A viscosity scan shows the above, boundary, and below cases for the same threshold. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Low viscosity leaves the ratio above the boundary

Density, speed, and length stay fixed. Viscosity 1 Pa*s gives Reynolds number 24, which is above the threshold 12.

Re=ρvLμ=24Re=\frac{\rho vL}{\mu}=24
Reynolds classificationA dimensionless training ratio is compared with a threshold.flowclassification

The middle viscosity sits exactly on the boundary

Viscosity 2 Pa*s gives Reynolds number 12. The helper classifies equality as at-or-above the threshold, so the boundary case is not hand-waved.

Re=ρvLμ=12Re=\frac{\rho vL}{\mu}=12
Reynolds classificationA dimensionless training ratio is compared with a threshold.flowclassification

High viscosity pulls the ratio below the boundary

Viscosity 4 Pa*s gives Reynolds number 6. The comparison is a dimensionless training gate, not a full microfluidic stability model.

Re=ρvLμ=6Re=\frac{\rho vL}{\mu}=6
Reynolds classificationA dimensionless training ratio is compared with a threshold.flowclassification