**21** Publications

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Proc Natl Acad Sci U S A 2021 May;118(19)

Nonlinear Physical Chemistry Unit, Université libre de Bruxelles, 1050 Bruxelles, Belgium;

Many bees possess a tongue resembling a brush composed of a central rod (glossa) covered by elongated papillae, which is dipped periodically into nectar to collect this primary source of energy. In vivo measurements show that the amount of nectar collected per lap remains essentially constant for sugar concentrations lower than 50% but drops significantly for a concentration around 70%. To understand this variation of the ingestion rate with the sugar content of nectar, we investigate the dynamics of fluid capture by as a model system. During the dipping process, the papillae, which initially adhere to the glossa, unfold when immersed in the nectar. Combining in vivo investigations, macroscopic experiments with flexible rods, and an elastoviscous theoretical model, we show that the capture mechanism is governed by the relaxation dynamics of the bent papillae, driven by their elastic recoil slowed down through viscous dissipation. At low sugar concentrations, the papillae completely open before the tongue retracts out of nectar and thus, fully contribute to the fluid capture. In contrast, at larger concentrations corresponding to the drop of the ingestion rate, the viscous dissipation strongly hinders the papillae opening, reducing considerably the amount of nectar captured. This study shows the crucial role of flexible papillae, whose aspect ratio determines the optimal nectar concentration, to understand quantitatively the capture of nectar by bees and how physics can shed some light on the degree of adaptation of a specific morphological trait.

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http://dx.doi.org/10.1073/pnas.2025513118 | DOI Listing |

http://www.ncbi.nlm.nih.gov/pmc/articles/PMC8126835 | PMC |

May 2021

Phys Chem Chem Phys 2021 Jan;23(2):1684-1693

Université libre de Bruxelles (ULB), Faculté des Sciences, Non Linear Physical Chemistry Unit, C. P. 231, 1050 Brussels, Belgium.

The oscillatory growth of chemical gardens is studied experimentally in the budding regime using a co-flow of two reactant solutions within a microfluidic reactor. The confined environment of the reactor tames the erratic budding growth and the oscillations leave their imprint with the formation of orderly spaced membranes on the precipitate surface. The average wavelength of the spacing between membranes, the growth velocity of the chemical garden and the oscillations period are measured as a function of the velocity of each reactant. By means of materials characterization techniques, the micro-morphology and the chemical composition of the precipitate are explored. A mathematical model is developed to explain the periodic rupture of droplets delimitated by a shell of precipitate and growing when one reactant is injected into the other. The predictions of this model are in good agreement with the experimental data.

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http://dx.doi.org/10.1039/d0cp05668e | DOI Listing |

January 2021

Phys Chem Chem Phys 2020 May 1;22(18):10278-10285. Epub 2020 May 1.

Department of Physical Chemistry and Materials Science, University of Szeged, Rerrich Béla tér 1., Szeged, H-6720, Hungary.

The spatio-temporal dynamics of an A + B → C front subjected to radial advection is investigated experimentally in a thin solution layer confined between two horizontal plates by radially injecting a solution of potassium thiocyanate (A) into a solution of iron(iii) nitrate (B). The total amount and spatial distribution of the product FeSCN (C) are measured for various flow rates Q and solution thicknesses h. The long-time evolution of the total amount of product, n, is compared to a scaling obtained theoretically from a one-dimensional reaction-diffusion-advection model with passive advection along the radial coordinate r. We show that, in the experiments, n is significantly affected when varying either Q or h but scales as n∼QV where V is the volume of injected reactant A provided the solution thickness h between the two confining plates is sufficiently small, in agreement with the theoretical prediction. Our experimental results also evidence that the temporal evolution of the width of the product zone, W, follows a power law, the exponent of which varies with both Q and h, in disagreement with the one-dimensional model that predicts W∼t. We show that this experimental observation can be rationalized by taking into account the non-uniform profile of the velocity field of the injected reactant within the cell gap.

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http://dx.doi.org/10.1039/c9cp06370f | DOI Listing |

May 2020

J Chem Phys 2020 Feb;152(5):054716

Université libre de Bruxelles (ULB), Nonlinear Physical Chemistry Unit, Faculté des Sciences, CP231, 1050 Brussels, Belgium.

