Postdoc - Gelation and elastocapillarity in spinning beads

Surface tension is the driving force of a plethora of small-scale phenomena. In liquids, it is responsible for the spherical shape of small drops and for the shape of menisci [1]. In soft solids, surface tension rounds off sharp features [2] and more generally governs mechanical responses at small scales [3]. Despite the growing interest in soft solids for applications ranging from microchip fabrication to soft robotics [4-5], the essential nature of their surface properties remains elusive. In this respect chemical gels have been considered as model soft solids to shed light on such an issue. Chemical gels are made of cross-linked polymer networks swollen in a liquid solvent or obtained by fully crosslinking a pure polymeric liquid (elastomers). In both cases, it is generally assumed that molecules can seamlessly rearrange at the surface, resulting in liquid-like surface properties, with an interfacial tension that is independent of the applied strain. However, despite in the last decades this assumption has been repeatedly tested with wetting experiments, spinning drop tests [6], macroscopic [7] and microscopic experiments [8], a consensus has not been established to date. To set the impact of interfacial stresses on the equilibrium shape of elastic materials it is imperative to compute the elastocapillary length l, defined as the ratio of the interfacial tension G to the shear modulus G₀ of the body under consideration. When l is comparable with or larger than other characteristic lengths of the system [9] interfacial stresses must be considered to compute stationary material shapes and to predict possibly the onset of instabilities [10]. This is the case for soft elastic samples with small geometric features. For example, for a hydrogel with shear modulus G₀ ≈ 30 Pa and interfacial tension G ≈ 30 mN m^-1, the elastocapillary length is l = 1 mm. Therefore, the equilibrium shapes of millimetric and submillimetric elastic particles must be necessarily affected by the interfacial contribution to their total energy. This is particularly true for gels close to the liquid-to-gel transition, where low elastic moduli characterize the beads.

The successful candidate will use a Spinning drop tensiometer (SDT) apparatus to investigate the equilibrium shapes of liquid and elastic beads with a radius of the order of one millimeter and shear modulus spanning the range 1-10³ Pa. He/She will employ the analysis of the bead shape proposed in [6] that has been developed specifically for homogeneous beads covering both the regimes of large and small deformations to extract both elastic modulus and surface energy of the beads and he/she will accumulate more statistics at the liquid-to-gel transition where we expect important elastocapillary effects.

The recruited postdoc will be further in charge of performing finite element (FE) simulations that will aim at elucidating the extent of strain heterogeneities in the beads and at their interfaces and shed light on the impact of elasticity and shear heterogeneities on interfacial stresses. The numerical work will be performed under the co-supervision of Prof. Serge Mora (LMGC-Montpellier), leader in numerical simulations and macroscopic experiments involving soft interfaces, while meetings with Dr. Nicolas Bain (ILM-Lyon), expert in elastocapillary effect in soft gels, will be organized monthly.

[1] P.-G. De Gennes, F. Brochard Wyart, D. Quéré Capillarity and Wetting PhenomenaDrops, Bubbles (2013).                

[2] N. Lapinski et al., Soft Matter 15, 3817 (2019)  

[3] R.W. Style, Annu. Rev. Condens. Matter Phys. 8, 99 (2017)

[4] D. Huh et al., Science 328, 1662 (2010).       

[5] S. Kim et al, Trends Biotechnol. 31,287 (2013).                                               

[6] Carbonaro et al. Soft Matter, 16, 8412 (2020)

[7] R. D. Schulman et al., Nat. Commun. 9, 982 (2018).                     

[8] Q. Xu et al., Nat. Commun. 8, 555 (2017).                                                                                      

[9] J. Bico et al. Annu. Rev. Fluid Mech, 50:629–59 (2018) 

[10] B. Andreotti et al., Phys Rev E, 84(6), 061601 (2011)