Rotational friction of dipolar colloids measured by driven torsional oscillations

Abstract

Despite its prominent role in the dynamics of soft materials, rotational friction remains a quantity that is difficult to determine for many micron-sized objects. Here, we demonstrate how the Stokes coefficient of rotational friction can be obtained from the driven torsional oscillations of single particles in a highly viscous environment. The idea is that the oscillation amplitude of a dipolar particle under combined static and oscillating fields provides a measure for the Stokes friction. From numerical studies we derive a semi-empirical analytic expression for the amplitude of the oscillation, which cannot be calculated analytically from the equation of motion. We additionally demonstrate that this expression can be used to experimentally determine the rotational friction coefficient of single particles. Here, we record the amplitudes of a field-driven dipolar Janus microsphere with optical microscopy. The presented method distinguishes itself in its experimental and conceptual simplicity. The magnetic torque leaves the local environment unchanged, which contrasts with other approaches where, for example, additional mechanical (frictional) or thermal contributions have to be regarded.Frictional forces play a fundamental role in the dynamics of mesoscopic objects, which are omnipresent in microfluidic and biological systems. The frictional interaction of moving objects with the viscous environment affects e.g. transport, demixing, diffusion, and propulsion [1][2][3][4][5] . The study of friction during these processes also gives access to the rheological and the aggregation behavior of colloids such as ferrofluids and gels [6][7][8][9] . In incompressible fluids, the key quantity is the Stokes friction coefficient f, which is the proportionality factor between the particle velocity and the drag force. Often, many-body effects in dense systems can be expressed as an expansion of the single-particle friction. An explicit, simple equation of f exists for single spheres in an ideally homogeneous medium by the Stokes law. Real systems, however, face deviations from that, caused either by a non-spherical object shape [10][11][12][13][14][15] or by anisotropic environments such as in non-ideal fluids or at surfaces/interfaces [16][17][18][19][20] , e.g. in a cell or a microchannel [21][22][23] . As most of these problems cannot be solved analytically one relies on approximate solutions 24 or on experimental measurements. Friction from translational motion behaves differently from the friction during rotational motion 16,25,26 ; for analysis sometimes both need to be decoupled 27,28 . Experimentally, the translational friction, f t , can be simply derived from the spatial displacement of a diffusing particle via optical methods. Rotational friction, f r , however, remains difficult to determine since additionally the orientation of the object has to be determined, which requires optical or shape anisotropy.For nanoscopic objects, measurement methods rely on, e.g., scattering techniques 13,29,30 , time-resolved phospho...

A Two‐Parameter Model for Colloidal Particles with an Extended Magnetic Cap

“…Detailed data have been recorded for the interaction of single, magnetically activated particles with the surrounding aqueous medium and for the interparticle interactions in 2D aggregates . In the absence of external fields, such aggregates are composed of distinct structural motifs, which result from the interplay between the favorable trigonal dense packing of spheres and the spatially more complex magnetic interactions between the extended ferromagnetic caps .…”