Dynamic Surface Tension

Surface elasticity is a major factor determining thin liquid film stability [24]. Foam contains many bubbles separated by liquid films that are continuously enforced by dynamic change in the liquid, such as liquid drainage and bubble motion. In the case of surfactant-stabilized aqueous film, stretching causes local decrease in the surface concentration of the adsorbed surfactant. This decrease causes local surface tension increase (the Gibbs elasticity), which acts in opposition to the original stretching force. In time, the original surface concentration of the surfactant is restored. This time-dependent restoration force in thin liquid film is referred to as the Marangoni effect. Dynamic adsorption at the gas/ liquid interface must thus be considered in the assessment of foam stability. Although there are various techniques for measuring equilibrium tension [30], the maximum bubble

Table 1 Standard Methods for Foaming Assessment





Static methods

Dynamic methods


Shaking Beating Stirring Air injection


Ross & Miles Test Modified Ross & Miles Test Bottle Test Perforated Disk Test Blemder Test Diffuser Stone Test

Gas Bubble Separation Test Recycling and Fall Test

ASTM standard D 1173-53 ISO standard 696-1975(E) ASTM standard D 3601-88 DIN standard 53902 part 1 ASTM standard D 3519-88 ASTM standard D 892-92 ASTM standard D 1881-86 ASTM standard D 3427-86 AFNOR draft T73-421

Abbreviations: ASTM, American Society of Testing and Materials; ISO, International Standardization Organization; DIN, Deutsches Institut für Normung; AFNOR, Association Frances Normalization.

Figure 5 Effects of EO units on dynamic surface tension, yt, versus bubble surface lifetime, t, for 1 mM aqueous C12En solution at 25°C.

pressure method is used the most for this measurement to monitor dynamic surface tension on a short time scale.

A typical curve of dynamic surface tension shows induction, rapid fall, mesoequi-librium, and equilibrium [31,32]. All these parameters have significant effect on highspeed dynamics. Data for surface tension for aqueous solutions of polyoxyethylene dode-cyl ethers (C12En), C12H25O(C2H4O)nH, where n = 5 - 53, as a function of time, are presented in Figure 5. Maximum rate of decrease in surface tension (dyt/dt)max, was determined based on the data [33]. Dynamic surface tension (yt) at constant surfactant concentration may be obtained as

where Yt is the surface tension of the solution at time, t; Ym is the mesoequilibrium surface tension of the solution (where Yt shows little change—<lmNm-1 per 30s—with time), y> is the equilibrium surface tension of the solvent, and t* and n are constants for a given surfactant. The parameter t* is the time for Yt to reach a value midway between y> and Ym, and decreases with increase in surfactant concentration. The curves obtained with Eq. (1) are widely fitted for the observed time scale, as shown in Figure 5. The (dYt/dt)max may be derived from Eq. (2) as

Foamability and Foam Stability

Methods for foam formation and stability evaluation were established based on various sources of data, such as dynamic surface tension and liquid film movement, respectively, using a laminometer (LlameUae). Ross-Miles foam behavior of aqueous C12En solution is shown in Figure 6. Initial foam height increased linearly with EO. Residual foam height decreased sharply with increase in EO. Dynamic surface properties of aqueous C12En solution are shown in Figure 7. The (dYt/dt)max increased linearly with EO, whereas Liameliae decreased sharply with EO. Dynamic foam behavior by these methods was found

Figure 6 Effects of EO units on the Ross-Miles foam behavior for 1 mM aqueous C12En solution at 26°C.

consistent with conventional foam test results. Initial foam height in the Ross-Miles test was in good agreement with (dyt/dt)max, and residual foam height in good agreement with Liameliae. Foam formation would thus appear to depend primarily on the rate of adsorption of surfactants onto a gas/liquid interface and foam stability may also be a factor. For nonionic surfactants, initial foam height and stability are less compared with ionic surfactants in aqueous solution because of the large surface area per molecule of surfactant molecule. The effects of area per molecule (A) on foam stability and thinning of vertical films, monitored by FT-IR as a function of time, were examined [34,35]. Data for the Ross and Miles foam stability and aqueous core thickness of vertical foam film at rupture (Drup) as a function of A are shown in Figure 8 [35]. Linear increase in Dmp with A was noted, whereas residual foam height sharply decreased with A. Nonionic surfactants that occupy less surface area would thus appear to promote the disruption of foam. Accord-

Figure 8 Effects of area per molecule (A) on Ross & Miles foam stability (5 min) and aqueous core thickness (Drup) for 1 mM aqueous nonionics solution at ruptured 25°C.

ingly, hydrophobic interactions between surfactant molecules may significantly contribute to foam stabilization.


