Flow and mass transfer of fully resolved bubbles in non‐Newtonian fluids

Abstract

In this work, high-resolution 2-D numerical simulations were performed on the motion of deformable bubbles in non-Newtonian fluids and the associated mass transfer. For that purpose, we have implemented a semi-Lagrangian advection scheme and improved the fluid dynamic calculation by the usage of implicit algorithms. Non-Newtonian fluids are described by generalized Newtonian as well as viscoelastic model fluids. As shear-thinning model we use a Power-Law and a Carreau-Yasuda model, the viscoelastic fluid simulations are based on an Upper-Convected Maxwell model combined with a recently introduced model for the evolution of the effective shear rate. The mathematical challenges arising from the hyperbolic nature of the resulting set of equations are addressed by inclusion of artificial diffusion in the stress equation. In our work, it was found that shear thinning effects have impact on collision rates, and therefore, may influence coalescence of bubbles in non-Newtonian liquids. Furthermore, for the first time, concentration fields of dissolved gas in viscoelastic fluids are presented. The study shows that the fluid elasticity plays a major role for bubble rise velocity, and therefore, mass transfer. As the wake dynamics differ significantly from that in Newtonian liquids, abnormal mixing characteristics can be expected in the bubbly flow of viscoelastic fluids. 2007 American Institute of Chemical Engineers AIChE J, 53: [1861][1862][1863][1864][1865][1866][1867][1868][1869][1870][1871][1872][1873][1874][1875][1876][1877][1878] 2007 Keywords: numerical simulation, bubbles, non-Newtonian liquids, mass transfer IntroductionBecause of persistent uncertainties in the underlying models and system properties, the scale-up of bioreactors remains a challenging problem. For example, the rheology of media in bioreactors is non-Newtonian in most cases. [1][2][3][4][5][6][7][8] However, details of the non-Newtonian fluid characteristics, such as viscoelasticity or the tendency for shear thinning, are frequently unknown or neglected. Furthermore, in contrast to Newtonian media, there is a lack of general correlations for mass and heat transfer rates, which are needed for the prediction of oxygen supply and heat removal. Similar observations can be made for the properties needed to precisely predict transport of metabolites, nutrients, or CO 2 . So far, most studies are based on experimental investigations, which are usually interpreted with simple theoretical models. 3,4,[8][9][10][11] principles methods to predict mass-transfer coefficients, transport rates, and other parameters in non-Newtonian fluids have not been reported so far. Local mass transfer is not the only micro-effect of central importance in the design of bioreactors. Knowledge of the localized forces, such as shear and normal stresses in the cell's microenvironment, is also a key for determining whether a bioreactor is suitable to handle sensitive biosystems.12 Subcritical shear stresses found in the hydrodynamic environment of large-scale reactors may redu...

Numerical simulation of a bubble rising in shear-thinning fluids

“…Ohta et al [9,10] explored both experimentally and numerically the motion of a Newtonian, spherical and deformable drop rising in shearthinning fluids using the VOF method. Radl et al [11,12] Newtonian fluids and associated mass transfer using first principle methods. As the stability of numerical schemes depends strongly on the ratio between liquid and gaseous phase densities and viscosities, the above investigations [7,8,11,12] represent the bubble using a Newtonian drop of low density.…”

“…Radl et al [11,12] Newtonian fluids and associated mass transfer using first principle methods. As the stability of numerical schemes depends strongly on the ratio between liquid and gaseous phase densities and viscosities, the above investigations [7,8,11,12] represent the bubble using a Newtonian drop of low density. That is, the density and viscosity ratios of liquid over gas phase were up only to 10, which was much lower than that in real cases ( l / g ∼ 10 3 and Á l /Á g ∼ 10 4 ).…”

Numerical Simulation of the Solute‐Induced Marangoni Effect with the Semi‐Lagrangian Advection Scheme

“…In this work, the semi-Lagrangian convection scheme [25] is introduced to give an accurate and stable resolution of the convection term in an Eulerian cylindrical coordinates grid. This is achieved by choosing a set of points, referred as departure points, which would exactly arrive at Eulerian grid nodes, referred as arrival points.…”

“…In this work, to overcome the defect of the above literature work, the semi-Lagrangian convection scheme [24,25] is introduced to eliminate artificial diffusion and give an accurate and stable resolution of the convection term in an Eulerian cylindrical coordinates grid. The improved level set method and the concentration transformation method [21] are applied to capture the free interface of a deformable drop with acceptable mass conservation and deal with the discontinuity of solute concentration across the interface.…”

VOF-based simulation of conjugate mass transfer from freely moving fluid particles

“…a constant concentration value inside the bubble is assumed. Radl et al [5] performed 2D simulations of deformable bubbles and bubble swarms with mass transfer in non-Newtonian liquids using a semi-Lagrangian advection scheme. To prevent stability problems, a reduced density ratio between gas and liquid is used there.…”