Topic description:
Amongst the large variety of innovating coatings addressing industrial needs, 
Super-Hydrophobic Surfaces (SHS) have received a particular attention for the 
last twenty years [7,9]. Controlling the physicochemical properties of these 
bio-inspired surfaces allows for allows for encapsulating a gas layer inside the 
roughness elements, within the coating. This plastron thereby acts as a 
lubricating layer reducing the contact between the liquid and the solid. This 
particular characteristic, also called the “Lotus effect”, may turn out to be 
particularly interesting when wetting matters. A growing number amount of 
studies showed that SHS can allow for reducing friction drag at the laboratory 
scale within a well-controlled environment. However, extrapolating these 
performances towards extreme conditions, for instance met in strongly turbulent 
flows, representative of industrial applications (i.e. water-repellent clothing, 
ships’ hull, anti-fogging and anti-icing coatings in the aeronautical 
industry...), is a key challenge. In particular, understanding how SHS should be 
engineered in order to improve the aerodynamics and aeroacoustics properties is 
still an open question [2,3,5,6].
This PhD program aims at establishing an optimisation procedure for the optimal 
design of super hydrophobic surfaces with the aim of improving the hydrodynamic 
properties of a turbulent separated flow over a canonical configuration [10-14]. 
The objective of this approach is to improve the hydrodynamic performances of 
super-hydrophobic coatings over a simple wall profile and reduce pressure 
fluctuations induced by the separated flow [15]. In this particular framework, 
direct numerical simulations will be performed alongside laboratory experiments 
for validation. In particular, the design of super hydrophobic surfaces will be 
obtained by an adjoint optimisation approach which will be computed using the 
results obtained from the DNS. 

This PhD program will be undertaken at PRISME laboratory at the University of 
Orleans. The research work will focus on the analysis of large-scale numerical 
simulations using high-performance mixed numerical methods. The first part of 
the PhD will consist in a literature review of the main physical mechanism 
involved, an introduction to parallel computing, and the simulation and analysis 
of the separated turbulent flow for increasing Reynolds numbers. The second part 
of the PhD will consider the implementation of the adjoint-based Lagrangian 
optimisation for the design of optimal slippery surfaces. Depending on the work 
achieved by the candidate during the first two years, the third part of the PhD 
will include the fabrication of the newly designed surfaces and an experimental 
validation of the effect of slippery surfaces in water flume.

Work Environment:
The person recruited for this PhD program will become part of the Aerodynamics 
group (ESA) of PRISME laboratory at the University of Orleans. In this group, 
research activities are carried on the understanding, the physical modelling and 
control of turbulent shear flows, representative of industrial applications. In 
particular, this work will build on the knowledge developed within the 
department for the last ten years on SHS [1,3,5] and the control of separated 
flows [10,16]. For this PhD, numerical simulations will be carried out on the 
regional super-computing facilities (Cascimodot). A european citizenship is 
mandatory.

This thesis fits in a collaborative project, ANR LOTUS (ANR-23-ASTR-0017-01), 
coordinated by PRISME laboratory and where ENSTA-Paris is a partner. The person 
recruited for this project will benefit from a strong and stimulating scientific 
environment and will be part of a dynamic consortium, recognized for its 
international expertise on the topic. Interactions and innovating work with the 
other members of the consortium are also encouraged. 

Skills:
We are looking for a strongly motivated individual (F/M), with a Master thesis 
or an engineering degree with strong knowledge in fluid mechanics, numerical 
methods, and an interest for experimental work. The selected candidate will 
demonstrate a particular interest for numerical simulations and applied 
mathematics. A good expertise in MATLAB & Fortran is also recommended. The 
selected candidate will be strongly involved in the diffusion of the results. 
The candidate will thereby demonstrate a capacity for writing and communicating 
in both French and English.

