Boundary Layer Flow Dynamics in Non-Newtonian Fluids

Boundary layer flow in non-Newtonian fluids encompasses a wide range of shear-dependent and time-dependent rheological behaviours that depart from the linear viscosity law of Newtonian liquids. In these systems, the velocity profile close to a solid surface is shaped not only by momentum diffusion but also by the fluid’s constitutive relation, which may exhibit shear-thinning, shear-thickening or viscoelastic characteristics. Self-similar solutions and numerical methods often reveal how parameters such as the power-law index, relaxation times and normal stress differences influence boundary layer thickness, skin friction and flow separation. In practical terms, these dynamics underpin processes as diverse as polymer extrusion, coating flows, enhanced oil recovery and biomedical transport in blood vessels. Advances in analytical transformation techniques and high-fidelity computation have clarified the interplay between fluid microstructure and macroscopic boundary layer behaviour, enabling optimisation of surface drag, heat transfer and mixing efficiency. Global interest in these flows reflects their relevance to energy efficiency, materials manufacturing and environmental control.

Research from Nature Portfolio

Recent studies have developed a unified framework for the boundary layer behaviour of power-law (Ostwald-de Waele) fluids undergoing stretching and wedge-driven flows. By introducing novel similarity variables, the governing equations reduce to nonlinear ordinary differential equations that capture both shear-thinning and shear-thickening regimes. A spectral collocation method based on Chebyshev polynomials was used to resolve the transformed equations, revealing that shear-thinning fluids produce thinner boundary layers and elevated surface drag compared with Newtonian counterparts. The methodology further combines asymptotic analysis at large distances with numerical validation to ensure accuracy across the entire domain. These findings offer a consolidated computational approach for predicting velocity and viscosity profiles in industrial and geophysical applications.

Boundary Layer Flow Dynamics in Non-Newtonian Fluids publication trend

The graph below shows the total number of articles in boundary layer flow dynamics in non-newtonian fluids across all publications each year (not limited to Nature Index journals).

Technical terms

Boundary layer: Thin region adjacent to a solid surface where viscous forces dominate and velocity changes from zero at the wall to the mainstream value.

Non-Newtonian fluid: Fluid whose viscosity varies with shear rate or shear history, exhibiting behaviours such as shear-thinning, shear-thickening or viscoelasticity.

Power-law index (n): Exponent in the Ostwald-de Waele model that quantifies the degree of shear-thinning (n<1) or shear-thickening (n>1).

Similarity transformation: Mathematical reduction that collapses partial differential equations into ordinary differential equations by introducing scaled variables.

Skin friction coefficient: Dimensionless measure of shear stress at a surface relative to dynamic pressure, indicating the drag exerted by the boundary layer.

Crocco variables: Change of variables technique used to handle singularities and derive analytical relations for boundary layer flows.

References

1. Hydrodynamic flow of non-Newtonian power-law fluid past a moving wedge or a stretching sheet: a unified computational approach. Scientific Reports (2020).
2. Power-law fluids over a viscous sheet with mass suction/blowing: Multiple solutions. AIP Advances (2019).
3. Mutual Interdependence of the Physical Parameters Governing the Boundary-Layer Flow of Non-Newtonian Fluids. Applied Sciences (2022).