The literature model studied in this article describes bubble formation and growth in a highly viscous polymer liquid with support of a gaseous matter dispersed under pressure before foaming. The foam growth is induce...The literature model studied in this article describes bubble formation and growth in a highly viscous polymer liquid with support of a gaseous matter dispersed under pressure before foaming. The foam growth is induced by the application of vacuum and mass transport of volatile components dissolved in the polymer liquid. Based on this literature model, aeration processes are calculated for intermediate viscosity and low viscosity biological systems, as they are of interest for biomatter foams, in particular for food foams in industrial processes. At the end of this article, the numerical results are presented and discussed.展开更多
The steady laminar pipe flow of a suspension with a gas volume fraction ∅≤0.5 and small or intermediate bubble deformations in long, and straight sections of a circular pipe is calculated. The calcula...The steady laminar pipe flow of a suspension with a gas volume fraction ∅≤0.5 and small or intermediate bubble deformations in long, and straight sections of a circular pipe is calculated. The calculations are based on the constitutive equation that was originally derived for dilute emulsions and further developed for concentrated suspensions containing bubbles. In contrast to the literature, an analytical procedure is used to determine the solution of a pipe flow more accurately. The results are presented and discussed with respect to the Reynolds number Re and capillary number Ca. If Ca 1, a bubble suspension has a parabolic velocity profile indicating a Newtonian rheology. If Ca ≈1, two regimes of flow are observed in agreement with the literature;that is, an inner plug flow where deformation rates are low and an outer flow where deformation rates are high. These results imply that, if Ca ∅?and that, if Ca ≥1, the opposite effect occurs;that is, the Reynolds number Re increases with increasing gas volume fraction.展开更多
文摘The literature model studied in this article describes bubble formation and growth in a highly viscous polymer liquid with support of a gaseous matter dispersed under pressure before foaming. The foam growth is induced by the application of vacuum and mass transport of volatile components dissolved in the polymer liquid. Based on this literature model, aeration processes are calculated for intermediate viscosity and low viscosity biological systems, as they are of interest for biomatter foams, in particular for food foams in industrial processes. At the end of this article, the numerical results are presented and discussed.
文摘The steady laminar pipe flow of a suspension with a gas volume fraction ∅≤0.5 and small or intermediate bubble deformations in long, and straight sections of a circular pipe is calculated. The calculations are based on the constitutive equation that was originally derived for dilute emulsions and further developed for concentrated suspensions containing bubbles. In contrast to the literature, an analytical procedure is used to determine the solution of a pipe flow more accurately. The results are presented and discussed with respect to the Reynolds number Re and capillary number Ca. If Ca 1, a bubble suspension has a parabolic velocity profile indicating a Newtonian rheology. If Ca ≈1, two regimes of flow are observed in agreement with the literature;that is, an inner plug flow where deformation rates are low and an outer flow where deformation rates are high. These results imply that, if Ca ∅?and that, if Ca ≥1, the opposite effect occurs;that is, the Reynolds number Re increases with increasing gas volume fraction.
