge on its polar location.

2018

**Zusammenfassung:**

Inertial microfluidics is an active field of research that deals with crossflow positioning of the suspended entities in microflows. Until now, the majority of the studies have focused on the behavior of rigid particles in order to provide guidelines for microfluidic applications such as sorting and filtering. Deformable entities such as bubbles and droplets are considered in fewer studies despite their importance in multiphase microflows. In this paper, we show that the trajectory of bubbles flowing in rectangular and square microchannels can be controlled by tuning the balance of forces acting on them. A T-junction geometry is employed to introduce bubbles into a microchannel and analyze their lateral equilibrium position in a range of Reynolds (1 < Re < 40) and capillary numbers (0.1 < Ca < 1). We find that the Reynolds number (Re), the capillary number (Ca), the diameter of the bubble (), and the aspect ratio of the channel are the influential parameters in this phenomenon. For instance, at high Re, the flow pushes the bubble towards the wall while large Ca or moves the bubble towards the center. Moreover, in the shallow channels, having aspect ratios higher than one, the bubble moves towards the narrower sidewalls. One important outcome of this study is that the equilibrium position of bubbles in rectangular channels is different from that of solid particles. The experimental observations are in good agreement with the performed numerical simulations and provide insights into the dynamics of bubbles in laminar flows which can be utilized in the design of flow based multiphase flow reactors.

**Zusammenfassung:**

We investigate the Rayleigh-Taylor instability of a thin viscous film coating the inside of a spherical substrate. The aim of this work is to find and characterize the instability pattern in this spherical geometry. In contrast to the Rayleigh-Taylor instability under a planar substrate, where the interface is asymptotically unstable with respect to infinitesimal perturbations, the drainage induced by the component of gravity tangent to a curved substrate stabilizes the liquid interface, making the system linearly asymptotically stable. By performing a linear optimal transient growth analysis we show that the double curvature of a spherical substrate yields a critical Bond number, prescribing the ratio between gravitational and capillary forces, before an initial growth of perturbations is possible two-times larger than for a circular cylindrical substrate. This linear transient growth analysis however does not yield any selection principle for an optimal azimuthal wave number and we have to resort to a fully nonlinear analysis. By numerically solving the nonlinear lubrication equation we find that the most amplified azimuthal wave number increases with the Bond number. Nonlinear interactions are responsible for the transfer of energy to higher-order harmonics. The larger the Bond number and the farther away from the apex of the sphere, the richer the wave-number spectrum.

**Zusammenfassung:**

The aim of this study is to derive accurate models for quantities characterizing the dynamics of droplets of non-vanishing viscosity in capillaries. In particular, we propose models for the uniform-film thickness separating the droplet from the tube walls, for the droplet front and rear curvatures and pressure jumps, and for the droplet velocity in a range of capillary numbers, *Ca*, from 10−4 to 1 and inner-to-outer viscosity ratios,

2017

**Zusammenfassung:**

We investigate the Rayleigh–Taylor instability of a thin liquid film coated on the inside of a cylinder whose axis is orthogonal to gravity. We are interested in the effects of geometry on the instability, and contrast our results with the classical case of a thin film coated under a flat substrate. In our problem, gravity is the destabilizing force at the origin of the instability, but also yields the progressive drainage and stretching of the coating along the cylinder’s wall. We find that this flow stabilizes the film, which is asymptotically stable to infinitesimal perturbations. However, the short-time algebraic growth that these perturbations can achieve promotes the formation of different patterns, whose nature depends on the Bond number that prescribes the relative magnitude of gravity and capillary forces. Our experiments indicate that a transverse instability arises and persists over time for moderate Bond numbers. The liquid accumulates in equally spaced rivulets whose dominant wavelength corresponds to the most amplified mode of the classical Rayleigh–Taylor instability. The formation of rivulets allows for a faster drainage of the liquid from top to bottom when compared to a uniform drainage. For higher Bond numbers, a two-dimensional stretched lattice of droplets is found to form on the top part of the cylinder. Rivulets and the lattice of droplets are inherently three-dimensional phenomena and therefore require a careful three-dimensional analysis. We found that the transition between the two types of pattern may be rationalized by a linear optimal transient growth analysis and nonlinear numerical simulations.