In the presence of advection at a constant flow rate in a rectilinear geometry, the properties of planar A + B → C reaction fronts feature the same temporal scalings as in the pure reaction-diffusion case. In a radial injection geometry where A is injected into B radially at a constant flow rate Q, temporal scalings are conserved, but the related coefficients depend on the injection flow rate Q and on the ratio γ of initial concentrations of the reactants. We show here that this dependence of the front properties on the radial velocity allows us to tune the amount of product obtained in the course of time by varying the flow rate. We compare theoretically the efficiency of the rectilinear and radial geometries by computing the amount of product C generated in the course of time or per volume of reactant injected. We show that a curve γ(Q) can be defined in the parameter space (γ, Q) below which, for similar experimental conditions, the total amount of C is larger in the radial case. In addition, another curve γ(Q) < γ(Q) can be defined such that for γ < γ, the total amount of C produced is larger in the radial geometry, even if the production of C per unit area of the contact interface between the two reactants is larger in the rectilinear case. This comes from the fact that the length of the contact zone increases with the radius in the radial case, which allows us to produce in fine more product C for a same injected volume of reactant or in reactors of a same volume than in the rectilinear case. These results pave the way to the geometrical optimization of the properties of chemical fronts.

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http://dx.doi.org/10.1063/1.5135292 | DOI Listing |

February 2020

Phys Rev E 2019 Nov;100(5-1):052213

Université libre de Bruxelles (ULB), Nonlinear Physical Chemistry Unit, CP231, 1050 Brussels, Belgium.

The dynamics of A+B→C reaction fronts is studied both analytically and numerically in three-dimensional systems when A is injected radially into B at a constant flow rate. The front dynamics is characterized in terms of the temporal evolution of the reaction front position, r_{f}, of its width, w, of the maximum local production rate, R^{max}, and of the total amount of product generated by the reaction, n_{C}. We show that r_{f}, w, and R^{max} exhibit the same temporal scalings as observed in rectilinear and two-dimensional radial geometries both in the early-time limit controlled by diffusion, and in the longer time reaction-diffusion-advection regime. However, unlike the two-dimensional cases, the three-dimensional problem admits an asymptotic stationary solution for the reactant concentration profiles where n_{C} grows linearly in time. The timescales at which the transition between the regimes arise, as well as the properties of each regime, are determined in terms of the injection flow rate and reactant initial concentration ratio.

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http://dx.doi.org/10.1103/PhysRevE.100.052213 | DOI Listing |

November 2019

Soft Matter 2019 Jan 15;15(4):803-812. Epub 2019 Jan 15.

Instituto Andaluz de Ciencias de la Tierra, CSIC-Universidad de Granada, 18100 Armilla, Granada, Spain. and Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada, 18071 Granada, Spain.

Filiform corrosion produces long and narrow trails on various coated metals through the detachment of the coating layer from the substrate. In this work, we present a combined experimental and theoretical analysis of this process with the aim to describe quantitatively the shape of the cross-section, perpendicular to the direction of propagation, of the filaments produced. For this purpose, we introduce a delamination model of filiform corrosion dynamics and show its compatibility with experimental data where the coating thickness has been varied systematically.

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http://dx.doi.org/10.1039/c8sm01928b | DOI Listing |

January 2019

Phys Chem Chem Phys 2018 Jan;20(2):784-793

Université libre de Bruxelles (ULB), Nonlinear Physical Chemistry Unit, Faculté des Sciences, CP-231, 1050 Brussels, Belgium.

Two reaction systems that are at first sight very different produce similar macroscopic filamentary product trails. The systems are chemical gardens confined to a Hele-Shaw cell and corroding metal plates that undergo filiform corrosion. We show that the two systems are in fact very much alike. Our experiments and analysis show that filament dynamics obey similar scaling laws in both instances: filament motion is nearly ballistic and fully self-avoiding, which creates self-trapping events.

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http://dx.doi.org/10.1039/c7cp06003c | DOI Listing |

January 2018

Phys Rev Lett 2017 Mar 31;118(13):134101. Epub 2017 Mar 31.

Université libre de Bruxelles (ULB), Nonlinear Physical Chemistry Unit, CP231, 1050 Brussels, Belgium.

The dynamics of A+B→C fronts is analyzed theoretically in the presence of passive advection when A is injected radially into B at a constant inlet flow rate Q. We compute the long-time evolution of the front position, r_{f}, of its width, w, and of the local production rate R of the product C at r_{f}. We show that, while advection does not change the well-known scaling exponents of the evolution of corresponding reaction-diffusion fronts, their dynamics is however significantly influenced by the injection. In particular, the total amount of product varies as Q^{-1/2} for a given volume of injected reactant and the front position as Q^{1/2} for a given time, paving the way to a flow control of the amount and spatial distribution of the reaction front product. This control strategy compares well with calcium carbonate precipitation experiments for which the amount of solid product generated in flow conditions at fixed concentrations of reactants and the front position can be tuned by varying the flow rate.

