Scaling law of correlated diffusion of colloidal particles confined to a rugged surface

Using optical microscopy and multiparticle tracking techniques, we investigate the correlated diffusion of colloidal particles over a rugged surface. Our findings demonstrate that the correlated diffusion caused by the hydrodynamic interactions of particles confined to energy landscapes displays a distinctive power-law behavior. The local energy landscape on the rugged surface reduces the long-range hydrodynamic interactions between colloidal particles. The energy landscape influences the strength of hydrodynamic interactions, but not their power-law form. The responding factor of the colloidal particles over the energy landscape to hydrodynamics decays exponentially with the potential energy minimum. We propose a scaling method, with which the correlated diffusion of colloidal particles over various energy landscapes can be scaled onto a master curve. The master curve characterizes the response of the particles over the energy landscape to the hydrodynamics. The scale factors used for the master curve allow for the calculation of the energy landscape. The findings provide physical insights into the confinement hydrodynamics and would be helpful for designing material surfaces and controlling the motion of particles on rough surfaces.Published versionThis work was partially supported by the Key Academic Discipline Project of China University of Mining and Technology (Grant No. 2022WLXK10), the China Scholarship Council (Grant No. 202006425022), the Basic Research Program Project of Xuzhou (Grant No. KC21020), the National Natural Science Foundation of China (Grant No. 11774417) and the Natural Science Foundation of Jiangsu Province (Grant No. BK20160238)