J. Phys. Chem. C 2010, 114, 2273–2281
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The Interaction between a Very Small Rising Bubble and a Hydrophilic Titania Surface Luke Parkinson and John Ralston* Ian Wark Research Institute, UniVersity of South Australia, Mawson Lakes SA 5095, Australia ReceiVed: October 18, 2009; ReVised Manuscript ReceiVed: December 22, 2009
Very small bubbles are ideal for making measurements of both the film drainage process and the disjoining force between a bubble and a hydrophilic titania surface, immersed in water. Their small buoyancy, combined with high Laplace pressure, minimizes bubble deformation, in a flow regime where the Reynolds number approaches zero. We have used high-speed, dynamic, thin-film interferometry to measure film drainage rate and film thickness as a function of buoyancy force. Single gas bubbles, in the diameter range of 15-120 µm, were allowed to rise freely, before collision with a planar, hydrophilic titania surface. Experiments were conducted in 0 to 10-1 M aqueous KCl or (CH3)4NBr at pH 3.5 or pH 6.3, both below and above the titania isoelectric point. We have observed a transition in bubble boundary condition from full-slip to no-slip. Importantly, this effect is reversible and dependent on electrolyte pH, ionic strength, and film thickness. The true origin of these effects remains obscure; however, they seem to reflect the influence of surface conductance on flow through a charged capillary, particularly when the bulk conductance is small and κa is small. Introduction The hydrodynamic and surface force interaction between bubbles, as well as between bubbles and a solid, is of interest to many industrial processes, such as flotation, food processing, foam and froth behavior, and in biological systems. The rate at which two such bodies approach in a fluid is a balance between the driving force pushing them together and the opposing forces keeping them apart. Viscous hydrodynamic drag resists drainage of the intervening liquid and increases as the gap becomes thinner and the fluid more confined. This drag force changes drastically, depending on the nature of the hydrodynamic boundary conditions at the surface of the approaching bodies, particularly at small separations. The boundary conditions defining this flow will dramatically affect the kinetics of natural and industrial processes that rely on the interaction between bubbles, drops, and solids. Therefore, to properly understand and predict these processes, the nature of the drainage process and the physicochemical phenomena that influence it must be known. Our previous contributions to bubble-particle interactions have dealt with collision theory3,4 attachment,5 force measurement6 with applications,7 and stability.8 We now turn our attention to the behavior of a single bubble as it encounters a solid surface, focusing upon film drainage and interaction forces. The technique used in this study provides both high force and separation distance resolution with sensitive force measurements down to 10-11 N and beyond the limit probed by surface force and atomic force microscope colloid probe measurements. This allows dynamic measurements to be made where the force scale reflects that of natural bubble-particle interactions.9 The approach of a gas bubble and a solid is also influenced by surface forces at small separations. Electrical double-layer interactions between a charged solid and a bubble may either oppose or enhance the driving force at short-range, as the bubble is also known to be charged, though there is much argument as to its magnitude and even its sign.10-13 van der Waals interactions also affect the approach of a bubble and a particle in a * To whom correspondence should be addressed. E-mail: john.ralston@ unisa.edu.au. Phone: 61 8 8302 3066. Fax: 61 8 8302 3683.
liquid, for there is a repulsive interaction between the bubble and solid when the approach takes place in water. This repulsion stabilizes the thin intervening aqueous film at short separations and prevents film rupture when the solid is completely hydrophilic. In the case of a hydrophobic solid, surface decoration by nanosized bubbles may cause film rupture at long distances,9 while the hydrophobic interaction acts at short-range.14 The nature of film drainage and the magnitude and range of surface forces on the approach of a bubble to a solid are insufficiently understood, particularly in a dynamic interaction. For example, during the drainage of a thin film between a solid and a gas bubble, it is unknown whether or not there is a slip or no-slip hydrodynamic boundary condition at the liquid-vapor (LV) interface. The no-slip boundary condition accounts for drainage of a liquid from between two smooth, wetting solids.15-17 A gas bubble rising freely in water or electrolyte does so with complete mobility (i.e., complete slip) at the LV interface, when there are no surfactants present.11,18,19 It is, therefore, reasonable to expect that drainage of the thin liquid film between a wetting solid and a pristine bubble surface might occur with a no-slip boundary condition at the solid interface, yet with complete slip at the surface of the bubble. Connor et al.20,21 adapted a surface forces apparatus (SFA) to study the approach of a clean mercury drop to a mica plate. This technique was extended by Pushkarova and Horn22,23 to measure the interaction between a large, deformable captive bubble and a planar hydrophilic silica or mica surface. Using a drainage model that incorporates the Young-Laplace equation, modified to account for surface forces,24 the Reynolds equation described the observed drainage rates very closely, inferring a no-slip boundary condition at the LV interface. This was so even after drastic cleaning measures were taken to create a pristine interface. The same behavior was observed for the approach of a pristine mercury drop to a hydrophilic solid in aqueous electrolyte25 and between 50 µm oil drops26,27 in electrolyte solutions containing sodium dodecylsulphate. Practical investigations into the hydrodynamic boundary condition at liquid-liquid or gas-liquid interfaces are notori-
10.1021/jp9099754 2010 American Chemical Society Published on Web 01/15/2010
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J. Phys. Chem. C, Vol. 114, No. 5, 2010
ously complicated by the adsorption of trace surfactant contamination. Under tangential shear, a surface tension gradient opposes liquid motion at the interface,28 causing the bubble to behave as a solid. Surface tension measurements are commonly used as a test for the presence of surfactant contamination in a liquid. We have shown previously,18,19 by measuring the terminal rise velocity of very small gas bubbles, that trace contamination can change the boundary condition at the liquid-vapor interface from full-slip (Hadamard-Rybczynski rise velocity) to no-slip (Stokes rise velocity), at levels of contamination that are insufficient to induce any detectable change in surface tension (i.e.,
