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The impact of pressure oscillations on bubble rising in shear-thinning fluids

Mario Riccio, Marco De Corato

TL;DR

This study investigates how externally applied periodic pressure affects the rise of millimeter-scale bubbles in a shear-thinning fluid modeled by the Carreau–Yasuda constitutive equation. By solving the fully coupled Navier–Stokes equations using an ALE framework, the authors capture bubble deformation, gas-volume fluctuations, and viscosity thinning, revealing that pressure-driven volume changes induce large local strain rates that dramatically reduce drag and boost rising speeds by orders of magnitude. The results show strong nonlinearity with multi-harmonic bubble kinematics and indicate unsteady/inertial effects may emerge under driving, particularly at higher amplitudes, frequencies, and bubble sizes. While qualitatively consistent with Iwata et al. experiments, quantitative discrepancies point to missing viscoelastic effects, suggesting future work should incorporate elasticity to bridge the gap and enable more accurate predictions for industrial degassing and related processes.

Abstract

We study the rising dynamics of a bubble driven into periodic volumetric oscillations by an external pressure driving within a highly viscous shear-thinning fluid. We perform axisymmetric direct numerical simulations employing the Carreau-Yasuda model to describe the rheological behavior of the fluid and the finite element method to discretize the equations. We carry out a parametric study of the bubble rising dynamics, changing the amplitude and the frequency of the external pressure driving, and the bubble radius. Due to the external pressure oscillations, the bubble undergoes volume changes that strain the liquid at much larger rates than those due to natural rising, causing the surrounding fluid viscosity to thin. The numerical results show that the rising dynamics become highly nonlinear and unsteady due to the interplay of the shear-thinning rheology and the external driving. As a result, the period-averaged rising velocity of the bubble can increase by orders of magnitude compared to its natural rising velocity. These nonlinear effects become progressively more important as the amplitude and the frequency of the pressure driving or the bubble radius are increased. Qualitatively, the simulation model agrees with previous experimental findings in terms of average rising velocity. However, the experiments exhibit terminal velocities that are smaller than those predicted numerically, along with differences in bubble shape during the ascent. These discrepancies may be attributed to modeling the fluid rheology as a generalized Newtonian fluid rather than as a viscoelastic one.

The impact of pressure oscillations on bubble rising in shear-thinning fluids

TL;DR

This study investigates how externally applied periodic pressure affects the rise of millimeter-scale bubbles in a shear-thinning fluid modeled by the Carreau–Yasuda constitutive equation. By solving the fully coupled Navier–Stokes equations using an ALE framework, the authors capture bubble deformation, gas-volume fluctuations, and viscosity thinning, revealing that pressure-driven volume changes induce large local strain rates that dramatically reduce drag and boost rising speeds by orders of magnitude. The results show strong nonlinearity with multi-harmonic bubble kinematics and indicate unsteady/inertial effects may emerge under driving, particularly at higher amplitudes, frequencies, and bubble sizes. While qualitatively consistent with Iwata et al. experiments, quantitative discrepancies point to missing viscoelastic effects, suggesting future work should incorporate elasticity to bridge the gap and enable more accurate predictions for industrial degassing and related processes.

Abstract

We study the rising dynamics of a bubble driven into periodic volumetric oscillations by an external pressure driving within a highly viscous shear-thinning fluid. We perform axisymmetric direct numerical simulations employing the Carreau-Yasuda model to describe the rheological behavior of the fluid and the finite element method to discretize the equations. We carry out a parametric study of the bubble rising dynamics, changing the amplitude and the frequency of the external pressure driving, and the bubble radius. Due to the external pressure oscillations, the bubble undergoes volume changes that strain the liquid at much larger rates than those due to natural rising, causing the surrounding fluid viscosity to thin. The numerical results show that the rising dynamics become highly nonlinear and unsteady due to the interplay of the shear-thinning rheology and the external driving. As a result, the period-averaged rising velocity of the bubble can increase by orders of magnitude compared to its natural rising velocity. These nonlinear effects become progressively more important as the amplitude and the frequency of the pressure driving or the bubble radius are increased. Qualitatively, the simulation model agrees with previous experimental findings in terms of average rising velocity. However, the experiments exhibit terminal velocities that are smaller than those predicted numerically, along with differences in bubble shape during the ascent. These discrepancies may be attributed to modeling the fluid rheology as a generalized Newtonian fluid rather than as a viscoelastic one.
Paper Structure (8 sections, 18 equations, 11 figures, 2 tables)

This paper contains 8 sections, 18 equations, 11 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Governing equations
  3. Characteristic dimensionless numbers
  4. Validation of the code
  5. Results
  6. Comparison with Iwata Experiments
  7. Conclusions
  8. Data Availability Statement

Figures (11)

  • Figure 1: Sketch of the axisymmetric computational domain used in this study. A fixed cylindrical reference frame is employed. The bubble is initially a sphere of radius $R$ placed at the origin and is suspended in a shear-thinning fluid. A periodic disturbance to the hydrostatic pressure is applied at the outer boundary $\Gamma_2$, which drives volumetric oscillation of the bubble.
  • Figure 2: Zoom view of the mesh used for simulations. (a) Undeformed the mesh for a bubble of $R=1\rm{mm}$ at time $t=0$. (b) Deformed mesh for the maximum deformation. The plotted case is for a $k=0.75$ and for $f = 10 \ \text{Hz}$
  • Figure 3: Mesh convergence study for two different mesh resolutions. We consider the bubble volume normalized with respect its initial value as a mesh convergence metric in function of the time normalized with the period $T = 1 \ s$. Increasing the number of elements, $N_e$, by 2000 results in nearly identical curves, indicating that the results are independent of the mesh.
  • Figure 4: Temporal evolution of the bubble radius and radial velocity for $f = 10~\text{Hz}$ and $R = 0.5~\text{mm}$. In panel (a), the radius of the bubble is plotted for different driving amplitudes. In panel (b), the radial velocity of the bubble, normalized by the bubble natural rising velocity, is shown. The time is normalized by the period of the external pressure driving $T=1/f$.
  • Figure 5: Panels (a-c), snapshots of the normalized viscosity field with respect to the zero-shear viscosity. The bubble is shown in red, for comparison. Panel (d), radius of the bubble as a function of time, inside the plot are marked the radii values for each panel (a-c). Panel (e) external driving pressure as a function of time. The parameters used in these figures are $(f, k, R) = (300~\text{Hz}, 0.75, 0.5~\text{mm})$.
  • ...and 6 more figures