Drop and Bubble Shape Analysis

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... 

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 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]. 

H.M. Princen, The Equilibrium Shape of Interfaces, Drops and Bubbles. Rigid and Deformable Particles at Interfaces, in Surface and Colloid Science, E. Matijevic, Ed., Wiley-Interscience (1969), 1. (Analysis of a variety of shapes, including those around floating fluid or solid objects.)... 

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. 

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... 

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... 

Fig. 12. Typical results reported by Tomiyama ei al. (1993) on the effect of the Morton number M (atEotvSs number Eo = 10) on the shape and dynamics of a single bubble rising in (a) a Newtonian liquid, and (b) graphical correlation due to Grace (1973) and Grace et al. (1976). [Part (a) reprinted from Nuclear Engineering and Design, Volume 141, Tomiyama, A., Zun, I., Sou, A., and Sakaguchi, T., Numerical analysis of bubble motion with the VOF method, pp. 69-82, Copyright 1993, with permission from Elsevier Science. Part (b) reprinted from Grace, R., Clift, R., and Weber, M.E., Bubbles, Drops, and Particles. Academic Press, Orlando, 1976. Reprinted by permission of Academic Press.)...

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. 

One point that has not been emphasized is that all of the preceding analysis and discussion pertains only to the steady-state problem. From this type of analysis, we cannot deduce anything about the stability of the spherical (Hadamard Rybczynski) shape. In particular, if a drop or bubble is initially nonspherical or is perturbed to a nonspherical shape, we cannot ascertain whether the drop will evolve toward a steady, spherical shape. The answer to this question requires additional analysis that is not given here. The result of this analysis26 is that the spherical shape is stable to infinitesimal perturbations of shape for all finite capillary numbers but is unstable in the limit Ca = oo (y = 0). In the latter case, a drop that is initially elongated in the direction of motion is predicted to develop a tail. A drop that is initially flattened in the direction of motion, on the other hand, is predicted to develop an indentation at the rear. Further analysis is required to determine whether the magnitude of the shape perturbation is a factor in the stability of the spherical shape for arbitrary, finite Ca.21 Again, the details are not presented here. The result is that finite deformation can lead to instability even for finite Ca. Once unstable, the drop behavior for finite Ca is qualitatively similar to that predicted for infinitesimal perturbations of shape at Ca = oo that is, oblate drops form an indentation at the rear, and prolate drops form a tail. 

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]. 

The analysis of many technological processes involving dissolution, extraction, vaporization, combustion, chemical transformations in dispersions, sedimentation of colloids, etc. are based on the solution of the problem of mass exchange between particles, drops, or bubbles and the ambient medium. For example, in industry one often deals with processes of extraction from drops or bubbles or with heterogeneous transformations on the surface of catalyst particles suspended in a fluid. The rate of extraction and the intensity of a catalytic process to a large extent are determined by the value of the total diffusion flux of a reactant to the surface of particles of the disperse phase, which, in turn, depends on the character of flow and the particle shape, the influence of neighboring particles, the kinetics of the surface chemical reaction, and some other factors. 

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... 

The analysis in Subset II may point to the choice of countercurrent operation through a packed bed. The most commonly used regimes here are trickle flow and bubble flow. The possibility of flooding places an important constraint on the choice of the operating gas and liquid flow velocities. The pressure drop is significant for small catalyst particles this precludes countercurrent operation unless shaped catalyst particles are used. 

E.A. Boucher, Capillary Phenomena Properties of Systems with Fluid/Fluid Interfaces, Rep. Progr. Phys. 43 (1980) 496-546. (Analysis of basic capillarity laws, application to the shapes of drops, bubbles, holms and fluid bridges and the determination of interfacial tensions.)... 

The analysis of the preceding section was carried out by use of a spherical coordinate system, but the majority of the results are valid for an axisymmetric body of arbitrary shape. The necessity to specify a particular particle geometry occurs only when we apply boundary conditions on the particle surface (that is, when we evaluate the coefficients Cn and Dn in the spherical coordinate form of the solution). For this purpose, an exact solution requires that the body surface be a coordinate surface in the coordinate system that is used, and this effectively restricts the application of (7-149) to streaming flow past spherical bodies, which may be solid, as subsequently considered, or spherical bubbles or drops, as considered in section H. 

---