Irreversible shear-induced vitrification of droplets into elastic nanoemulsions by extreme rupturing

Many materials weaken through fracturing when subjected to extreme stresses. By contrast, we show that breaking down repulsive bits of matter dispersed in a viscous liquid can cause a dramatic and irreversible increase in the dispersion’s elasticity. Anionically stabilized microscale emulsions subjected to a history of high-pressure microfluidic flow can develop an unusually large elastic modulus as droplets are ruptured to the nanoscale, yielding “nanonaise.” As the droplet size approaches the Debye screening length, the nanoemulsion vitrifies. Consequently, the onset of elasticity for disordered uniform nanoemulsions can occur at droplet volume fractions far below maximal random jamming of spheres.

Figure 1

(Color online) Frequency dependence of the storage, $G^{\prime }\left(\omega \right)$ (solid symbols), and loss $G^{″}\left(\omega \right)$ (open symbols) moduli, of an oil-in-water emulsion with $\varphi =0.40$ and $C_{\mathrm{SDS}}=116\mathrm{mM}$ subjected to $N=2$ (triangles), 3 (squares), and 6 (circles) passes of extreme microfluidic shear at an air pressure $p=3.4\mathrm{atm}$. As $N$ increases, the nanoemulsion becomes a highly elastic glass with $G^{\prime }>G^{″}$ down to low $\omega$.

Figure 2

(Color online) Shear-induced vitrification of an emulsion (see Fig. 1) is associated with droplet breakdown as the number of passes N increases. (a) The average droplet radius $⟨a⟩$ decreases and then saturates. Bars denote the standard deviation $\delta a$, not the error in the mean. An exponential decay with a constant saturation fits the data (line). (b) The storage modulus $G^{\prime }$ at frequency $\omega =10\mathrm{rad}∕\mathrm{s}$ increases many decades and saturates; this is fit by an exponential increase to a saturation (line). (c) The lower crossover frequency ${\omega }_{\mathrm{lc}}$ becomes very small for $N\ge 4$, signaling vitrification.

Figure 3

(Color online) Plateau storage modulus $G_{\mathrm{p}}^{\prime }$ as a function of droplet volume fraction $\varphi$ for monodisperse nanoemulsions at $C_{\mathrm{SDS}}=10\mathrm{mM}$ for average radii $⟨a⟩:28\mathrm{nm}$ (triangles), $47\mathrm{nm}$ (circles), and $73\mathrm{nm}$ (squares). The elastic onset for nanoemulsions occurs for $\varphi$ well below ${\varphi }_{\mathrm{MRJ}}\approx 0.64$. $G_{\mathrm{p}}^{\prime }$ for a microscale emulsion with $⟨a⟩=0.74\mathrm{\mu }\mathrm{m}$ and the same $C_{\mathrm{SDS}}$ is also shown (open circles) [8].

Figure 4

(Color online) Scaled interaction potential as a function of separation between the droplet surfaces, $U\left(h\right)∕a^4$, determined from all nanoemulsion data shown in Fig. 3 (same symbols). The line is a fit to a Debye-screened surface repulsion, yielding a Debye-screening length of ${\lambda }_{\mathrm{D}}=3.8\pm 0.5\mathrm{nm}$. Inset: To determine $h$, $G_{\mathrm{p}}^{\prime }$ from Fig. 3 are scaled with $\sigma ∕a$ and shifted in $\varphi$ onto a master curve: $G_{\mathrm{p}}^{\prime }\left({\varphi }_{\mathrm{eff}}\right)∕(\sigma ∕a)$.