Simplifying the Methodology to Estimate the Separation Time of a Particle at 1-g under Unsteady Conditions

According to Stokes, the time required for a particle to precipitate depends on several conditions such as sphericity and laminar flow, as well as key parameters like particle size, densities (particle and fluid) and fluid viscosity. Therefore, if any of these conditions or parameters are unknown or not met, it becomes impossible to estimate the precipitation time. Additionally, when the separation under 1-g (Earth gravity) takes days or months but an estimation is needed in just minutes, the separation time at 1-g can be approximated by relating it to conditions at other values of gravity (n-g). For example, in a centrifuge. However, this n-g value is not reached instantaneously but require to consider the acceleration, plateau, and deacceleration phases to obtain a reliable estimation. This task has been addressed before; however, the resulting models tend to be either complex for practical laboratory use, or fail to account for the relationship between distance travelled by a particle under 1-g and the distance travelled under centrifugal forces. Moreover, even during the plateau phase, centripetal acceleration is unsteady because the radial distance of the precipitating particle is constantly changing. Thus, the aim of this study is to simplify the methodology for estimating particle separation time at 1-g by using separation time obtained under the unsteady conditions of centrifugation, even when the properties of the particle and fluid are unknown, through a numerical approach.