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http://dx.doi.org/10.1103/PhysRevLett.118.134101 | DOI Listing |

March 2017

Phys Chem Chem Phys 2016 Sep;18(36):25592-25600

Université libre de Bruxelles (ULB), Nonlinear Physical Chemistry Unit, CP231, 1050 Brussels, Belgium.

Upon injection of an aqueous solution of carbonate into a solution of calcium ions in the confined geometry of a Hele-Shaw cell, various calcium carbonate precipitation patterns are observed. We discuss here the properties of these precipitation structures as a function of the injection flow rate and concentrations of the reactants. We show that such flow-controlled conditions can be used to influence the total amount and the spatial distribution of the solid phase produced as well as the reaction efficiency defined here as the amount of product formed for a given initial concentration of the injected solution.

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http://dx.doi.org/10.1039/c6cp05067k | DOI Listing |

September 2016

Phys Rev Lett 2016 Sep 1;117(10):104301. Epub 2016 Sep 1.

Laboratoire Interfaces Fluides Complexes, Université de Mons, 20 Place du Parc, B-7000 Mons, Belgium.

Twisted ribbons under tension exhibit a remarkably rich morphology, from smooth and wrinkled helicoids, to cylindrical or faceted patterns. This complexity emanates from the instability of the natural, helicoidal symmetry of the system, which generates both longitudinal and transverse stresses, thereby leading to buckling of the ribbon. Here, we focus on the tessellation patterns made of triangular facets. Our experimental observations are described within an "asymptotic isometry" approach that brings together geometry and elasticity. The geometry consists of parametrized families of surfaces, isometric to the undeformed ribbon in the singular limit of vanishing thickness and tensile load. The energy, whose minimization selects the favored structure among those families, is governed by the tensile work and bending cost of the pattern. This framework describes the coexistence lines in a morphological phase diagram, and determines the domain of existence of faceted structures.

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http://dx.doi.org/10.1103/PhysRevLett.117.104301 | DOI Listing |

September 2016

Phys Rev E Stat Nonlin Soft Matter Phys 2015 May 29;91(5):052408. Epub 2015 May 29.

Raymond & Beverly Sackler School of Chemistry, Tel Aviv University, Tel Aviv 6997801, Israel.

A laterally confined thin elastic sheet lying on a liquid substrate displays regular undulations, called wrinkles, characterized by a spatially extended energy distribution and a well-defined wavelength λ. As the confinement increases, the deformation energy is progressively localized into a single narrow fold. An exact solution for the deformation of an infinite sheet was previously found, indicating that wrinkles in an infinite sheet are unstable against localization for arbitrarily small confinement. We present an extension of the theory to sheets of finite length L, accounting for the experimentally observed wrinkle-to-fold transition. We derive an exact solution for the periodic deformation in the wrinkled state, and an approximate solution for the localized, folded state. We find that a second-order transition between these two states occurs at a critical confinement Δ(F)=λ(2)/L.

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http://dx.doi.org/10.1103/PhysRevE.91.052408 | DOI Listing |

May 2015

Phys Chem Chem Phys 2015 May;17(19):12804-11

Nonlinear Physical Chemistry Unit, Faculté des Sciences, Université libre de Bruxelles (ULB), CP231, 1050 Brussels, Belgium.

The growth of chemical gardens is studied experimentally in a horizontal confined geometry when a solution of metallic salt is injected into an alkaline solution at a fixed flow rate. Various precipitate patterns are observed-spirals, flowers, worms or filaments-depending on the reactant concentrations. In order to determine the relative importance of the chemical nature of the reactants and physical processes in the pattern selection, we compare the structures obtained by performing the same experiment using different pairs of reactants of varying concentrations with cations of calcium, cobalt, copper, and nickel, and anions of silicate and carbonate. We show that although the transition zones between different patterns are not sharply defined, the morphological phase diagrams are similar in the various cases. We deduce that the nature of the chemical reactants is not a key factor for the pattern selection in the confined chemical gardens studied here and that the observed morphologies are generic patterns for precipitates possessing a given level of cohesiveness when grown under certain flow conditions.

