Microliter viscometry using a bright-field microscope: η-DDM

The rheological properties of a medium can be inferred from the Brownian motion of colloidal tracer particles using the microrheology procedure. The tracer motion can be characterized by the mean-squared displacement (MSD). It can be calculated from the intermediate scattering function determined by Differential Dynamic Microscopy (DDM). Here we show that DDM together with the empirical Cox-Merz rule is particularly suited to measure the steady-shear viscosity, i.e. the viscosity towards zero frequency, due to its ability to provide reliable information on long time and length scales and hence small frequencies. This method, η-DDM, is tested and illustrated using three different systems: Newtonian fluids (glycerol-water mixtures), colloidal suspensions (protein samples) and a viscoelastic polymer solution (aqueous poly(ethylene oxide) solution). These tests show that common lab equipment, namely a bright-field optical microscope, can be used as a convenient and reliable microliter viscometer. Because η-DDM requires much smaller sample volumes than classical rheometry, only a few microliters, it is particularly useful for biological and soft matter systems.