Wire active microrheology to differentiate viscoelastic liquids from soft solids

Viscoelastic liquids are characterized by a finite static viscosity and a zero yield stress, whereas soft solids have an infinite viscosity and a non-zero yield stress. The rheological nature of viscoelastic materials has long been a challenge, and it is still a matter of debate. Here, we provide for the first time the constitutive equations of linear viscoelasticity for magnetic wires in yield stress materials, together with experimental measurements using Magnetic Rotational Spectroscopy (MRS). With MRS, the wires are submitted to a rotational magnetic field as a function of frequency and the wire motion is monitored by time-lapse microscopy. The soft solids studied are gel-forming polysaccharide aqueous dispersions (gellan gum) at concentrations above the gelification point. It is found that soft solids exhibit a clear and distinctive signature compared to viscous and viscoelastic liquids. In particular, the wire average rotation velocity equals zero over a broad frequency range. We also show the MRS technique is quantitative. From the wire oscillation amplitudes, the equilibrium elastic modulus is retrieved and agrees with polymer dynamics theory.