Foam free drainage and bubbles size for surfactant concentrations below the CMC

doi:10.1016/j.colsurfa.2015.09.050

Colloids and Surfaces A: Physicochemical and Engineering Aspects

Volume 487, 20 December 2015, Pages 92-103

https://doi.org/10.1016/j.colsurfa.2015.09.050 Get rights and content

Highlights

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Role of bubble size on the free drainage of moderately stable foams.
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Incorporation of data into the modified L–L model yields surface shear viscosity values.

Abstract

Foams produced with surfactant concentration below the Critical Micelle Concentration (CMC) are usually moderately stable due to high drainage rates and intense bubbles coarsening/coalescence. Aim of this work is to examine how such low surfactant concentration affects foam destabilization and elucidate the interplay between free drainage and bubble size variation. Foam destabilization experiments are conducted at varying SDS concentrations (below the CMC) where the evolution of liquid fraction and bubbles size is registered simultaneously. Instantaneous volume measurements of the drained liquid and the remaining foam yield the evolution of the global liquid fraction and drainage rate in the foam. Continuous electrical conductance measurements give the local liquid fraction and drainage rate in the foam. Microphotographs allow estimation of bubble size distribution and bubble population at regular time intervals. The present data show that the lifetime of moderately stable foams depend largely on surfactant concentration below the CMC but this effect does not scale linearly with surfactant concentration. Furthermore, measurements are fitted to semi-empirical expressions and are compared to a modified Leonard and Lemlich (L–L) drainage model that has been expanded to incorporate bubble size evolution. The latter is a rough approximation based on certain assumptions but it is a fair approach given the excessive difficulty of detailed numerical calculations. The comparison reveals the significant role of bubble size on the free drainage of moderately stable foams. Interestingly, incorporation of global liquid fraction data into the modified L–L model yields surface shear viscosity values in agreement with literature.

Graphical abstract

Introduction

A foam comprises a mixture of liquid and bubbles, stabilized by surfactant, having an anisotropic distribution of liquid fraction and bubble size that both evolve dynamically [3], [36]. Free foam drainage is a complex process since each of the following may take place simultaneously: gravitational liquid flow (liquid drains out of the foam chiefly through Plateau Borders (PB) and nodes), shear stresses imparted by the gas–liquid interfaces, capillarity induced liquid suction (opposing gravity especially at the foam bottom), bubbles size increase and bubble population decrease because of coalescence (merging of adjacent bubbles as result of rupture of the liquid films between them), and coarsening (enlargement of large bubbles by gas diffusion from smaller adjacent bubbles due to pressure differential between bubbles of unequal size-Ostwald ripening) [3].

The presence of surfactants in a foam can, in principle, influence both the gas–liquid interfacial properties (e.g., surface tension, surface dilatational viscosity, surface shear viscosity, surface elasticity) and the bulk liquid viscosity. Yet, for the bulk viscosity to be affected very large concentrations -well above the CMC- are required. Many preceding works (extended reviews on this topic can be found elsewhere e.g. [9], [44] have shown that the type and concentration of surfactant modifies considerably the gas–liquid interfacial properties and, therefore, can change the flow type inside the foam’s liquid network (i.e. PB, nodes and films) and can lead to significant alteration of drainage rates. However, most studies examine the above either in foam systems that maintain their initial bubbles size during drainage (i.e. surfactant concentrations well above the CMC and at high liquid fractions) or/and overlook the evolution of bubbles size, e.g., Cervantes-Martinez et al. [8], Boos et al. [3].

Several works have shown that bubble size evolution due to coarsening and free foam drainage are closely interrelated. Hilgenfeldt et al. [18], have shown that strong bubble coarsening leads to shorter drainage time (accelerated drainage) which is independent from the initial liquid content, ϵ₀. Both Magrabi et al. [25] and Vera and Durian [47] measured bubble size and liquid void fraction at various positions along the foam column during free drainage. Magrabi et al. [25] concluded that at their particular system, foam destabilization takes place at three stages: initially (<200s) drainage dominates over coarsening, later (200s–900s) drainage and coarsening occur concurrently and eventually (>900s) coarsening prevails over drainage. Vera and Durian [47] measured increased coarsening rates for drier foams and suggested that coarsening plays an unavoidable role in free drainage. Saint-Jalmes and Langevin [36] studied the coupling between drainage and coarsening of aqueous foams and showed that the type of flow inside the PBs depends on both bubbles size and gas–liquid interfacial properties. The above works do not take into account the effect of the type or/and surfactant concentration on the interaction between drainage and coarsening and, additionally, consider bubbles coalescence negligible.

It is known that for low surfactant concentrations, especially below the CMC, bubble coalescence may contribute significantly to bubble size variation during foam destabilization [10]. To the best of our knowledge, only Carrier and Colin [7], isolated bubble coalescence from coarsening by using a mixture of gases that has very low mass diffusivity in water. These authors examined the influence of various surfactants (i.e. SDBS and TTAB) at different concentrations on the interplay between coalescence and free drainage. They found that coalescence is dramatically enhanced below a critical liquid fraction which depends on the surfactant concentration and nature of the surfactant but does not depend on bubble size.

