Study of non-equilibrium interactions between an air bubble and a hydrophilic/hydrophobic solid surface with the non-linearized Stokes-Reynolds-Young-Laplace model (NSRYL model)

• Author / Creator

  Shahalami, Seyedehmansoureh

• The interaction between bubbles and solid surfaces is important to a broad range of industrial and biological processes. Various experimental techniques have been developed to measure the interactions of bubbles approaching solids in a liquid. In this thesis the consistency and accuracy of such measurement are tested against Stokes-Reynolds-Young-Laplace model in which the augmented Young Laplace equation is linearized within the interaction zone. The main focus of this thesis is to model thin liquid film drainage using the non-linearized Young Laplace equation in combination with the Stokes Reynolds equation. The scaled equations of the non-linearized SRYL model do not have a universal nature and depend on the physical parameters of system via capillary number. The numerical results show that in contrast to the linearized SRYL model, the hydrodynamic resistance force predicted from the non-linearized SRYL model strongly depends on the capillary number, Ca. The non-linearized SRYL model is compared with the linearized SRYL model at a broad range of capillary number from 10-8 to 10-3. The numerical results show that at low Ca number of 10-8 and smaller, both the non-linearized and linearized SRYL models lead to the same prediction for bubble deformation, time dependent force and hydrodynamic force. Therefore, over this range of Ca number both the non-linearized and linearized SRYL models can be confidently used to obtain the spatial and temporal evolutions of the film profile, once these models are shown to be able to give an accurate prediction of time dependent force profiles. For systems of Ca number larger than 10-8, the linearized SRYL model predicts a stronger hydrodynamic repulsive force, and the maximum difference in prediction between the two models occurs at the Ca number around ~ 3.4×10-5. The numerical results show that in comparison with the non-linearized SRYL model at the same rmax (the boundary of the solution domain), the linearized SRYL model overestimates the hydrodynamic resistance force for the Ca numbers tested which in turn influences the prediction of bubble deformation and time dependent force profiles. However over this high Ca number range, both the non-linearized and linearized SRYL models can predict the same time dependent force profiles with different overlaps (different adjustable parameters), while there are differences in the prediction of bubble shape and hydrodynamic repulsive force. Therefore, even if the linearized SRYL model is shown to be able to give an accurate prediction for time variations of the interaction forces over this range of Ca numbers, we cannot confidently use the linearized SRYL model to predict the spatial and temporal evolutions of the shape of the film trapped between interacting interfaces. Validation of simulation results by thin film profile measurement using thin film force apparatus (TFFA), conclude that the non-linearized SRYL model is more accurate for high Ca number systems. For a system of very high capillary numbers the non-linearized SRYL model predicts a solid-like bubble that does not deform in the approach phase. In contrast, the linearized SRYL model is unable to show the bubble rigidity at high capillary numbers. Furthermore the non-linearized SRYL model is able to predict the critical bubble approach velocity above which the bubble behaves like a solid sphere. This study shows that the non-linearized SRYL model is needed to study the effect of individual parameters of system such as bubble size, interfacial tension and liquid viscosity on the critical bubble approach velocity at which bubble behaves like a solid sphere. The non-linearized SRYL model is used to model the measurements of the recently developed integrated thin film drainage apparatus (ITFDA) which has been used to measure the bubble-particle interactions over a wide range of hydrodynamic conditions. The excellent agreement between the predicted and measured interaction forces between an air bubble and solid surface in three liquids of very distinct physicochemical properties demonstrates that the non-linearized SRYL model can be applied to the systems of a wider range of bubble approach velocity, liquid interfacial tension and viscosity. The excellent agreement suggests that the non-linearized SRYL model can be used to obtain quantitative information on film profiles during the bubble approach-retract cycle. The simulation results indicate that the minimum film thickness between an air bubble and hydrophilic solid surface in a liquid over a given approach period is thinner for the system of low bubble approach velocity, and/or low viscosity and high surface tension of the liquids. In this thesis the non-linearized SRYL is further developed to account for the effect of solid surface hydrophobicity. The experimental data quantified with the integrated thin film drainage apparatus (ITFDA) and the thin film force apparatus (TFFA) was used to validate the extended non-linearized SRYL model. The hydrophobic force which was considered as the driving force for destabilizing water films on hydrophobic surface was evaluated with the best fit between the measured and predicted time evolution forces. The numerical results showed that the longer-range hydrophobic force with increasing the surface hydrophobicity was responsible for film rupture. The effect of surface hydrophobicity and bubble approach velocity on the drainage rate of intervening liquid film was studied. The results showed that the wetting films formed on hydrophobic glass sphere of increasing surface hydrophobicity, thin much faster. Film drainage resistance or force barrier are determined to reduce greatly with increasing the solid surface hydrophobicity. Moreover the film drainage resistance or force barrier is found to increase with increasing bubble approach velocity. Decreasing bubble approach velocity or/and increasing surface hydrophobicity are found to decrease the film radius. As a result the film ruptures at locations closer to the center of the film. The extended non-linearized SRYL model incorporating proper form of hydrophobic force is able to predict the critical film thickness where the film ruptures. The prediction of the critical film thickness is achieved by solving non-linear SRYL equations without simplifications. The simulation results indicate that the critical film thickness increases with increasing surface hydrophobicity and bubble approach velocity.

• Subjects / Keywords

  • Hydrodynamic force
  • Induction time
  • Critical film thickness
  • Film drainage dynamics
  • Hydrophobicity
  • Bubble-particle interaction

• Graduation date

  Fall 2014

• Type of Item

  Thesis

• Degree

  Doctor of Philosophy

• DOI

  https://doi.org/10.7939/R3154DX4D

• License

  This thesis is made available by the University of Alberta Libraries with permission of the copyright owner solely for non-commercial purposes. This thesis, or any portion thereof, may not otherwise be copied or reproduced without the written consent of the copyright owner, except to the extent permitted by Canadian copyright law.