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 - 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
SN - 2469-990X
VL - 6
JO - Physical Review Fluids
JF - Physical Review Fluids
IS - 8
M1 - L081301
ER -