Instability and stress fluctuations of a probe driven through a worm-like micellar fluid
A particle moving through a worm-like micellar fluid (WLM) shows instability and large fluctuations beyond a threshold \textcolor{black}{velocity/force (depending on the control parameter used)}. Despite many detailed studies, a direct measurement of the time-dependent stress on the probe particle remains unexplored. To address this, we have designed a measuring geometry coupled with a commercial rheometer to study the dynamics of a cylindrical probe through a WLM system of 2 wt.\% cetyltrimethyl ammonium tosylate(CTAT) + 100 mM sodium chloride(NaCl) for a wide range of velocity and stress scales. We map out the in-situ velocity distribution using particle imaging velocimetry. Beyond a velocity threshold, we observe large stress fluctuation with gradual stress build-up followed by sudden stress drop indicating storage and release of elastic energy. The length scale constructed from the stress build-up time scale and the probe's velocity match the length scale of extensile deformation just before the stress drop, confirming the strong correlation of storage and release of energy with the unstable probe motion. Interestingly, the Weissenberg number ($Wi$) for the onset of flow instability obtained from the shear and extensile components remains almost the same. We also find that the turbulent motion of the probe at higher $Wi$ results from the complex mixing of the stick-slip events originating from the partial release of the stored elastic energy. Further, we show that the magnitude of the stick-slip events depends on the detailed micellar structure and dynamics controlled by salt concentration and temperature.