Bubble shape analysis

The apparatus used in the present study is based on the axi-symmetric bubble shape analysis, i.e., a firmly established technique for the measurement of static and dynamic surface tension as well as of the geometrical properties of the bubble (Loglio et al. 1996, 2001, Kovalchuk et al. 2001, Miller et al. 2000, Rusanov and Prokhorov 1996, Neumann and Spelt 1996, Cheu et al. 1998). In essence, the shape of a bubble (or of a drop) is determined by a combination of surface tension and gravity effects. Surface forces tend to make drops and bubbles spherical whereas gravity tends to elongate them. 

Loglio G, Pandolfini P, Tesei U, and Noskov B (1998b) Measurements of interfacial properties with the axisymmetric bubble-shape analysis technique effects of vibrations. Colloids Surfaces A 143 301-310 Loglio G, Pandolfini P, Miller R, Makievski AV, Ravera F, Ferrari M and Liggieri L (2001) "Drop and Bubble Shape Analysis as Tool for Dilational Rheology Studies of Interfacial Layers", in "Novel Methods to Study Interfacial Layers", Studies in Interface Science, Vol. 11, D. Mobius and R. Miller (Eds.), Elsevier, Amsterdam, pp 439-485... 

The method with the largest capacity is obviously the drop and bubble shape analysis, in the literature often named ADSA. This methodology does not provide data at extremely short adsorption times, however, it has quite a number of advantages. First of all it is applicable to hquid/gas and hquid/liquid interfaces, it requires very small amounts of samples, and it is easy to temperature control. Moreover, it gives access to surface rheology. Equipped with an additional... 

Figure 26. Schematic of a drop or bubble shape analysis set-up...

Loglio, G. Pandolfmi, P Miller, R. Makievski, A. V. Ravera, R Ferrari, M. Lig-gieri, L. Drop and bubble shape analysis as tool for dUational rheology studies of interfacial layers. In Novel Methods to Study Interfacial Layers, Studies in Interface Science. Mobius, D. Miller, R., Eds., 2001 II, 439 84. 

Loglio G, Pandolflni P, Miller R, Makievski AV, Ravera R, Ferrari M, Liggieri L (2001) Drop and bubble shape analysis as a tool for dilational rheological studies of interfacial... 

Drop and Bubble Shape Analysis as a Tool for Dilational Rheological Studies of Interfacial Layers... 

The fundamentals of drop and bubble shape analysis have been discussed in detail above. In the next section examples are given to demonstrate the various applications of the profile analysis tensiometer. Besides dynamic surface and interfacial tensions, results are shown for trapezoidal and sinusoidal relaxation experiments from which the dilational elasticity can be derived. The experiments selected are not only for model surfactants of high chemical purity but also for technical surfactants for which effective data can be deduced. 

Makievski, A. V., Loglio, G., Kragel, J., Miller, R., Fainerman, V. B. and Neumann, A. W., Adsorption of protein layers at the water/air interface as studied by axisymmetric drop and bubble shape analysis, J. Phys. Chem., 103, 9557-9561 (1999). 

The axisymmetric drop shape analysis (see Section II-7B) developed by Neumann and co-workers has been applied to the evaluation of sessile drops or bubbles to determine contact angles between 50° and 180° [98]. In two such studies, Li, Neumann, and co-workers [99, 100] deduced the line tension from the drop size dependence of the contact angle and a modified Young equation... 

Newtonian liquid viscosity, U is the bubble velocity, and aQ is the equilibrium surface tension), where surface tension and viscous forces dominate the bubble shape (15). Using a lubrication analysis, Bretherton established that the bubble slides over a stationary, constant-thickness film whose thickness divided by the radius of the tube, h R., varies as the... 

Here we also consider sorption kinetics as the mass-transfer barrier to surfactant migration to and from the interface, and we follow the Levich framework. However, our analysis does not confine all surface-tension gradients to the constant thickness film. Rather, we treat the bubble shape and the surfactant distribution along the interface in a consistent fashion. 

Various experimental methods for dynamic surface tension measurements are available. Their operational timescales cover different time intervals. - Methods with a shorter characteristic operational time are the oscillating jet method, the oscillating bubble method, the fast-formed drop technique,the surface wave techniques, and the maximum bubble pressure method. Methods of longer characteristic operational time are the inclined plate method, the drop-weight/volume techniques, the funnel and overflowing cylinder methods, and the axisym-metric drop shape analysis (ADSA) " see References 54, 55, and 85 for a more detailed review. 

