СЕДИМЕНТАЦИЯ МАЛОКОНЦЕНТРИРОВАННОЙ ПОЛИДИСПЕРСНОЙ ВЗВЕСИ СТОКСОВСКИХ ЧАСТИЦ В ПЛОСКОМ СЛОЕ

V.I Ryazhskikh,A.V Ryazhskikh

doi:10.14529/mmph180308

Abstract

On the basis of the diffusion-kinetic approach, an analytical analysis of the precipitation of a low-concentration polydisperse suspension of Stokes particles in a flat layer of a stationary dispersive phase (viscous incompressible liquid) is performed. In the absence of mixing, the mathematical model for monodisperse particles, generalized to a polydisperse case using the principle of superposition of concentration fields, is presented in the form of an initial-boundary value problem for a first-order partial differential equation with respect to the particle size distribution function in dimensions, the solution of which is written in the analytic relation with the help of the generalized Heaviside function. The calculated expressions are obtained for the local counting function of the density of the particle distribution in the space of dimensions, mass concentration in the volume, and growth of the sediment, which are invariant to the physicochemical properties of the heterogeneous system. It is shown that the generalized solution found can be applied to the dispersion analysis of suspended matter as an alternative technique to sedimentometric analysis if the empirical relative sedimentation curve is known. If the initial counting function of the particle size distribution density refers to the exponential type, then the average number particle size of the suspension can easily be calculated from the unconditional minimization problem. This approach can be generalized to the case of coarse suspended solids, the rate of deposition of which does not obey the Stokes law, and also for arbitrary initial counting functions of the particle size distribution of the slurry in size. In this case, to find the particle density function with respect to size, we use the objective function written in the form of a functional and the minimization problem leads to a certain degree of approximation to the required experimental countable density distribution function for particles.

Highlights

Процесс осаждения малоконцентрированной полидисперсной взвеси находит широкое использование в энергетике, химической и пищевой технологиях [1, 2], а если при этом несущая среда является условно неподвижной, то этот процесс имеет фундаментальное значение в седиментометрическом анализе дисперсной фазы [3]
In the absence of mixing, the mathematical model for monodisperse particles, generalized to a polydisperse case using the principle of superposition of concentration fields, is presented in the form of an initial-boundary value problem for a first-order partial differential equation with respect to the particle size distribution function in dimensions, the solution of which is written in the analytic relation with the help of the generalized Heaviside function

Summary

Introduction

Процесс осаждения малоконцентрированной полидисперсной взвеси находит широкое использование в энергетике, химической и пищевой технологиях [1, 2], а если при этом несущая среда является условно неподвижной, то этот процесс имеет фундаментальное значение в седиментометрическом анализе дисперсной фазы [3]. ∂x где τ , x – время и декартова координата; n( x,τ ) – локальная счетная концентрация частиц размера l; w – стоксовская скорость осаждения частиц размера l; D – коэффициент конвективного перемешивания взвеси; k – кинетический коэффициент встраивания частиц в структуру осадка. Где f0 (l ) , f ( x,l,τ ) – исходная и локальная счетные функции плотности распределения частиц по размерам.

Results

Conclusion