Chemical and Petroleum Engineering, Vol. 54, Nos. 1–2, May, 2018 (Russian Original Nos. 1–2, Jan.–Feb., 2018)
0009-2355/18/0102-0003 ©2018 Springer Science+Business Media, LLC
Moscow Polytechnic University, Moscow, Russia; e-mail: firstname.lastname@example.org. Translated from Khimicheskoe i Neftegazovoe Mashino-
stroenie, No. 1, pp. 3–6, January, 2018.
RESEARCH, DESIGN, CALCULATIONS,
AND OPERATING EXPERIENCE
PROCESSES AND EQUIPMENT FOR CHEMICAL
AND OIL-GAS PRODUCTION
SPECIAL FEATURES OF DISPERSED MATERIAL
DISSOLUTION PROCESS IN SHEAR FLOW
OF A VISCOUS LIQUID
M. V. Lebedev and O. V. Tin’kov
A theoretical study is made of the solid dispersed materials dissolution process in shear ﬂ ow of a viscous
liquid. A sphere-in-cell model that takes account of the effect of the solid disperse phase concentration on
the conditions of mass transfer on the surface of a random particle is analyzed. Analytical equations for
calculating the shear stress and Sherwood number averaged over the surface of the particles in a shear ﬂ ow
are derived. The basic mechanisms of shear ﬂ ow of a viscous liquid around spherical particles are disclosed.
Keywords: viscous liquid, shear ﬂ ow, disperse phase, Sherwood number, sphere-in-cell model, shear stresses.
A topical issue of chemical engineering is development of new systems and improvement of the existing ones for
preparing highly viscous solutions of solid dispersed materials. Designs of these systems depend on the properties of the
source materials and the ﬁ nished products and must ensure generation of intense shear ﬂ ows in mixing chambers, which en-
hances the dissolution process efﬁ ciency markedly.
Notwithstanding signiﬁ cant achievements in the domain of creation of systems for preparing high-viscosity solu-
tions, there is still no theoretically validated procedure for calculating process parameters that would have taken account of
the inﬂ uence of velocity gradient inside the working medium. Development of such a procedure involves solution of the
problems of ﬂ ow of a viscous liquid around the particles of a dispersed material. This problem generally comes down to de-
termination of the velocity ﬁ eld in the liquid ﬂ ow near the particle surface. A solution to this problem was offered in  for
the case where a solitary particle is streamlined by an axisymmetric liquid ﬂ ow. However, for systems having mixing devices,
intense ﬂ ow of the working medium with a high velocity gradient in the ﬂ ow is typical.
For solving the problems of shear ﬂ ow of a viscous liquid around a solitary particle, a highly intricate asymptotic
expansion method is used . Here, if the disperse phase content in the system is high, the geometric parameters and mutual
disposition of the particles signiﬁ cantly affect the conditions of their streamlining, which reduces the calculation accuracy
substantially. Mathematical models describing the inﬂ uence of particle parameters on the liquid ﬂ ow pattern are given in .
Each of these models ensures the best convergence with the experiment in a ﬁ xed disperse phase concentration range.
In many cases, the dissolution process occurs in systems having a small and moderate content of solid disperse phase
(the volume fraction of this phase ε < 0.3). For such systems, use is generally made of a sphere-in-cell model, according to