Solubilization-emulsification mechanisms of detergency

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184 C.A. Miller and K.H. Raney/Colloids Surfaces A: Physicochem. Eng. Aspects 74 (1993) 169-215 triolein. The D phase is seen, however, for surfactant concentrations well above that of Fig. 16. Note that the amounts of oleyl alcohol needed to depress the temperatures of the various phase boundaries are much greater than are shown in Fig. 15 for hydrocarbon systems. A likely explanation is that much of the oleyl alcohol is dissolved in the bulk triglyceride phase, leaving relatively little alcohol in the surfactant films which, to a large extent, determine the basic phase behavior by controlling the aggregate shape. 4. Diffusion path analysis Being of rather short duration and typically involving small quantities of soils, detergency processes are strongly influenced by dynamic, diffusional phenomena which occur on a microscopic scale. Oily soil removal, in particular, depends on phase transitions which occur at the oil-washing solution interface. The preceding section described equilibrium phase behavior in both water-surfactant systems, representing the washing solution, and oil-water-surfactant systems, As demonstrated below, such equilibrium phase behavior can be combined with the theory of diffusion processes to interpret certain dynamic behavior such as intermediate phase formation and spontaneous emulsification that occurs during detergent processes. A mathematical technique called diffusion path analysis has been used with success in predicting certain dynamic phenomena in multicomponent solid and liquid systems when two phases not in equilibrium are brought into contact with one another [62-64]. Essentially, a time-invariant path of compositions can be plotted across an equilibrium phase diagram by-solving component transport equations with certain assumptions and boundary conditions. First, convection in the system from any source is assumed to be negligible. Second, the two phases are assumed to be semiinfinite in extent. This assumption simplifies the mathematical analysis and is probably reasonable at least for short times after contacting. Third, diffusion of each species is assumed to be dependent only on its own concentration gradient with a uniform diffusion coefficient in each phase. Also, local equilibrium is assumed at all interfaces which form; this means that the compositions at the interfaces are defined by equilibrium tie lines. Diffusion path analysis is most conveniently applied to three-component, i.e. ternary, systems. In this situation, the phase diagram can be represented in the form of a two-dimensional triangle as, for instance, in Fig. 8, with two-phase regions shown as regions of varying shape containing equilibrium tie lines and three-phase regions represented as triangles in which the compositions of the equilibrium phases are shown as the vertices. The analysis in this case consists of solving in each phase the following transport equations for two of the species (∂wi/∂t) = Di(∂ 2 wi/∂x 2 ) i = 1,2 (3) where x is the distance from the initial surface of contact, t is time and wi and D i are the mass fraction and diffusivity of species i, respectively. The value of W3 for the third species is found by invoking Σw i = 1. The semi-infinite phase assumption allows transformation of the above equations to ordinary differential equations in the similarity variable η i = [x/(4D it) 1/2 ]. Integration yields the following error function solutions for the diffusion path segment in each phase w i = A i + B i erf η I i = 1,2 (4) where A i and B i are constants which are evaluated from the boundary conditions. Since η i varies from - ∞ to + ∞ at each value of time, the set of compositions given by Eq. (4) is independent of time although the position x of a specific composition does vary with time. It is often convenient to plot the compositions or "diffusion path" directly on the equilibrium phase diagram. In evaluating A i and B i for phases in contact. iteration on a tie line is performed until the individual species mass balances at the interface are satisfied. In addition to obtaining the path of compositions that forms between the initial
C.A. Miller and K.H. Raney/Colloids Surfaces A: Physicochem. Eng. Aspects 74 (1993) 169-215 185 phases, one may also calculate the relative velocities of all interfaces, and therefore the growth rates of intermediate phases. More detailed descriptions of the mathematical analysis and the specific error function solutions can be found elsewhere for a ternary system forming a single interface [63] or two or more interfaces [65]. The utility of diffusion path theory in ternary liquid systems was first shown for predicting the occurrence of spontaneous emulsification in alcohol-water-oil systems [63]. Specifically, when an alcohol-oil mixture denoted d in Fig. 17 is brought into contact with water, spontaneous emulsification of oil drops in the water phase is observed. In this situation, the construction of a diffusion path between the initial compositions shows the formation of an interface with equilibrium compositions b and c connected by the tie line represented by the broken line. Spontaneous emulsification in the aqueous phase can be explained by the passage of that path segment from b to W through the corner of the two-phase envelope, thereby predicting the formation of small drops of oil-alcohol mixture below the interface. Experiments showed that, in the absence of interfacial turbulence, interfacial displacement Fig. 17. Schematic diffusion path in alcohol(A)water(W)-oil(O) system showing supersaturation leading to spontaneous emulsification. is proportional to the square root of time, as predicted by the theory [65,66]. This diffusion mechanism of spontaneous emulsification is distinct from other modes of spontaneous emulsification in which interfacial instability results in the mechanical dispersion of one phase in another [67]. Diffusion path analysis was later applied to oil-water-surfactant systems [20,64,68]. In these cases, the use of pseudoternary phase diagrams was required. For example, commercial surfactants are almost always complex mixtures containing numerous species of surfactants. Rather than solving the diffusion equations for each species, one can sometimes combine all surfactant components together and treat them as a pseudocomponent. Mixtures of hydrocarbons can also be considered as pseudocomponents. Although diffusion path studies are typically performed when single-phase systems are originally present, the ability to calculate diffusion paths in which one of the initial compositions is a stable dispersion of one phase in another, e.g. a liquid crystalline dispersion, has also been demonstrated [64]. 5. Dynamic contacting studies Direct observation of the dynamic phenomena that occur when non-equilibrated liquid phases are brought into contact can be made in various ways. On a macroscopic scale, a liquid can be gently placed on top of another liquid in a tube, and rather large-scale phenomena can be observed. This simple technique was used in the early studies of spontaneous emulsification in oil-water-alcohol systems [63] and has been used with surfactant systems to monitor the formation of microemulsion and liquid crystalline phases between oil and surfactant solutions [68-71]. In these cases, the oil is gently layered on top of the aqueous phase, and dynamic phenomena are observed without magnification. Crossed polarizers aid in the identification of birefringent liquid crystalline phases. A shortcoming of this technique is the inability to observe events which occur immediately after the contacting of the two
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Solubilization-emulsification mechanisms of detergency

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