Oscillatory flow in a cone-and-plate bioreactor

Area of Science:

• Fluid Dynamics
• Rheology
• Biomechanical Engineering

Background:

• Cone-and-plate rheometry is crucial for characterizing non-Newtonian fluids.
• Understanding oscillatory flow is vital for applications like biometric sensing and medical device design.
• Previous studies often simplified flow conditions, necessitating analysis of more complex oscillatory regimes.

Purpose of the Study:

• To analytically investigate oscillatory flow within a small-angle cone-and-plate geometry.
• To derive expressions for shear stresses on the plate surface under laminar flow conditions.
• To explore the influence of Womersley and Reynolds numbers on flow behavior.

Main Methods:

• Employed a perturbation method to solve the governing flow equations.
• Assumed a small angle between the cone and plate for analytical tractability.
• Analyzed the flow in terms of two dimensionless parameters: Womersley number (local acceleration) and Reynolds number (centripetal force).

Main Results:

• Developed analytical working equations for shear stresses induced by both primary and secondary flows.
• The perturbation method provided insights into the interplay between inertial and viscous forces.
• Quantified the contributions of laminar primary and secondary flows to the overall shear stress.

Conclusions:

• The study provides a foundational analytical framework for oscillatory cone-and-plate flow.
• Results are applicable to optimizing biometric devices and understanding fluid behavior in similar geometries.
• The derived equations enable precise prediction of shear stresses in specific oscillatory flow regimes.