Free drainage of aqueous foams stabilized by mixtures of a non-ionic (C12DMPO) and an ionic (C12TAB) surfactant

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Abstract

The study at hand investigates the influence of the composition of a surfactant mixture on the free drainage of the respective foams. The Foam Conductivity Apparatus (FCA) was used to study free drainage of foams of homogeneous initial liquid fraction εinit. The foams were stabilized with mixtures of the non-ionic surfactant dodecyldimethyl phosphineoxide (C12DMPO) and the cationic surfactant dodecyl trimethylammonium bromide (C12TAB) at mixing ratios of C12DMPO:C12TAB = 1:0, 50:1, 1:1, 1:50 and 0:1. In all cases the liquid fraction ε follows a power law with respect to time t, i.e. εtη with −1.0 < η < −0.8. The η-values are all very similar which indicates a Poiseuille-like flow (−1 < η < −2/3) for all samples irrespective of changes in composition and bubble size. For all studied mixtures drainage led to fairly dry foams (ε ∼ 10−3), which then either coalesce (C12DMPO and 50:1 mixture) or drain further (1:1 mixture). An evaluation of the critical liquid fraction εcrit (liquid fraction at which foam coalescence sets in abruptly) revealed that εcrit is independent of the foam height and the bubble size which is in line with literature. However, it depends on the composition of the surfactant mixture and decreases with increasing content of C12TAB.

Graphical abstract

Highlights

► Influence of the composition of a surfactant mixture, the bubble size and the initial liquid fraction on free drainage. ► Immobile surfaces and thus Poiseuille-like flow under all experimental conditions. ► Drainage behavior is not correlated with respective foam stabilities.

Introduction

In order to measure the drainage of aqueous foams one needs to determine the time evolution of the liquid fraction ε. The latter is typically calculated from the foam’s conductivity. Although the conductivity of aqueous foams has been investigated in numerous experimental studies [1], [2], [3], [4], [5], [6], conductivity measurements still need to be optimized [7], [8]. Recently, Karapantsios et al. examined critical design aspects for measuring the liquid fraction ε in foams such as electrode size, shape, separation distance, intrusiveness, excitation current frequency and multiplexing of electrical conductance probes [7]. Theoretical considerations of how to calculate the liquid fraction ε from the conductivity of a foam has made significant strides. Lemlich developed the relationship between the foam conductivity and its liquid fraction ε for low liquid fractions (ε  0) through theoretical analysis [9]. For high liquid fractions (ε  1) Lemlich [10] suggests to use the Maxwell formula [11]. Recently, Feitosa et al. successfully used an empirical relationship based on a large amount of current and historical experimental data to calculate liquid fractions from conductivity data over the entire ε range [12], [13].

The exponent η of power law fits to drainage curves (liquid fraction ε plotted as a function of time t) allows characterizing the surface mobility of the foam during drainage [14]. The surface mobility depends on the bubble size as well as on the interfacial and bulk properties [14], [15]. Indeed models predict that the surface mobility is inversely proportional to the bubble size [16]. In case of a high surface mobility the surfaces are fluid and mobile and a plug-like flow of the liquid through the Plateau Borders is observed [17], [18], [19], [20]. In the case of a low surface mobility the surfaces are rigid and immobile which results in a Poiseuille-like flow [16], [17], [20], [21], [22] and thus a slower drainage rate. The drainage regime depends on the type and concentration of the surfactant [23]. Another parameter of interest which is obtained via free drainage measurements is the critical liquid fraction εcrit, i.e. the liquid fraction at which the foam collapses[1], which, in turn, is an important parameter for foam stability [24].

Free drainage of aqueous foams stabilized by the non-ionic surfactant dodecyldimethyl phosphineoxide (C12DMPO), the cationic dodecyl trimethylammonium bromide (C12TAB), and their mixtures at mixing ratios of C12DMPO:C12TAB = 1:0, 50:1, 1:1, 1:50, and 0:1 are investigated in the present work. This work follows a line of studies on this particular mixture in which their respective water–air surfaces, foam films and foaming behaviour have been investigated [25], [26]. To truly characterise foams, it is necessary to also examine the individual components of the foam structure, namely the surfaces and the foam films. This has been demonstrated recently in an extensive study of mixtures of two non-ionic surfactants, namely hexaoxyethylene dodecyl ether (C12E6) and n-dodecyl-β-D-maltoside (β-C12G2) [27]. Here within for the C12DMPO:C12TAB mixtures adsorption at the water–air surface was studied via surface tension measurements, while the properties of horizontal foam films of thickness h < 100 nm were examined via a thin film pressure balance [25]. Foaming behaviour – both foamability and foam stability – was studied by the commercially available FoamScan method [26]. However, the FoamScan method did not allow for the study of foams with a uniform liquid fraction. This is exactly where the present work jumps in: foams with uniform liquid fractions were generated and their drainage behaviour was studied. To get a clear picture we studied drainage as a function of the bubble size, the initial liquid fraction, the composition and the total surfactant concentration.

Section snippets

Materials

The non-ionic surfactant dodecyldimethyl phosphineoxide (C12DMPO) was synthesised and purified as described elsewhere [28]. The cationic surfactant dodecyl trimethylammonium bromide (C12TAB) (purity ∼ 99%) was purchased from Aldrich and purified by three-fold recrystallizing from pure acetone to which traces of ethanol were added. Perfluorohexane (purity, 99%) was purchased from Aldrich and used as received. Sodium chloride (NaCl) was obtained from Merck and roasted at 500 °C over night to drive

Results and discussion

Foams stabilized with a surfactant mixture consisting of the non-ionic dodecyldimethyl phosphineoxide (C12DMPO) and the cationic dodecyl trimethylammonium bromide (C12TAB) with mixing ratios of C12DMPO:C12TAB = 1:0, 50:1, 1:1, 1:50, 0:1 have been studied with the home-built Foam Conductivity Apparatus (FCA). In the following the results obtained are separated into two main sections, namely foams produced by the single surfactants (Section 3.1) and by surfactant mixtures (Section 3.2). Section 3.1

Conclusions and outlook

We used the Foam Conductivity Apparatus (FCA) to examine foams stabilized by C12DMPO, C12TAB, and their mixtures. The exponents η of the power law fits of the ε(t)-curvesare similar (h = −0.8 to −1.0) for all samples studied, which indicates the same flow regime, namely Poiseuille-like flow. The similar drainage behaviour can be explained qualitatively with similar surfactant structures and bulk viscosities. However, it was not expected that these surfactants and their mixtures have immobile

Acknowledgments

E.C. would like to acknowledge UCD Ad Astra Research Scholarship funding. Part of the work was funded by the European Community’s Marie Curie Research Training Network ‘‘Self-Organisation under Confinement (SOCON)'', contract number MRTN-CT-2004-512331. We thank Dr. Wiebke Drenckhan for very helpful discussions.

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