The only systematic work that we were able to identify on foam free drainage using surfactant below the CMC is that by Harvey et al. [17] These authors studied the effect of different types (i.e. Dowfroth-250, Dowfroth-400 and SDS) and different concentrations of surfactants (always below the CMC) on foam lifetime and on initial bubbles size. They showed that foam stability is controlled not only by the liquid drainage process, which is a function of surface shear viscosity, μ_s, but also by coalescence which is a function of other interfacial properties (e.g. surface dilatational viscosity of adsorbed layers). However, this study, being chiefly of technological orientation, did not investigate the effect of surfactant concentration on the evolution of bubble size and liquid fraction during foam drainage.

Scope of this work is to study the influence of surfactant concentration below the CMC on the interplay between bubbles size evolution (due to coarsening and coalescence) and free drainage. Surfactant concentrations below the CMC are used, because at these concentrations foams are only moderately stable. Novel data are presented concerning bubble size evolution and liquid fraction profiles both locally (electrical resistance measurements) and globally (volumetric measurements) for various surfactant concentrations. Additionally, it is examined if the present findings can be described by the well known drainage model of Leonard and Lemlich (1965, L–L model) [53] after incorporating the experimentally observed bubble size evolution to cope with coarsening and coalescence. In the following sections, the foam preparation procedure and a few essential physicochemical properties of the foam solution are presented first, being followed by an outline of the experimental setup and the employed measuring techniques. A section comes next with experimental results and discussion on the underlying phenomena.

Section snippets

Foam preparation

Surfactant solutions are produced using deionized water and sodium dodecyl sulfate (SDS ≥ 98% purity; Fluka). Foams are produced employing four concentrations of SDS (300, 600, 1000 and 2000 ppm) which are below the reported CMC value at 30 °C (∼2500 ppm). SDS is known for producing foams unstable with respect to coalescence [12]. A small amount of NaCl 4 × 10⁻³ M; (≥99% purity Merk) is added to deionized water to yield the ionic strength met in applications where foams are produced from fresh

Evolution of drained liquid volume and foam volume

Table 1 presents initial foam volume produced by whipping 200 ml of the different surfactant solutions. As surfactant concentration increases foamability increases, too. This means that less initial liquid volume, V_L,0 is used to produce the same initial amount of foam, V_F,0and as a result the foam becomes dryer and more stable (i.e. initial global liquid fraction, ϵ₀, decreases). Fig. 2a presents the evolution of foam volume, V_F, and drained liquid volume, V_L, for different surfactant

Comparison with model

Relation of measurable global drainage quantities to characteristics of a foam is not straightforward since free drainage is difficult to analyze. The situation is different from that of forced drainage where the front velocity is an easily measured variable directly related to foam characteristics [43]. In case of free drainage, there is a continuous spatio-temporal evolution of liquid fraction from the initial to the equilibrium state. This means that a complex spatially distributed foam

Conclusions

In this study we examine the effect of varying surfactant concentrations below the CMC on the free drainage of moderately stable foams. In such systems high drainage rates are combined with intense bubbles coarsening and coalescence.

Larger surfactant concentrations result to dryer foams, with a more packed structure. Concerning the drainage process, the successful fitting of a sigmoid equation on the drainage data reveals a maximum value on the drainage rate profiles. This maximum value is the

Acknowledgments

The present activity was under the umbrella of COST Actions MP1106 and CM1101 and the European Space Agency funded programs: FASES (Fundamental and Applied Studies of Emulsion Stability) and PASTA (PArticle STAbilised Emulsions and Foams).

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Foam free drainage and bubbles size for surfactant concentrations below the CMC

Highlights

Abstract

Graphical abstract

Introduction

Section snippets

Foam preparation

Evolution of drained liquid volume and foam volume

Comparison with model

Conclusions

Acknowledgments

Colloids Surf. A Physicochemical Eng. Aspects

LWT-Food Sci. Technol.

J. Colloid Interface Sci.

Int. J. Miner. Process.

Miner. Eng.

Colloids Surfaces A: Physicochem. Eng. Aspects

Chem. Eng. Sci.

Curr. Opin. Colloid Interface Sci.

Colloids Surf. A Physicochemical Eng. Aspects

J. Colloid Interface Sci.

J. Colloid Interface Sci.

Chem. Eng. Sci.

J. Colloid Interface Sci.

J. Colloid Interface Sci.

J. Colloid Interface Sci.

Chem. Eng. Sci.

Colloids Surf. A Physicochemical Eng. Aspects

Colloids Surf. A Physicochemical Eng. Aspects

Colloids Surfaces A Physicochemical Eng. Aspects

J. Food Eng.

Chem. Eng. Sci.

Minerals Eng.

Decay of standing foams: drainage, coalescence and collapse

Adv. Colloid Interface Sci.

Protocol for studying aqueous foams stabilized by surfactant mixtures

J. Surfactants Deterg.

Foams Struct. Dyn.

Coalescence in draining foams

Langmuir

The role of surfactant type and bubble surface mobility in foam rheology

Soft Matter

Physicochemical approach to the theory of foam drainage

Eur. Phys. J. E