Scaling laws for near-wall flows of thixo-elasto-viscoplastic fluids in a millifluidic channel

Thixo-elasto-viscoplastic (TEVP) fluids are very complex fluids. In addition to elasticity and viscoplasticity, they exhibit thixotropy, i.e., time-dependent rheology due to breakdown and recovery of internal structures at different length- and timescales. General and consistent methods for a priori flow prediction of TEVP fluids based on rheological characteristics are yet to be developed. We report a combined study of the rheology and flow of 18 samples of different TEVP fluids (three yogurts and three concentrations of Laponite and Carbopol, respectively, in water in both the unstirred and a stirred state). The rheology is determined both with standard protocols and with an ex situ protocol aiming at reproducing the shear history of the fluid in the flow. Micrometer resolution flow measurements in a millimeter scale rectangular duct are performed with Doppler Optical Coherence Tomography (D-OCT). As expected, the results show the existence of a plug flow region for samples with sufficiently high yield stress. At low flow rates, the plug extends almost all the way to the wall and the extent of the plug decreases not only with increased flow rate but also with increased thixotropy. The ex situ rheology protocol enables estimation of the shear rate and shear stress close to the wall, making it possible to identify two scaling laws that relates four different non-dimensional groups quantifying the key properties wall-shear stress and slip velocity. The scaling laws are suggested as an ansatz for a priori prediction of the near-wall flow of TEVP fluids based on shear flow-curves obtained with a rheometer.