Reciprocal theorem for calculating the flow rate–pressure drop relation for complex fluids in narrow geometries
Evgeniy Boyko, Howard A. Stone
Abstract
A key aspect in understanding pressure-driven flows of non-Newtonian fluids in narrow and confined geometries is the relationship between the flow rate and pressure drop. Using the Lorentz reciprocal theorem, we derive a closed-form expression for the flow rate-pressure drop relation of complex fluids in narrow channels of arbitrary shape, which holds for a wide class of viscoelastic and shear-thinning 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.
Topics & Concepts
Newtonian fluidPressure dropReciprocalMechanicsNon-Newtonian fluidMathematicsFlow (mathematics)Drop (telecommunication)ViscoelasticityShear thinningVolumetric flow rateClassical mechanicsCalculus (dental)PhysicsStatistical physicsViscosityThermodynamicsComputer scienceTelecommunicationsMedicineLinguisticsPhilosophyDentistryRheology and Fluid Dynamics StudiesPhase Equilibria and ThermodynamicsBlood properties and coagulation