Figure 1

Schematic of a bridged microemulsion. The telechelic polymers can either link two oil droplets or loop on a single one. (Left) Before the crack nucleation (bold dashed line) polymers can bridge oil droplets on both side of the bold dashed line. (Right) When the crack occurs, the same polymers cannot cross the bold dashed line anymore and form bridges in the other directions.Reuse & Permissions

Figure 2

(Left) shear stress (${\sigma }_{yz}$) and normal stress ($N_1={\sigma }_{zz}-{\sigma }_{yy}$) versus shear rate for a bridged microemulsion with $r=9$. The continuous lines are fits (Maxwell model). (Right) Development of a fracture, occurring at the surface of the sample, for a shear rate equal to $0.8{\mathrm{s}}^{-1}$, corresponding to the critical normal stress $\sigma =1190\mathrm{Pa}$.Reuse & Permissions

Figure 3

(a) Elongation of a drop of a solution of bridged microemulsion ($r=9$) under gravity. The fracture occurs at the surface of the filament. The critical measured tensile stress is $\sigma =1720\mathrm{Pa}$. (b) Zoomed images of the same fracture which propagates across the sample. (c) Typical fracture profile corresponding to the picture b (middle one) (circles). The black line represents a power law $u(x)\propto \sqrt{x}$.Reuse & Permissions

Figure 4

(a) Bubble growth at a fixed pressure 2000 Pa inside the same solution as in Fig. 2. (b) A disklike fracture appears at the bubble surface. (c),(d),(e) Fracture propagation. The critical pressure is equal to 1800 Pa which gives a critical stress (after taking into account the Laplace pressure $\sim 160\mathrm{Pa}$) equals to 1640 Pa.Reuse & Permissions

Figure 5

Plot of the rupture stress coming from the pendant drop experiments (circles) and the expected values from Eq. (4) as a function of the connectivity $r$. $f$ has been fixed to its expected value: $f=0.5$. The only free parameter is $\alpha =0.9$ ($\alpha \sim 1$ as expected). The vertical dashed line corresponds to the percolation threshold ($r=3$). The inset gives the variation of the experimental rupture stress with the Young modulus, corresponding to the different connectivity. Note that the observed deviation of ${\sigma }_c$ from its linear dependence with $Y$ observed at small $r$, originates from the vicinity of the percolation threshold [5].Reuse & Permissions