TY - JOUR

T1 - Reciprocal theorem for calculating the flow rate-pressure drop relation for complex fluids in narrow geometries

AU - Boyko, Evgeniy

AU - Stone, Howard A.

N1 - Funding Information:
We thank C. A. Browne, S. S. Datta, and L. G. Leal for helpful discussions. This research was partially supported by NSF through the Princeton University's Materials Research Science and Engineering Center (Grant No. DMR-2011750). E.B. acknowledges the support of the Yad Hanadiv (Rothschild) Foundation and the Zuckerman STEM Leadership Program.
Publisher Copyright:
© 2021 American Physical Society.

PY - 2021/8

Y1 - 2021/8

N2 - We study the mechanically driven flows of non-Newtonian fluids in narrow and confined configurations. Using the Lorentz reciprocal theorem, we derive a closed-form expression for the flow rate-pressure drop relation of complex fluids in such geometries, which holds for a wide class of non-Newtonian constitutive models. For the weakly non-Newtonian limit, our theory provides the first-order non-Newtonian correction for the flow rate-pressure drop relation solely using the corresponding Newtonian solution, eliminating the need to solve the non-Newtonian flow problem. In particular, for the flow-rate-controlled situation, we find that the first-order non-Newtonian pressure drop correction may increase, decrease, or not change the total pressure drop for a viscoelastic second-order fluid, depending on the geometry, but always decreases it for a shear-thinning Carreau fluid.

AB - We study the mechanically driven flows of non-Newtonian fluids in narrow and confined configurations. Using the Lorentz reciprocal theorem, we derive a closed-form expression for the flow rate-pressure drop relation of complex fluids in such geometries, which holds for a wide class of non-Newtonian constitutive models. For the weakly non-Newtonian limit, our theory provides the first-order non-Newtonian correction for the flow rate-pressure drop relation solely using the corresponding Newtonian solution, eliminating the need to solve the non-Newtonian flow problem. In particular, for the flow-rate-controlled situation, we find that the first-order non-Newtonian pressure drop correction may increase, decrease, or not change the total pressure drop for a viscoelastic second-order fluid, depending on the geometry, but always decreases it for a shear-thinning Carreau fluid.

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U2 - 10.1103/PhysRevFluids.6.L081301

DO - 10.1103/PhysRevFluids.6.L081301

M3 - Article

AN - SCOPUS:85114388436

VL - 6

JO - Physical Review Fluids

JF - Physical Review Fluids

SN - 2469-990X

IS - 8

M1 - L081301

ER -