Development of the Couple Stress Relationships for the Power Law Fluid and the Solution of Flow in Ceramic Tape Casting Process

The absence of characteristic material length in the Navier-Stokes equations has led to the development of different couple stress theories. In the present study, for the first time, the relations of a couple stress theory are extended to power-law fluids. Moreover, considering the significance of the length scale in nano- and micromechanics, the relations of the extended theory were applied to Newtonian and power-law fluids in tape casting of ceramics. The obtained velocity was used to calculate the volumetric flow rate as well as the thickness of the ceramic tape. A comparison between the results of the Newtonian fluid and the analytical and experimental results indicated a close agreement between the present results and the results of other studies. Moreover, the tape thickness was obtained for different length scales (L) by numerically solving the velocity relations obtained for the non-Newtonian fluid. Also, the impact of casting speed on the tape thickness was shown for four power-law fluids assuming L=0.35.