Viscous-elastic dynamics of power-law fluids within an elastic cylinder. Boyko, E., Bercovici, M., & Gat, A., D. Phys. Rev. Fluids, 2(7):073301, American Physical Society, 2017. ![Viscous-elastic dynamics of power-law fluids within an elastic cylinder [link]](https://bibbase.org/img/filetypes/link.svg "link")
Website doi abstract bibtex In a wide range of applications, microfluidic channels are implemented in soft substrates. In such configurations, where fluidic inertia and compressibility are negligible, the propagation of fluids in channels is governed by a balance between fluid viscosity and elasticity of the surrounding solid. The viscous-elastic interactions between elastic substrates and non-Newtonian fluids are particularly of interest due to the dependence of viscosity on the state of the system. In this work, we study the fluid-structure interaction dynamics between an incompressible non-Newtonian fluid and a slender linearly elastic cylinder under the creeping flow regime. Considering power-law fluids and applying the thin shell approximation for the elastic cylinder, we obtain a nonhomogeneous p-Laplacian equation governing the viscous-elastic dynamics. We present exact solutions for the pressure and deformation fields for various initial and boundary conditions for both shear-thinning and shear-thickening fluids. We show that in contrast to Stokes’ problem where a compactly supported front is obtained for shear-thickening fluids, here the role of viscosity is inversed and such fronts are obtained for shear-thinning fluids. Furthermore, we demonstrate that n for the case of a step in inlet pressure, the propagation rate of the front has a t n+1 dependence on time (t), suggesting the ability to indirectly measure the power-law index (n) of shear-thinning liquids through measurements of elastic deformation.
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abstract = {In a wide range of applications, microfluidic channels are implemented in soft substrates. In such configurations, where fluidic inertia and compressibility are negligible, the propagation of fluids in channels is governed by a balance between fluid viscosity and elasticity of the surrounding solid. The viscous-elastic interactions between elastic substrates and non-Newtonian fluids are particularly of interest due to the dependence of viscosity on the state of the system. In this work, we study the fluid-structure interaction dynamics between an incompressible non-Newtonian fluid and a slender linearly elastic cylinder under the creeping flow regime. Considering power-law fluids and applying the thin shell approximation for the elastic cylinder, we obtain a nonhomogeneous p-Laplacian equation governing the viscous-elastic dynamics. We present exact solutions for the pressure and deformation fields for various initial and boundary conditions for both shear-thinning and shear-thickening fluids. We show that in contrast to Stokes’ problem where a compactly supported front is obtained for shear-thickening fluids, here the role of viscosity is inversed and such fronts are obtained for shear-thinning fluids. Furthermore, we demonstrate that n for the case of a step in inlet pressure, the propagation rate of the front has a t n+1 dependence on time (t), suggesting the ability to indirectly measure the power-law index (n) of shear-thinning liquids through measurements of elastic deformation.},
bibtype = {article},
author = {Boyko, E. and Bercovici, M. and Gat, A. D.},
doi = {10.1103/PhysRevFluids.2.073301},
journal = {Phys. Rev. Fluids},
number = {7}
}
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