Bashforth F and Adams JC (1883) An attempt to test the capillary action, Cambridge University Press and Deighton Bell Co., Cambridge Chen P, Kwork DY, Prokop RM, del-Rio 01, Susnar SS and Neumann AW (1998) Axisymmetric drop shape analysis (ADSA) and its applications , in Drops and bubbles in interfacial research, D. Moebius and R. Miller Eds., Studies in Interface Science Series, Vol. 6, Elsevier, Amsterdam Dukhin SS, Kretzschmar G and R. Miller R (1995) Dynamic of adsorption at liquid interfaces. Theory, experiments, applications, D. Moebius and R. Miller Eds., Studies in Interface Science Series, Vol. 1, Elsevier, Amsterdam Joos P (1999) Dynamic Surface Phenomena, VSP, Utrecht, 1999 Kovalchuk VI, Zholkovskij EK, Kragel J, Miller R, Fainerman VB, Wiistneck R, Loglio G and Dukhin SS (2000) Bubble Oscillations in a Closed Cell. J Colloid Interface Sci 224 245-254... 

One complication is that the boundary conditions (4-264)-(4-266) must be applied at the bubble surface, which is both unknown [that is, specified in terms of functions R(t) and fn(9,tangent unit vectors n and t, that appear in the boundary conditions are also functions of the bubble shape. In this analysis, we use the small-deformation limit s 1 to simplify the problem by using the method of domain perturbations that was introduced earlier in this chapter. First, we note that the unit normal and tangent vectors can be approximated for small e in the forms... 

As the size of rising bubbles and drops grows, their shape tends to the equilibrium shape, which more and more differs from spherical. If for low and moderate Re and low We, the bubble shape is close to spherical, for moderate Re = 102 to 103 and We of the order of several units, the bubble shape may approximately be modeled by an oblate ellipsoid, and its trajectory by a helix. If We continues to grow, the bottom of the bubble becomes more and more flat. Finally, for We >10 and high Re the bubble acquires the shape of a turned-over cup or a spherical segment and rises along the vertical. A detailed analysis of various regimes is presented in [94]. 

Automated Droplet Tensiometer. Surface tension and surface dilational moduli were measured by an automated droplet tensiometer (ADT) (IT concept, France) as a function of ageing time of the droplet.22 Surface tension was determined by drop shape analysis of a gas bubble formed in a cuvette containing the protein solution. The bubble was illuminated by a uniform light source and its profile imaged and digitised by a CCD camera and a computer. The profile was used to calculate the surface tension using Laplace s equation. The... 

Onset of shape oscillation of a bubble also excites the translational motion of it. Since the forces on the bubble, which govern its translational motion, depend on the shape of the bubble, shape oscillation induces an imbalance on the position of the bubble, and its center of mass starts to move. When equations governing volume oscillations, shape oscillations, and translational motion are solved simultaneously, it reveals that any perturbation in any of these motions, if large enough, can excite other motiOTis. These motions are coupled leading to nonlinear behavior of bubbles under forced oscillation [44]. Excitation of translational motion was also interpreted as Self-propulsion of asymmetrically vibrating bubbles by Benjamin and Ellis [45] who used a nonlinear analysis to explain the so-called erratic motion of bubble in acoustic fields. 

The drop and bubble shape tensiometer allows one to perform oscillation experiments. However, in contrast to similar studies with small spherical drops it is limited to slow oscillations. Depending on the hydrodynamic conditions, mainly the rheological behaviour of the bulk phases, oscillation from a certain frequency onwards do not provide drops or bubbles with a Laplacian shape, so that the data analysis will fail and yield unrealistic data. Even for liquids of high grade of purity interfacial tension changes are simulated and hence misinterpretations can be the consequence. Thus, the use of high speed video technique is not really relevant for shape analysis tensiometry (although provided by several companies), as the hydrodynamic relaxation can take much time to yield Laplacian menisci. 

The examples have shown that the drop and bubble shape tensiometer PATl from SINTECH Berlin, Germany, is an accurate instrument with a large number of measurement procedures. It is shown that the mode of keeping the surface area constant is a vital prerequisite for experiments with bubbles. Only experiments with constant surface area give the opportunity for an easy data analysis of adsorption processes. It is demonstrated that experiments at the liquid/liquid interface provide extra information about distribution of the studied surfactant between the two adjacent phases, which is a measure for the HLB of this surfactant [76]. 

Figure 2 Theoretical analysis of the experimental data depicted in Figure 1 2a) Comparison between measured bubble shapes (symbols) and model fitting lines (Eqs.1,3) for difierent cooling rate conditions 2b) Comparison between toeoretically predicted temperature profiles (Eqs. 16-17) for the bubbles depicted in Figure 1.

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