Pressure drop reduction due to coupling between shear-thinning fluid flow and a weakly deformable channel wall: A reciprocal theorem approach
arXiv:2407.07224 · doi:10.1016/j.jnnfm.2024.105347
Abstract
We employ the Lorentz reciprocal theorem to derive a closed-form expression for the pressure drop reduction due to the coupling between shear-thinning fluid flow and a weakly deformable channel wall in terms of the shear rate and the viscosity function (and its derivative) of the underlying rigid-channel flow. The methodology is applied in parallel to fluids for which the generalized Newtonian viscosity depends on either the shear rate or the shear stress magnitude. When the viscosity model allows for a closed-form solution for the axial velocity profile in a straight and rigid channel, the pressure drop reduction can be evaluated in closed form, which we demonstrate for the power-law and Ellis viscosity models as featured examples and to enable comparisons to previous works. Importantly, the pressure drop reduction under the Ellis model is valid for both small and large Carreau (or Ellis) numbers, and we show that it reduces to the analytical expression under the power-law model for large Carreau (small Ellis) numbers.
11 pages, 3 figures; v2: minor revisions, published in JNNFM
References in corpus (15)
- Soft lubrication
- Squirming through shear-thinning fluids
- Locomotion in complex fluids: Integral theorems
- Non-Newtonian fluid--structure interactions: Static response of a microchannel due to internal flow of a power-law fluid
- Validity of Winkler's mattress model for thin elastomeric layers: Beyond Poisson's ratio
- Soft hydraulics: from Newtonian to complex fluid flows through compliant conduits
- Mobility of Power-law and Carreau Fluids through Fibrous Media
- Force moments of an active particle in a complex fluid
- Non-Newtonian fluid-structure interaction: Flow of a viscoelastic Oldroyd-B fluid in a deformable channel
- Viscous-elastic dynamics of power-law fluids within an elastic cylinder
- Experimental observation of a confined bubble moving in shear-thinning fluids
- Flow rate-pressure drop relations for shear-thinning fluids in deformable configurations: theory and experiments
- An efficient algorithm of solution for the flow of generalized Newtonian fluid in channels of simple geometries
- Optimising non-Newtonian fluids for impact protection of laminates
- Dynamics of spheroids in pressure driven flows of shear thinning fluids