Baranets V. Problems of the mechanics of aggregating particles suspensions.

The thesis research is devoted to the study of the mathematical models of the sedimentation of aggregating particles of two- and three-phase suspensions in vertical and inclined tubes in an inhomogeneous field. Using method of characteristics the equations of families of characteristics and the conditions on them are found. The conditions of existence of various types of solutions are studied. One of the main considered problems is the evolution of strong discontinuities. A detailed analysis of the relations for the characteristic velocities and the velocity of the discontinuity surface moving is performed in the work. The obtained results are confirmed by numerical calculations by the method of particle dynamics. On the basis of the three-phase model the formation of a blurred boundary between zone of a pure fluid and settling aggregates is explained for the first time. The Boycotte effect in the case of aggregating suspensions is generalized. The dependence of the sedimentation rate on the inclination angle of the tube is investigated. The solutions of the problems of three-layer laminar flow of immiscible micro/nanofluids between moving plates and coaxial cylinders rotating at different angular velocities and having different roughness are found. A generalization of the calculation formulas for a rotary viscometer for measuring the viscosity of micro- and nanofluids is performed. In the experimental part of the work the sedimentation of erythrocytes in standard tubes and microtubes is investigated. The analysis of experimental researches and their comparison with numerical calculations is carried out. Based on the obtained data a new index for detection of allergies to drugs and food and a rapid method on small volumes of blood using microtubes are proposed. Key words: aggregation, sedimentation, sedimentation rate, aggregation rate, two-phase suspension, three-phase suspension, quasilinear system, method of characteristics, particle dynamics method, microparticles, nanoparticles, slip conditions, Couette flow, Poiseuille flow, sedimentation curves.