Adsorption at the solid/liquid interface is an important feature requiring consideration in mechanics, electronics, biological systems, agriculture, foods, and cosmetics. When the adsorption isotherm of a surfactant on a solid surface is measured, several quantitative aspects of surfactant adsorption can be clarified.

Adsorption of Surfactants on Inorganic Solid Surfaces

The surface properties of a solid surface primarily determine the adsorption capacity of a surfactant. There are nonpolar and hydrophobic surfaces, polar and uncharged surfaces, and charged surfaces [36]. Inorganic oxides using cosmetics (e.g., silica, alumina, titania) have charged surfaces. Thus, interactions between a charged surface and ionic surfactant should be understood for controlling the properties on the surface.

The adsorption of SDS onto alumina in aqueous solution has been studied extensively and the mechanisms of adsorption have been made clear [37,38]. The adsorption isotherm of SDS on alumina is presented in Figure 9 and comprises the following four regions [39]: region I with a slope of unity derived from electrostatic interactions between SDS and an oppositely charged solid surface; region II shows steep increase in adsorption attributable to surfactant aggregation at the surface through lateral interactions between hydrocarbon chains—the surface of alumina is not fully covered and there are still positive sites where adsorption may take place; in region III, decrease in the slope of the isotherm attributable to increased electrostatic hindrance of surfactant adsorption is evident—the transition from region II to III corresponds to the isoelectric point of the solid, in which the adsorbent and adsorbate have the same charge; and for region IV, there is maximum

J.ng Surfactant Con central i mi Figure 9 Schematic diagram of typical adsorption isotherm. (From Ref. 39.

surface coverage at cmc and further increase in surfactant concentration has no effect on adsorption density.

Binding of Surfactant to Human Hair

The binding of a surfactant to human hair or wool has been well studied. The thermodynamic aspects of surfactant binding are thus considered in this section. The binding of ionic surfactants to globular proteins has been extensively investigated by thermodynamic analysis of binding interactions [40-44]. In consideration of the fine structure of human hair, surfactants should bind to the cuticle, cortex, and fibrils, all comprising proteins. Thus, continuous binding of a surfactant with human hair would appear the same as that of surfactants with globular proteins.

Binding isotherms of SDS for normal and damaged hair are shown in Figure 10 [45]. SDS bound to cold-waved hair increased remarkably compared with normal and bleached hair. Each isotherm has two regions. Region I shows Langmuir binding attributable to interactions of SDS with ionic sites on the surface of hair. For region II, there was noted sharp increase in adsorption as a result of surfactant aggregation at the surface brought about by lateral interactions between hydrocarbon chains. Damaged hair may possibly be an indication of disruption of disulfide crosslinks. This increase involving the consequent binding of SDS on polypeptides in the hair because of electrostatic repulsion among micelle-like clusters. Rigid disulfide bonds are maintained, and thus such binding was noted to a slight degree for the isotherms of normal hair. The binding isotherms of dodecyltrimethylammonium chloride (DTAC) for normal and damaged hair indicated no increase in binding.

In the Langmuir binding region, the equation of Klotz [Eq. (3)] has quantitative application, as

Figure 10 Binding of SDS to normal hair (<>), bleached hair (*), and cold-waved hair (->) at 25°C.

where y is total bound surfactants; n, total number of binding sites; K, binding constant; and C, concentrations of surfactants at equilibrium. n and K may be obtained from plot of 1/y versus 1/C. The free energy change, -AG, is related to the binding constant as

Thermodynamic parameters for binding between surfactants and normal hair are listed in Table 2. n and -AG for anionic surfactants were the same in all cases regardless of alkyl chain length. -AG, when SDS was bound to BSA, was twice that in the case of SDS binding to hair. In the case of BSA, electric and hydrophobic interactions contribute to the free energy change of binding. Electrostatic interactions between an anionic surfactant and hair would thus appear quite weak, and no alkyl chains at all would be in a hydropho-bic area. n and - AG for cationic surfactants were also the same regardless of alkyl chain length. -AG, in the case of DTAC binding to BSA and cationic surfactant binding to keratin powder, were the same as for binding to hair. The force of cationic surfactant

Table 2 Thermodynamic Parameters of Binding Between Ionic Surfactants and Normal Hair


n(X10-5 mol/g)

K(X102 L/mol)

-AG (KJ/mol)

SDS (C12)




SDeS (C10)




SOS (C8)




DTAC (C12)




DeTAC (C10)




Figure 11 Schematic diagrams of the binding of surfactants to human hair.

binding to hair would thus appear to arise mainly from hydrophobic interactions and alkyl chains would not be present in a hydrophobic area on the surface of hair, as also in the case of anionic surfactants. Binding sites for ionic surfactants on hair are shown in Figure 11 [45]. Dissociated carboxyl and amino groups of polypeptides may possibly be present just inside the surface of the hydrophobic layer.

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