2016

**Zusammenfassung:**

Various manufacturing techniques exist to produce double-curvature shells, including injection, rotational and blow molding, as well as dip coating. However, these industrial processes are typically geared for mass production and are not directly applicable to laboratory research settings, where adaptable, inexpensive and predictable prototyping tools are desirable. Here, we study the rapid fabrication of hemispherical elastic shells by coating a curved surface with a polymer solution that yields a nearly uniform shell, upon polymerization of the resulting thin film. We experimentally characterize how the curing of the polymer affects its drainage dynamics and eventually selects the shell thickness. The coating process is then rationalized through a theoretical analysis that predicts the final thickness, in quantitative agreement with experiments and numerical simulations of the lubrication flow field. This robust fabrication framework should be invaluable for future studies on the mechanics of thin elastic shells and their intrinsic geometric nonlinearities.

**Zusammenfassung:**

We investigate the stability of thin viscous films coated on the inside of a horizontal cylindrical substrate. In such a case, gravity acts both as a stabilizing force through the progressive drainage of the film and as a destabilizing force prone to form droplets via the Rayleigh-Taylor instability. The drainage solution, derived from lubrication equations, is found asymptotically stable with respect to infinitesimally small perturbations, although in reality, droplets often form. To resolve this paradox, we perform an optimal transient growth analysis for the first-order perturbations of the liquid's interface, generalizing the results of Trinh *et al.* [Phys. Fluids **26**, 051704 (2014)]. We find that the system displays a linear transient growth potential that gives rise to two different scenarios depending on the value of the Bond number (prescribing the relative importance of gravity and surface tension forces). At low Bond numbers, the optimal perturbation of the interface does not generate droplets. In contrast, for higher Bond numbers, perturbations on the upper hemicircle yield gains large enough to potentially form droplets. The gain increases exponentially with the Bond number. In particular, depending on the amplitude of the initial perturbation, we find a critical Bond number above which the short-time linear growth is sufficient to trigger the nonlinear effects required to form dripping droplets. We conclude that the transition to droplets detaching from the substrate is noise and perturbation dependent.

2015

**Zusammenfassung:**

This study investigates the inviscid, linear spatio-temporal stability of heated, compressible, and incompressible coaxial jet flows. The influence of the temperature ratio and the velocity ratio between the core jet and the bypass stream on the transition from convectively to absolutely unstable flows is studied numerically. The investigation shows that for coaxial jets, absolute instability can occur for considerably lower core-stream temperatures than for single jets. The reason for this modified stability character is the appearance of an additional unstable mode as a result of the outer velocity shear layer between the bypass stream and the ambient flow. The presence of two shear layers enables the interaction between otherwise free waves to give rise to new instabilities. When the bypass-stream velocity is increased, the classical absolute mode known from single jets (inner mode) is first stabilized and then destabilized for high bypass-stream velocities, whereas the outer mode reaches maximum spatio-temporal growth rates when the core-stream velocity is approximately equal to twice the bypass-stream velocity. Additionally, it is demonstrated that the spatio-temporal character of the modes is very sensitive to the shear-layer thickness and to the distance separating the two layers. Increasing the Mach number strongly dampens the onset of an absolute instability for both modes.

**Zusammenfassung:**

We revisit the canonical Rayleigh-Taylor instability and investigate the case of a thin film of fluid upon the underside of an inclined plane. The presence of a natural flow along the plane competes with the conventional droplet forming instability. In particular, experiments reveal that no drops form for inclinations greater than a critical value. These features are rationalized in the context of the absolute/convective analysis conducted in this article.

2021

*Proceedings of European Coating Symposium (ECS) 2021, 7-9 September 2021, Brussels, Belgium*

**Zusammenfassung:**

We discuss the pattern formation of a thin film flowing under an inclined plane, with theoretical, experimental and numerical analyses, in the context of the Rayleigh-Taylor instability and in the absence of inertia.