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http://dx.doi.org/10.1039/c5cp00068h | DOI Listing |

May 2015

Phys Rev E Stat Nonlin Soft Matter Phys 2014 Dec 29;90(6):062406. Epub 2014 Dec 29.

Nonlinear Physical Chemistry Unit, Faculté des Sciences, Université libre de Bruxelles (ULB), CP231, 1050 Brussels, Belgium.

We study the interaction between two cracks propagating quasistatically during the tearing of a thin brittle sheet. We show that the cracks attract each other following a path described by a power law resulting from the competition between elastic and fracture energies. The power law exponent (8/11) is in close agreement with experiments. We also show that a second (asymptotic) regime, with an exponent of 9/8, emerges for small distances between the two crack tips due to the finite transverse curvature of the elastic ridge joining them.

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http://dx.doi.org/10.1103/PhysRevE.90.062406 | DOI Listing |

December 2014

Proc Natl Acad Sci U S A 2014 Dec 10;111(49):17363-7. Epub 2014 Nov 10.

Nonlinear Physical Chemistry Unit, Faculté des Sciences, Université libre de Bruxelles (ULB), CP231, 1050 Brussels, Belgium; and

Chemical gardens are mineral aggregates that grow in three dimensions with plant-like forms and share properties with self-assembled structures like nanoscale tubes, brinicles, or chimneys at hydrothermal vents. The analysis of their shapes remains a challenge, as their growth is influenced by osmosis, buoyancy, and reaction-diffusion processes. Here we show that chemical gardens grown by injection of one reactant into the other in confined conditions feature a wealth of new patterns including spirals, flowers, and filaments. The confinement decreases the influence of buoyancy, reduces the spatial degrees of freedom, and allows analysis of the patterns by tools classically used to analyze 2D patterns. Injection moreover allows the study in controlled conditions of the effects of variable concentrations on the selected morphology. We illustrate these innovative aspects by characterizing quantitatively, with a simple geometrical model, a new class of self-similar logarithmic spirals observed in a large zone of the parameter space.

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http://dx.doi.org/10.1073/pnas.1409552111 | DOI Listing |

http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4267335 | PMC |

December 2014

Phys Rev Lett 2011 Oct 12;107(16):164303. Epub 2011 Oct 12.

Laboratoire Interfaces and Fluides Complexes, CIRMAP, Université de Mons, Mons, Belgium.

Flaps can be detached from a thin film glued on a solid substrate by tearing and peeling. For flat substrates, it has been shown that these flaps spontaneously narrow and collapse in pointy triangular shapes. Here we show that various shapes, triangular, elliptic, acuminate, or spatulate, can be observed for the tears by adjusting the curvature of the substrate. From combined experiments and theoretical models, we show that the flap morphology is governed by simple geometric rules.

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http://dx.doi.org/10.1103/PhysRevLett.107.164303 | DOI Listing |

October 2011

Phys Rev Lett 2011 Jun 2;106(22):224301. Epub 2011 Jun 2.

Laboratoire Interfaces et Fluides Complexes, CIRMAP, Université de Mons, Mons, Belgium.

We show that thin sheets under boundary confinement spontaneously generate a universal self-similar hierarchy of wrinkles. From simple geometry arguments and energy scalings, we develop a formalism based on wrinklons, the localized transition zone in the merging of two wrinkles, as building blocks of the global pattern. Contrary to the case of crumpled paper where elastic energy is focused, this transition is described as smooth in agreement with a recent numerical work [R. D. Schroll, E. Katifori, and B. Davidovitch, Phys. Rev. Lett. 106, 074301 (2011)]. This formalism is validated from hundreds of nanometers for graphene sheets to meters for ordinary curtains, which shows the universality of our description. We finally describe the effect of an external tension to the distribution of the wrinkles.

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http://dx.doi.org/10.1103/PhysRevLett.106.224301 | DOI Listing |

June 2011

Phys Rev E Stat Nonlin Soft Matter Phys 2009 Jun 26;79(6 Pt 2):066211. Epub 2009 Jun 26.

Centrum Wiskunde & Informatica ,GB Amsterdam, The Netherlands.

Recently a moving boundary approximation for the minimal model for negative streamer ionization fronts was extended with effects due to front curvature; this was done through a systematic solvability analysis. A central prediction of this analysis is the existence of a nonvanishing electric field in the streamer interior, whose value is proportional to the front curvature. In this paper we compare this result and other predictions of the solvability analysis with numerical simulations of the minimal model.

