Modelling non-homogeneous flow and residence time distribution in a single-screw extruder by means of Markov chains

Abstract

Nomenclature a Coefficient of the homographic equation (m/s) b Coefficient of the homographic equation (m 2 /s) B Distance between flanks (m) d Diameter of the screw (m) d z Transition probability along the axis z (-) d y Transition probability along the axis yInternal diameter of the barrel (m) eWidth of the screw flank (m)Coefficient of the homographic equation (m) g z The down channel pressure gradient (Pa/m) H Cross channel depth (m) j The transition number (-) L Length of the screw shaft (m) L f Length of the die (m) L s Length of the channel (m) L t Total path length (m) m Row number (-) M Mass of material in the extruder (kg) n Column number (-) P Matrix of transition probabilities (-) P ik Matrix of transition probabilities from kth to ith columns Q Mass flow rate (kg/s) r Throttle ratio (-) S State vector (-) t Time at which the calculated results are obtained (s) T Temperature of the barrel ( • C) v Transition probability describing convection (-) V z Average velocity along the axis z (m/s) V ex Free volume of the extruder (m 3 ) W Channel width (m) Z Zero matrix (-) Greek symbols t Time interval (s) t exp Experimental time of sampling (s) y Height of a cell (m) z Length of a cell (m) ρ Average density of the material (kg/s) µ Viscosity (Pa s)

Modeling of Sewage Sludge Flow in a Continuous Paddle Dryer

“…Markov chains proved to be efficient to model bulk particulate flow in a great variety of processes. [22][23][24][25] This approach has been widened to describe heat and mass transfers between stochastically moving particulate and gas flows. [26,27] In this article, we assume that the agitated contact drying process is a Markov process and we propose a cell model, based on a 1D homogeneous Markov chain, to describe the flow of the anhydrous solids in a paddle dryer.…”

The Journal of Mathematical Chemistry: a bibliometric profile

“…However, consideration of some of the other citing journals reveals a surprising breadth of interest in the material that is published in the journal. For example: an article in Acta Alimentaria entitled "Extrusion of corn grits with native or modified starch addition -influence on starch digestibility fractions, shear stress-at-break, and expansion ratio" [3] cites a JMC article on the use of Markov chains to model non-homogeneous flows [4]; and an article in Desalination entitled "Recent applications of nanomaterials in water desalination: A critical review and future opportunities" [5] cites a JMC article modelling the transportation of sodium and chloride ions [6]. Similar behaviour is observed if one analyses the citing publications in terms of the WoS subject category to which they belong.…”

Extrusion of Corn Grits with Native or Modified Starch Addition — Influence on Starch Digestibility Fractions, Shear Stress-at-Break, and Expansion Ratio

“…Velocity distribution is closely related to the rheological properties of the material. Therefore, by knowing how changes in rheological properties may modify the velocity distribution, it becomes possible to study how the fl ow characteristics change (PONOMAREV et al, 2012). …”