Figure 1

Repulsive emulsions become fluid-like below random close packing. Linear storage and loss moduli, $G^{\prime }\left(\omega \right)$ and $G^{\prime \prime }\left(\omega \right)$, of repulsive emulsions with $U=0$, $a=128$ nm, and ${\phi }_{\text{eff}}\approx$ 0.70, 0.65, and 0.60 (progressively lighter colors).Reuse & Permissions

Figure 2

Attractive emulsions are elastic both above and below random close packing. Linear storage and loss moduli, (a) $G^{\prime }\left(\omega \right)$ and (b) $G^{\prime \prime }\left(\omega \right)$, of attractive emulsions with $U\approx 9k_{B}T$, $a=100$ nm, and ${\phi }_{\text{eff}}\approx$ 0.73, 0.70, 0.66, and 0.62 (progressively lighter colors). For clarity, $G^{\prime }$ and $G^{\prime \prime }$ data are multiplied by a factor of 0.5, 0.2, or 0.07 for ${\phi }_{\text{eff}}=0.70,0.66,$ or 0.62, respectively.Reuse & Permissions

Figure 3

Elasticities of attractive and repulsive emulsions differ below random close packing but are similar above it. Linear storage and loss moduli, $G_p^{\prime }$ (solid points) and $G^{\prime \prime }$ (open points), measured at $\omega =1$ rad/s, normalized by the Laplace pressure $\sigma /a$, for both attractive and repulsive emulsions of varying ${\phi }_{\text{eff}}$. Attractive emulsions have $a=128$ nm, $U\approx 9k_{B}T$ (circles), $a=106$ nm, $U\approx 7k_{B}T$ (upward-pointing triangles), and $a=100$ nm, $U\approx 9k_{B}T$ (squares); repulsive emulsions have $a=128$ nm (diamonds) and $a=106$ nm (downward-pointing triangles). The interfacial tension $\sigma =6-9$ mN/m for the range of surfactant concentrations used. Previous measurements of $G_p^{\prime }$ (solid line) and $G^{\prime \prime }$ (dashed line) for monodisperse repulsive emulsions [1], horizontally shifted to account for polydispersity, agree with our data. We find ${\phi }_{\text{RCP}}\approx 0.68-0.72$, characteristic of ${\phi }_{\text{RCP}}$ for spheres of comparable polydispersity [19].Reuse & Permissions

Figure 4

Repulsive emulsions above random close packing exhibit one peak in $G^{\prime \prime }\left(\gamma \right)$ at ${\gamma }_r^{*}$ while those below random close packing do not exhibit a peak in $G^{\prime \prime }\left(\gamma \right)$. Viscoelastic moduli $G^{\prime }\left(\gamma \right)$ and $G^{\prime \prime }\left(\gamma \right)$ measured at $\omega =1$ rad/s of repulsive emulsions with $U=0$, $a=128$ nm, and ${\phi }_{\text{eff}}\approx$ 0.70, 0.65, and 0.60 (progressively lighter colors).Reuse & Permissions

Figure 5

Attractive emulsions above random close packing exhibit two peaks in $G^{\prime \prime }\left(\gamma \right)$ at ${\gamma }_1^{*}$ and ${\gamma }_2^{*}$ while those below random close packing exhibit one peak at ${\gamma }_1^{*}$. Viscoelastic moduli $G^{\prime }\left(\gamma \right)$ and $G^{\prime \prime }\left(\gamma \right)$ measured at $\omega =1$ rad/s of attractive emulsions with $U\approx 9k_{B}T$ and $a=100$ nm (a)-(b) above ${\phi }_{\text{RCP}}$ (${\phi }_{\text{eff}}\approx 0.73$ and 0.70, progressively lighter colors) and (c)-(d) below ${\phi }_{\text{RCP}}$ (${\phi }_{\text{eff}}\approx 0.66$ and 0.62, progressively lighter colors). For clarity, $G^{\prime }$ and $G^{\prime \prime }$ data are multiplied by a factor of 0.7, 0.3, 0.8, or 0.2 for each ${\phi }_{\text{eff}}$ going from top to bottom. Straight lines indicate $G^{\prime },G^{\prime \prime }\sim {\gamma }^{-{\nu }^{\prime },-{\nu }^{\prime \prime }}$ for large $\gamma$.Reuse & Permissions