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http://dx.doi.org/10.1103/PhysRevE.79.066211 | DOI Listing |

June 2009

Phys Rev E Stat Nonlin Soft Matter Phys 2008 Nov 21;78(5 Pt 2):056212. Epub 2008 Nov 21.

Centrum Wiskunde & Informatica (CWI), P.O. Box 94079, 1090 GB Amsterdam, The Netherlands.

The minimal density model for negative streamer ionization fronts is investigated. An earlier moving boundary approximation for this model consisted of a "kinetic undercooling" type boundary condition in a Laplacian growth problem of Hele-Shaw type. Here we derive a curvature correction to the moving boundary approximation that resembles surface tension. The calculation is based on solvability analysis with unconventional features, namely, there are three relevant zero modes of the adjoint operator, one of them diverging; furthermore, the inner-outer matching ahead of the front must be performed on a line rather than on an extended region; and the whole calculation can be performed analytically. The analysis reveals a relation between the fields ahead and behind a slowly evolving curved front, the curvature and the generated conductivity. This relation forces us to give up the ideal conductivity approximation, and we suggest to replace it by a charge neutrality approximation. This implies that the electric potential in the streamer interior is no longer constant but solves a Laplace equation; this leads to a Muskat-type problem.

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http://dx.doi.org/10.1103/PhysRevE.78.056212 | DOI Listing |

November 2008

Phys Rev E Stat Nonlin Soft Matter Phys 2008 Jul 11;78(1 Pt 2):016206. Epub 2008 Jul 11.

CWI, P.O. Box 94079, 1090 GB Amsterdam, The Netherlands.

Bunches of streamers form the early stages of sparks and lightning but theory presently concentrates on single streamers or on coarse approximations of whole breakdown trees. Here a periodic array of interacting streamer discharges in a strong homogeneous electric field is studied in density or fluid approximation in two dimensions. If the period of the streamer array is small enough, the streamers do not branch, but approach uniform translation. When the streamers are close to the branching regime, the enhanced field at the tip of the streamer is close to 2Einfinity, where Einfinity is the homogeneous field applied between the electrodes. We discuss a moving boundary approximation to the density model. This moving boundary model turns out to be essentially the same as the one for two-fluid Hele-Shaw flows. In two dimensions, this model possesses a known analytical solution. The shape of the two-dimensional interacting streamers in uniform motion obtained from the PDE simulations is actually well fitted by the analytically known "selected Saffman-Taylor finger." This finding helps to understand streamer interactions and raises new questions on the general theory of finger selection in moving boundary problems.

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http://dx.doi.org/10.1103/PhysRevE.78.016206 | DOI Listing |

July 2008

Phys Rev E Stat Nonlin Soft Matter Phys 2008 Feb 28;77(2 Pt 2):026219. Epub 2008 Feb 28.

Centrum voor Wiskunde en Informatica (CWI), PO Box 94079, 1090 GB Amsterdam, Netherlands.

Starting from the minimal model for the electrically interacting densities of electrons and ions in negative streamer discharges, we derive a moving boundary approximation for the ionization fronts. Solutions of the moving boundary model have already been discussed, but the derivation of the model was postponed to the present paper. The key ingredient of the model is the boundary condition on the moving front. It is found to be of kinetic undercooling type, and the relation to other moving boundary models is discussed. Furthermore, the model is compared to two-dimensional simulations of the underlying density model. The results suggest that our moving boundary approximation adequately represents the essential dynamics of negative streamer fronts.

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http://dx.doi.org/10.1103/PhysRevE.77.026219 | DOI Listing |

February 2008

Phys Rev Lett 2005 Feb 18;94(6):062001. Epub 2005 Feb 18.

Groupe de Physique Nucléaire Théorique, Université de Mons-Hainaut, Académie Universitaire Wallonie-Bruxelles, Place du Parc 20, B-7000 Mons, Belgium.

The masses of pentaquarks uudds are calculated within the framework of a semirelativistic effective QCD Hamiltonian using a diquark picture. This approximation allows a correct treatment of the confinement, assumed here to be similar to a Y junction. With only color antitriplet diquarks, the mass of the pentaquark candidate Theta with positive parity is found around 2.2 GeV. It is shown that, if a color sextet diquark is present, the lowest uudds pentaquark is characterized by a much smaller mass with a negative parity. A mass below 1.7 GeV is computed if the masses of the color antitriplet and color sextet diquarks are taken similar.

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http://dx.doi.org/10.1103/PhysRevLett.94.062001 | DOI Listing |

February 2005