Laminar flow of suspensions turned out to be possible only with uniform particle distribution and a certain combination of suspension properties.

Not all suspensions were capable of calm laminar movement. Their transition to a turbulent flow can be predicted by knowing the key hydrodynamic characteristics of the flow. Russian scientists write about this in an article published by the journal Physics of Fluids.

A suspension is a set of small solid particles suspended in a liquid. Most of the practically important materials, including enamel paints and cement, are suspensions. Depending on the size, density and number of particles in this two-phase system, they can be distributed evenly or slowly settle under the influence of gravity.

The flow of these two-phase systems, like that of ordinary liquids, can be smooth, laminar, or, conversely, turbulent, with active mixing and vortices. It is characterized by the Reynolds number, which depends on the velocity, density, viscosity and other parameters of the medium. The transition of the Reynolds number through the critical value reflects the occurrence of instabilities — and the transition from a calm current to a turbulent one.

Moscow scientists: Alexander Osiptsov, head of the Laboratory of Mechanics of Multiphase Media at the Moscow State University Institute of Mechanics, and Sergey Boronin, a leading researcher at the Skoltech Hydrocarbon Production Center (SCHR), examined the parameters under which the two—phase flow of uniform and uneven suspensions will be laminar, and under which — turbulent. They were able to show that the flow transition through the critical Reynolds number is determined by the properties of the suspension, which describe the Stokes and Froude numbers.

The Stokes number shows the ratio of the kinetic energy of particles to the energy of their interaction with a liquid. If the first one dominates, then when the liquid bends around the obstacle, the particles will collide with it; if the interaction energy prevails, then they will go around the obstacle together with the liquid. The Stokes number depends on the viscosity and velocity of the liquid flow, the size and density of suspended particles, and other parameters. The Froude number reflects the ratio of the inertia of the current to the action of an external force. It describes the stability of the flow under the influence, for example, gravitational.

Osiptsov and Boronin found combinations of Stokes and Froude numbers in which the flow of a suspension with a uniform particle distribution will be laminar. These combinations appear for the Stokes numbers, at which the solid particles move sufficiently independently of the liquid phase. "The mismatch of the phase velocities," explains Alexander Osiptsov, "can lead to noticeable stabilization of the flow and prolongation of the laminar regime."

At the same time, the flow of the suspension with unevenly distributed particles remains turbulent under almost any conditions, since the Reynolds number remains above the critical one. "In the presence of inhomogeneities in the concentration of particles along the channel section, a new type of instability arises," adds Alexander Osiptsov.