2020

*APS Division of Fluid Dynamics*, 22.11.2020 - 24.11.2020, Virtual

2019

*APS Division of Fluid Dynamics*, 23.11.2019 - 26.11.2019, Seattle

**Zusammenfassung:**

We discuss the pattern formation of a thin film flowing under an inclined planar substrate, combining theoretical, experimental and numerical results. The phenomenon is related to the Rayleigh-Taylor instability, in which one heavier fluid is placed above a lighter one. When an upper wall and the substrate inclination are considered, a variety of patterns are observed. The natural and forced dynamics of the flat film to spanwise perturbations and the resulting non-linear structures are studied; in both cases, spanwise-periodic, streamwise-aligned structures, called rivulets, arise. The impulse response of a flat film is numerically and experimentally studied. We analyze the linear response, which does not show any preferential direction; a weakly non-linear model highlights however the selection of the streamwise structures. The fully non-linear evolution leads to a steady pattern characterized by fully saturated rivulets, the profile of which is analyzed in detail. A secondary stability analysis reveals the presence of a range of parameters in which only rivulets are observed, in agreement with the experimental observations. Outside of this range, lenses appear on the rivulets, which may eventually drip.

2018

*European Fluid Mechanics Conference*, 09.09.2018 - 13.01.2019, Vienna

2017

*APS Division of Fluid Dynamics*, 19.11.2017 - 21.01.2020, Denver

**Zusammenfassung:**

A liquid film coated on the underside of a planar substrate is subject to the Rayleigh-Taylor instability so that its interface deforms into waves that lead to the formation of dripping droplets. When the substrate is curved, gravity not only acts as the destabilizing force at the origin of the instability but also as a stabilizing force originating in the progressive drainage of the film. As a consequence, a two-dimensional thin-film in a circular geometry is asymptotically stable to infinitesimal perturbations. Nevertheless, we have found that the system acts as a strong transient amplifier. A transverse instability appears for moderator Bond numbers (gravity over surface tension forces ratio). The liquid accumulates in equally spaced rivulets whose dominant wavelength corresponds to the most unstable mode of the classical Rayleigh-Taylor instability. On the other hand, when the Bond number is high, a two-dimensional lattice of droplets prevails. We investigate the characteristics of the rivulet flow, as well as the transition between the two instability types both theoretically and experimentally. A linear stability analysis based on lubrication equations is performed and the results are found to be in good agreement with experiments and numerical simulations.

*European Coating Symposium*, 08.11.2017 - 10.11.2017, Fribourg

2016

*European Fluid Mechanics Conference*, 13.09.2016 - 16.09.2016, Sevilla

2015

*APS Division of Fluid Dynamics*, 22.11.2015 - 24.11.2015, Boston

**Zusammenfassung:**

We investigate theoretically the stability of a thin viscous film on the underside of a curved cylindrical surface. Gravity acts both as a stabilizing force originating in the progressive drainage of the film and as a destabilizing force prone to form dripping droplets. The drainage solution, derived from lubrication equations, is found asymptotically stable with respect to infinitesimal perturbations. This result first reported by Trinh et al. when studying the region near the top of a coated cylinder is here generalized to the entire structure. The governing parameters, namely the Bond number, which prescribes the relative importance of gravity and surface tension forces, and the initial film thickness to cylinder radius ratio are found not to play a role in the long time stability of the film. However, the system displays a linear transient growth potential which increases exponentially with the Bond number. Depending on its value, there is a critical initial disturbance amplitude above which non-linear effects yield the formation of droplets, suggesting that the transition to dripping is noise and roughness dependent.

*APS Division of Fluid Dynamics*, 22.11.2015 - 24.08.2017, Boston

**Zusammenfassung:**

Inspired by the traditional chocolate egg recipe, we show that pouring a polymeric solution onto spherical molds yields a simple and robust path of fabrication of thin elastic curved shells. The drainage dynamics naturally leads to uniform coatings frozen in time as the polymer cures, which are subsequently peeled off their mold. We show how the polymer curing affects the drainage dynamics and eventually selects the shell thickness and sets its uniformity. To this end, we perform coating experiments using silicon based elastomers, Vinylpolysiloxane (VPS) and Polydimethylsiloxane (PDMS). These results are rationalized combining numerical simulations of the lubrication flow field to a theoretical model of the dynamics yielding an analytical prediction of the formed shell characteristics. In particular, the robustness of the coating technique and its flexibility, two critical features for providing a generic framework for future studies, are shown to be an inherent consequence of the flow field (memory loss). The shell structure is both independent of initial conditions and tailorable by changing a single experimental parameter.

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