Effective viscosity of the suspension
Fluid is a collection of many molecules that are randomly distributed and attached by weak cohesive forces. It isn't easy to study the motion of every individual particle of the fluid as a function of time. So, we describe the properties of the fluid at each point as a function of time. The motion of the fluid is divided into two groups: laminar and turbulent flow. Laminar flow is defined by $\Delta\times v=0$, which tells that the rotation of particles is zero and flow is along streamlines.
For the turbulent, the curl of the velocity field is non-zero; there is a rotation of streamlines and production of vortices.
Reynolds number is the dimensionless quantity that gives the information about the flow characteristics
Reynolds number is defined by the ratio of inertia force to viscous force;
\begin{equation}
Re=\frac{\rho v d}{\mu}
\end{equation}
where $d$ is the characteristic dimension and $\mu$
is the dynamic viscosity of the fluid.