Application:
Documents to send for the application:
•	Curriculum Vitae
•	Cover lettre
•	Grades for the last two years of Master
•	Contacts for two scientific advisors

The application is to be sent to Dr. Pierre-Yves Passaggia (pierre-
yves.passaggia@univ-orleans.fr), Prof. Nicolas Mazellier 
(nicolas.mazellier@univ-orleans.fr) and Prof. Azeddine Kourta 
(azeddine.kourta@univ-orleans.fr). Applications with missing documents will not 
be considered. Applications should be sent before October 14th 2024.

Bibliography:
[1]	Bettaieb, N., Castagana, M., Passaggia, P. Y., Kourta, A., & Mazellier, 
N. (2022). Prediction of resistance induced by surface complexity in lubricating 
layers: Application to super-hydrophobic surfaces.
[2]	Picella, F., Robinet, J. C., & Cherubini, S. (2020). On the influence of 
the modelling of superhydrophobic surfaces on laminar–turbulent transition. 
Journal of Fluid Mechanics, 901, A15.
[3]	Castagna, M., Mazellier, N. & Kourta, A. (2021) On the onset of 
instability in the wake of super-hydrophobic spheres, International Journal of 
Heat and Fluid Flow, 87:108709.
[4]	Picella, F., Robinet, J. C., & Cherubini, S. (2019). Laminar–turbulent 
transition in channel flow with superhydrophobic surfaces modelled as a partial 
slip wall. Journal of Fluid Mechanics, 881, 462-497.
[5]	Castagna, M., Mazellier, N. & Kourta, A. (2018) Wake of super-
hydrophobic falling spheres: influence of the air layer deformation, Journal of 
Fluid Mechanics, 850:646-673.
[6]	Seo, J., García-Mayoral, R. & Mani, A. 2015 Pressure fluctuations and 
interfacial robustness in turbulent flows over superhydrophobic surfaces. J. 
Fluid Mech. 783, 448–473.
[7]	Rothstein, J. P. 2010 Slip on superhydrophobic surfaces. Ann. Rev. Fluid 
Mech. 42, 89–109.
[8]	Legendre, D., Lauga, E. & Magnaudet, J. 2009 Influence of slip on the 
dynamics of two-dimensional wakes. J. Fluid Mech. 633, 437–447.
[9]	Min, T. & Kim, J. 2004 Effects of hydrophobic surface on skin-friction 
drag. Phys. Fluids 16, 55–58.
[10]	Passaggia, P.-Y. & Ehrenstein, U. Optimal control of a separated 
boundary-layer flow over a bump. Journal of Fluid Mechanics, 840:238–265, 2018
[11]	Passaggia, P.-Y. and Leweke, T. and Ehrenstein, U. Transverse 
instability and low-frequency flapping in incompressible separated boundary 
layer flows: an experimental study. Journal of fluid mechanics,703:363–373, 
2012.
[12]	Passaggia, P.-Y. and Ehrenstein, U. Adjoint based optimization and 
control of a separated boundary-layer flow. European Journal of Mechanics-
B/Fluids, 41:169–177, 2013.
[13]	Marquillie, U. Laval, J.-P. and Dolganov, R. Direct numerical simulation 
of a separated channel flow with a smooth profile. Journal of Turbulence, 
(9):N1, 2008
[14]	Marquillie, U. Ehrenstein, U. and Laval, J.-P. Instability of streaks in 
wall turbulence with adverse pressure gradient. Journal of Fluid Mechanics, 
681:205–240, 2011.
[15]	Gobert, M.-L. and Ehrenstein, U. and Astolfi, J.-A and Bot, P. Nonlinear 
disturbance evolution in a two-dimensional boundary-layer along an elastic plate 
and induced radiated sound. European Journal of Mechanics-B/Fluids, 29(2):105–
118, 2010.
[16]	Nastro, G., Robinet, J. C., Loiseau, J. C., Passaggia, P. Y., & 
Mazellier, N. (2023). Global stability, sensitivity and passive control of low-
Reynolds-number flows around NACA 4412 swept wings. Journal of Fluid Mechanics, 
957, A5.