Question

We know that the diffusion term of the Navier-Stokes equations can be neglected when the reynolds number is high. Assume we have a particulate flow, in which the effect of particle's presence is incorporated into the stress term of the N.S equations. Can we conclude that the effect of particle's presense can be neglected when the Reynolds number is high?

Answer 1

The presence of particles in a fluid may affect its dynamics in a particulate flow, and this effect may not be ignored at high Reynolds numbers simply because the diffusion term of the Navier-Stokes equations is negligible.

Step-by-step explanation:

The question refers to the Navier-Stokes equations and the role of the Reynolds number (NR) in determining the flow regime (laminar vs turbulent flow) in particulate flows, where particles' effects are included in the stress terms. The Reynolds number is calculated using the formula NR = (p * v * r) / n, where p is the fluid density, v is its speed, n its viscosity, and r the tube radius.

High Reynolds numbers, typically above 3000, indicate turbulent flow, whereas low Reynolds numbers, typically below 2000, indicate laminar flow. However, in the case of particulate flow, the presence of particles may affect the fluid dynamics in a way that is not solely dependent on the Reynolds number. Thus, it may not be accurate to conclude that the effects of particles can be neglected at high Reynolds numbers without additional analysis, as particulates could interact or cluster, thereby altering the flow in significant ways, independent of whether the flow is laminar or turbulent.