Stokes and Navier-Stokes equations under power law slip boundary condition: Numerical analysis

Analysis of the accumulation the sedimentary mass in coal-water slurries

“…With the advent of instruments analysing the sedimentation rate and sieve composition of particles smaller than 500 µm, the traditional task of calculating the particle size distribution of disperse systems has somewhat lost its meaning, since the direct (instrumental) method allows to do it faster and with greater accuracy. At the same time, other tasks [10][11][12][13][14][15] of practical importance can be solved at the same time, namely:…”

“…Usually, analysers present the results of analysis in the form of frequency distribution function (fractions 𝑓𝑓 𝑖𝑖 (𝑟𝑟 𝑖𝑖 )) by size or number of particles, with all particles divided into 𝑛𝑛 fractions 𝑖𝑖 = 1, 2, 3, … , 𝑛𝑛 of the minimum radius 𝑟𝑟 𝑚𝑚𝑖𝑖𝑚𝑚 to the maximum 𝑟𝑟 𝑚𝑚𝑚𝑚𝑚𝑚 . By type of histogram 𝑓𝑓 𝑖𝑖 (𝑟𝑟 𝑖𝑖 ) it can be approximated into any of the known theoretical distribution functions [13].…”

“…Based on the classical method of calculation of polydisperse systems of particles of different sizes, proposed by S. Oden, the whole settled per unit area, by the moment 𝑡𝑡 at depth 𝑧𝑧, particle mass 𝐺𝐺(𝑡𝑡; 𝑧𝑧) is divided into two parts: the mass of particle fractions that have settled completely and the mass of particulate fractions that have settled partially [12][13][14][15]. In this case, the mass of the sludge will be:…”

“…Coefficient 𝛽𝛽 was obtained from the Stokes equation. It is known that the Stokes equation is applicable to determine the finite fall velocity of relatively small particles at Reynolds number 𝑅𝑅𝑅𝑅 < 1, i.e., at laminar regime of grain flowing by the medium, at which the action of forces from viscosity prevails [12][13][14][15]. Thus, for water-coal suspensions containing particles with a diameter of 0-250 μm, for which the Reynolds number 𝑅𝑅𝑅𝑅 < 1, Stokes' law is applicable.…”