Determining the Size of an Undeformed Core in the Flow of an Unstructured Suspension from the Point of View of the Theory of Stability of Lipophobic Colloids

It has been shown for the first time that in the case of a pressure flow of a Newtonian fluid in a circular pipeline, the influence of forces of rheological origin, ion-electrostatic and Van der Waals nature on the radius of the undeformed flow core is described by a third-degree polynomial with respect to the thickness of the layer where the suspension structure is destroyed and its shear flow occurs. In this polynomial, the contribution of forces of rheological origin and the influence of the hydraulic size of the solid phase particles of the suspension are taken into account by a linear term. It has been proven that for the conditions of pressure flow of water-coal fuel, the influence of the hydraulic size of the solid phase particles of the suspension can be neglected in comparison with the influence of forces of rheological origin. The influence of ionic-electrostatic and Van der Waals forces is taken into account by quadratic and free terms. The quadratic term takes into account the influence of the distance between two adjacent particles in the suspension structure, and the free term is proportional to the total interaction energy of two spherical particles in a liquid. It has been proven that for conditions of pressure flow of water-coal fuel, the influence of the quadratic term of this polynomial can be neglected in comparison with the influence of its free term. Thus, for conditions of forced flow of water-coal fuel in a circular pipeline, it is proposed to determine the limiting value of the radius of the undeformed flow core as the root of a cubic equation containing cubic, linear and free terms. The free term of this polynomial at the points of equilibrium of ion-electrostatic and Van -der-Vaal nature is zero, and the limitation of the relative current radius of the undeformed flow core coincides with the dependence for determining the relative radius at which the structure of the suspension is still preserved during the flow of structured suspensions in a pipeline, exclusively according to rheological and hydraulic characteristics. At points of equilibrium between ionic-electrostatic and Van der Waals forces, the free term of this equation becomes either positive or negative. The results of the study of possible solutions to the cubic equation obtained using Cardan's method indicate that the sign of the free term does not affect the sign of the discriminant of the cubic equation. The sign of this discriminant depends on the ratio of the free term to its critical value, which depends on the relative radius of the undeformed flow core, determined by the ratio of the initial tangential stress to the tangential stress of hydraulic friction on the inner surface of the pipe. It is shown that with a positive discriminant, physically possible values of the radius of the undeformed flow core exist only in the case of a negative free term. When the free term of the cubic equation has positive values, they are physically impossible, since they imply the presence of a destruction boundary in the middle of the flow region where there is no deformation. With a negative discriminant, the sign of the free term affects the maximum value of the relative radius at which the structure of the suspension is still preserved when structured suspensions flow in a pipeline. In the case of a positive free term, the maximum value of the relative radius at which the structure of the suspension is still preserved during the flow of structured suspensions in a pipeline will exceed the relative radius of the undeformed flow core, which is determined by the rheological characteristics of structured suspensions. Conversely, in the case of a negative free member, the maximum value of the relative radius at which the structure of the suspension is still preserved during the flow of structured suspensions in a pipeline will be less than the relative radius of the undeformed flow core, which is determined by the rheological characteristics of structured suspensions.