Correlated dynamics of weakly charged silica spheres at an air-water interface

Optical microscopy and multi-particle tracking are used to investigate the spatially correlated motion of weakly charged silica spheres at an air-water interface for different area fraction $n$ occupied by the particles. When the area fraction is very small, e.g. $n=0.03$, the correlation function along the line joining the centers of particles $D_{rr}$ decays with inter-particle distance $R$ as $1\mathrm{/}{R}^{0.86\pm 0.02}$, and the function perpendicular to this line $D_{\theta \theta }$ decays with $R$ as $1\mathrm{/}{R}^{1.45\pm 0.03}$, which differs from the results of [Phys. Rev. Lett. 97, 176001 (2006)] with low surface viscosity (where $D_{rr}\propto 1\mathrm{/}R$, $D_{\theta \theta }\propto 1\mathrm{/}{R}^2$). We argue that the differences arise from the Coulomb interaction between particles. The Coulomb interaction enhances the correlated motion of particles. Experimental results show that with the increase of $n$, the decay rate of $D_{rr}$ and $D_{\theta \theta }$ with $R$ decreases and the cross-correlation enhances for the Coulomb interaction increases. The Coulomb interaction between colloidal particles should serve as an effective surface viscoelastical role in our system. With the scaled separation $\frac R {d}(\frac {\eta_{w}d} {\eta_{es,2p}})^{3/2}$,thecorrelatedmotionsforvariousvaluesof$n$ and different particles can be scaled onto a single master curve, where $d$ is particles’ diameter, ${\eta }_w$ is the viscosity of the water, and ${\eta }_{es,2p}$ is the effective surface viscosity whose measurements agree well with that of one-particle surface viscosity ${\eta }_{es,1p}$. The effective surface viscosity ${\eta }_{es,2p}$ as a function of the area fraction $n$ for different silica spheres is presented.