Can you tell me please the differences between Newtonian and Stokes regime in settling velocities of particles in moving fluids? I know that Newtonian applies to higher Reynolds numbers. Does that mean that Newtonian regime is for turbulent flow of fluid? Or what? Or is it that Newtonian regime is when the dominant drag is the pressure drag? Or what? Can you tell me please the differences for each regime? thanks!
[Physics] Newton and Stokes regime in settling velocity
fluid dynamicsviscosity
Best Answer
I assume that by 'Stokes regime' you mean the drag force a object travelling through a viscous fluid experiences, in laminar flow conditions. For a perfectly spherical object and assuming flow of the fluid around the object is laminar, then acc. Stokes' law:
$$F_d=6\pi \mu Rv$$
Where $\mu$ is the dynamic viscosity of the fluid, $v$ the object's speed and $R$ its radius.
But when speed increases flow around the object becomes turbulent and Stokes' elegant expression is no longer valid.
The Reynolds Number $Re$ (a dimensionless number) is defined as:
$$Re=\frac{\rho vD}{\mu}$$
When $Re$ exceeds a critical number $Re_c$, flow ceases to be laminar and becomes turbulent and then the drag force tends to obey a different expression:
$$F_d=\rho A C_d v^2$$
Where $\rho$ is the fluid's density, $A$ the object's cross-section perpendicular to the line of motion and $C_d$ a drag coefficient depending on the shape of the object.
But I doubt if the turbulent regime was ever called 'Newton's regime', as turbulent flow really only began to become well-described and understood considerably after Newton's life time. If anything, 'Newtonian flow' often refers to laminar flow (see e.g. Newtonian viscosity).