Modelagem matemática de escoamento de suspensões não coloidal em geometrias reométricas

Abstract

Suspensions are multiphase substances found in various industrial processes and nature. They are characterized by one continuous and one or more dispersed phases. Their rheological behavior is still not well understood, depending on several factors such as their composition and on how the phases interact. In the present work, a numerical study of the solid-liquid two-phase flow is presented, which characterizes a non-colloidal suspension flow between rheometric geometries. The mathematical model is based on the eulerian-eulerian approach, which employs mass and momentum equations for a two-phase flow, as well as constitutive equations to model the interphase interactions. The numerical study was carried out in three geometries, cone-plate, plate-plate and concentric cylinders, as a way to evaluate the effect of the geometric configuration on the suspension behavior during a rheometric test. The obtained results allowed to identify the behavior of the suspension particles as a function of several operational conditions, helping to understand how particle migration is associated with the calculated torque during the rheological characterization. The numerical results agree well with data from literature and with actual experimental tests, suggesting that the adopted model represents well the multiphase flow pattern between the plates and can provide quantitatively consistent rheological data. It is observed, with the study being carried out, that suspensions present apparent viscosities that depend on the concentration, the particle sizes, and the operating conditions to which the sample is subjected, such as shear rate, Reynolds number, among others. The study also revealed that particle migration in suspensions with particle density equal to that of the liquid, in cone-plate geometry, occurs from the cone truncation region to the center of the cone-plate. Different behavior was noticed for plate-plate geometry, in which particle migration occurs from regions of low shear rates, in the center of the plate, to regions of high shear rates, on the plates periphery. In turn, in cases where the particle density is different from that of the continuous phase, migration can also occur from regions of high to low shear rates, depending on the operating conditions. In addition, a critical test time was identified below which the apparent viscosity has negligible sedimentation effect. Additionally, a modified Reynolds number was identified above which the particles are kept in suspension and the effects related to sedimentation are minimized. It is expected that the results can contribute not only to guide rheometric tests of suspensions, but also to the understanding of the phenomena involved with the two-phase liquid-solid flows in rheometric geometries.