Bubble drag in contaminated non‐newtonian solutions

Abstract

The motion of a bubble in an infinite fluid is examined in the case where the surrounding fluid is nowNewtonian and contains impurities. An expression is developed for the drag force as a function of the shear-thinning character as well as of the concentration of surfactant of the fluid. The obtained expression for the drag force correlates quite nicely with experimental data for small bubbles.On examine le deplacement d'une bulle dans un fluide infini dans le cas ou le fluide environnant est non newtonien et contient des impuretes. Une expression est etablie pour la force de trainee en fonction du caractere rhkofluidifiant ainsi que de la concentration en surfactant du fluide. L'expression obtenue pour la force de trainee concorde assez bien avec les donnees experimentales pour des petites bulles.Keywords: bubble, drag force, contaminated non-Newtonian fluids.he motion of gaseous particles is of great importance in T chemical engineering since it is encountered in many unit operations, especially in bubble columns, Some examples are given in De Kee et al.( 1996). Most of the literature on the subject of the motion of a gas bubble in an infinite fluid has been confined to the case of uncontaminated Newtonian fluids. Unfortunately most industrial processes need to add other substances to the raw materials so as to increase the efficiency. This leads to the presence of impurities and the rheology of the fluids becomes complex. That is to say, long chain molecules and surface active agents can be present in small amounts. These two factors cause variable viscosity, elasticity and surface tension gradients. These effects are known to modify the hydrodynamics and the mass transfer of such multiphase systems. For example, polymer additives are known to produce a certain level of drag reduction and surfactants are known to retard interfacial motion and to increase the drag by setting up Marangoni stresses at the gas-liquid interface (Rodrigue et al., 1997). Keeping in mind that the drag force is a function of both viscosity and surface tension, the main objective of this note is to derive a convenient expression for the approximation of the drag force acting on a single gas bubble rising freely in an inelastic shear-thinning fluid containing surfactants. We note that the presence of a surfactant leads to an increase in drag and an increase in the shear rate. This in turn, lowers the viscosity of a shear-thinning fluid resulting in a lower drag. Thus it seems that one tends to counterbalance the other. The expression derived being valid only in the limit described herein. ResultsSolving the conservation equations analytically is a difficult task since momentum and mass transfer are coupled. In the past, several approximations have been made in order to decouple these equations and to obtain limiting cases such as the uniformly retarded motion and the stagnant cap approximations. A recent review on this subject is available in Rodrigue et al. (1997). Here we will approximate the drag *Author to whom correspondence should ...

Effect of the Surfactant Concentration on the Rise of Gas Bubbles in Power-Law Non-Newtonian Liquids

“…The average value of the surface tension was 0.063 N/m. These results agree well with previously published data 8 and show that the surfactant concentrations used are well below the critical micelle concentration.…”

“…[4][5][6] It has been shown that, in general, bubbles rising in pure liquids, containing no surfactants, have higher terminal velocities than bubbles rising in surfactant-containing liquids. [7][8][9][10] When gas bubbles are released into a solution containing a surfactant, the latter will accumulate on the liquid-gas interface created by the bubble and solution. They found that the presence of a surfactant would decrease the bubble velocity.…”

Effects of Contamination and Shear-Thinning Fluid Viscosity on Drag Behavior of Spherical Bubbles

“…For instance, Rodrigue et al 27 experimentally investigated the rising velocity of contaminated bubbles in Carreau model fluids and presented a correlation. Subsequently, they 28 employed the standard perturbation technique to obtain an approximate expression for drag of a contaminated bubble in Carreau model fluids in the limit of small Carreau numbers and Reynolds numbers, i.e., for weak shear-thinning and inertial conditions. In a later study, they 29 employed a thermodynamic approach (which assumes linear deviation in the surface tension from the equilibrium value) and a physical approximation (based on geometry and boundary conditions) in the limit of small Reynolds numbers.…”

Motion of partially contaminated bubbles in power-law liquids: Effect of wall retardation

“…Rodrigue et al (1996Rodrigue et al ( , 1997 experimentally and theoretically investigated the rising velocity of contaminated bubbles in Carreau model non-Newtonian fluids in the limit of small Carreau numbers. By the use of a thermodynamic approach and a physical approximation, Rodrigue et al (1999) further studied the rise of bubbles in power-law and Carreau model type non-Newtonian fluids in the limit of small Reynolds number.…”