Figure 6

Position of peaks in $G^{\prime \prime }\left(\gamma \right)$ for varying ${\phi }_{\text{eff}}$. Lower symbols represent ${\gamma }_1^{*}$, upper symbols represent either ${\gamma }_2^{*}$ or ${\gamma }_r^{*}$. Attractive emulsions have $a=128$ nm, $U\approx 9k_{B}T$ (circles), $a=106$ nm, $U\approx 7k_{B}T$ (upward-pointing triangles), and $a=100$ nm, $U\approx 9k_{B}T$ (squares); repulsive emulsions have $a=128$ nm (diamonds) and $a=106$ nm (downward-pointing triangles).Reuse & Permissions

Figure 7

Volume fraction-dependent behavior is similar for oil-in-water emulsions stabilized by SDS. (a) Linear plateau storage modulus, $G_p^{\prime }$ [18], normalized by the Laplace pressure $\sigma /a$ and (b) position of peaks in $G^{\prime \prime }\left(\gamma \right)$, for varying ${\phi }_{\text{eff}}$. Emulsions have $a=250$ nm; attractive emulsions have $U\approx 21k_{B}T$ (circles) while repulsive emulsions have $U<1k_{B}T$ (diamonds). The interfacial tension $\sigma =9.8$ mN/m for the range of surfactant concentrations used. Upper symbols in (b) represent ${\gamma }_2^{*}$ while lower symbols represent ${\gamma }_1^{*}$.Reuse & Permissions

Figure 8

Strain-dependent behavior is similar for oil-in-water emulsions stabilized by SDS. Viscoelastic moduli (a) $G^{\prime }\left(\gamma \right)$ and (b) $G^{\prime \prime }\left(\gamma \right)$ of attractive emulsions stabilized by SDS with $U\approx 21k_{B}T$ and $a=250$nm for ${\phi }_{\text{eff}}\approx 0.68$, 0.65, 0.62, and 0.59 (progressively lighter colors). Emulsions above ${\phi }_{\text{RCP}}$ (top two curves) show peaks in $G^{\prime \prime }$ at ${\gamma }_1^{*}$ and ${\gamma }_2^{*}$ while those below ${\phi }_{\text{RCP}}$ (lower two curves) show a single peak at ${\gamma }_1^{*}$. For clarity, $G^{\prime }$ and $G^{\prime \prime }$ data are multiplied by a factor of 0.7, 0.6, or 0.5 for ${\phi }_{\text{eff}}=0.65,0.62,$ or 0.59, respectively.Reuse & Permissions

Figure 9

Yielding of attractive emulsions is a shear-driven process. Constant $\dot{\gamma }$ frequency sweep measurements of viscoelastic moduli $G^{\prime }\left(\omega \right)$ and $G^{\prime \prime }\left(\omega \right)$ for two samples with $a=100$ nm and $U\approx 9k_{B}T$ above ${\phi }_{\text{RCP}}$ [(a) ${\phi }_{\text{eff}}\approx 0.73$] and below ${\phi }_{\text{RCP}}$ [(b) ${\phi }_{\text{eff}}\approx 0.66$], shifted onto a single master curve by normalizing by the shear-rate-dependent shift factors $a\left(\dot{\gamma }\right)$ and $b\left(\dot{\gamma }\right)$. Inset: corresponding amplitude and frequency shift factors $a\left(\dot{\gamma }\right)$ (triangles) and $b\left(\dot{\gamma }\right)$ vs $\dot{\gamma }$ (squares).Reuse & Permissions