Basic equations for interfacial rheology

The interfacial shear viscosity, is the ratio between the shear stress, a, and shear rate, y, in the plane of the interface, i.e. it is a two-dimensional viscosity. The unit for surface viscosity is, therefore, N s (surface Pa s). A liquid/liquid (or liquid/ vapour) interface with no adsorbed surfactant or polymer shows only a negligible interfacial shear viscosity. However, in the presence of an adsorbed surfactant or polymer layer, an appreciable interfadal shear viscosity is obtained (which can be orders of magnitude higher than the bulk viscosity of the film). This appreciable shear viscosity can be accounted for in terms of the orientation of the surfactant or polymer molecules at the interface. For example, surfactant molecules at the 0/W interface usually form a monolayer of vertically oriented molecules with the hydrophobic portion pointing to (or dissolved in) the oil, leaving the polar head groups pointing in the aqueous phase. A two-dimensional surface pressure, n, may be defined, i.e. 

The interfacial dilational viscosity, can be simply defined if one considers a uniform expansion of the interface at a constant rate d In A/dt, i.e. 

As mentioned above, interfacial films exhibit non-Newtonian flow, which can be treated in the same manner as for dispersions and polymer solutions. The steady-state flow can be described using Bingham plastic models. Viscoelastic behaviour can be treated using stress relaxation or strain relaxation (creep) models as well as dynamic (oscillatory) models. The Bingham-fluid model of interfacial rheological behaviour [54] assumes the presence of a surface yield stress, as, i.e. 

In stress relaxation experiments, a sudden strain is applied on the film, within a short period of time, and the stress a followed as a function of time. If r(t) is the stress at time t and co is the instantaneous value at the moment when the constant 

In strain relaxation (creep) experiments, a small constant stress is applied on the film and the strain or compliance J (where J = y/a) is followed as a function of time. The compliance at any time t,J(t), is given by the expression 

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