Generalized surface momentum balances for the analysis of surface dilatational data

Abstract

Dilatational rheological properties of interfaces are often determined using drop tensiometers, in which the interface of the droplet is subjected to oscillatory area changes. A dynamic surface tension is determined either by image analysis of the droplet profile or by measuring the capillary pressure. Both analysis modes tend to use the Young-Laplace equation for determining the dynamic surface tension. For complex fluid-fluid interfaces there is experimental evidence that this equation does not describe the response of the interface to deformations adequately. Generalizations of this equation are available, and in this comment we will discuss these generalizations, and the conditions for which they reduce to the Young-Laplace equation.

Dynamic surface tension of complex fluid-fluid interfaces: A useful concept, or not?

“…The latter contribution will in most cases be negligible, but there are some exceptions, such as vesicle membranes, or interfaces in phase separated biopolymer mixtures, where these contributions may be significant [1,[14][15][16][17][18][19][20]. In [6] we saw that for such a system the pressure difference over the interface is given by…”

“…In OBM and BPT experiments the dynamic surface tension is determined from the Young-Laplace equation, given by P (2) − P (2) = 2γH (5) where P (2) is the pressure in the interior of the droplet, P (1) is the pressure in the outer phase, and H is the mean curvature of the interface. Elsewhere in this issue [6], we have seen that for complex fluid-fluid interfaces we need to use a generalized form of this equation to analyze profile or pressure data, referred to as the jump or surface momentum balance [1,[7][8][9][10][11][12]. In [6] we have discussed conditions for which this generalized balance reduces to the Young-Laplace equation (5).…”

“…Elsewhere in this issue [6], we have seen that for complex fluid-fluid interfaces we need to use a generalized form of this equation to analyze profile or pressure data, referred to as the jump or surface momentum balance [1,[7][8][9][10][11][12]. In [6] we have discussed conditions for which this generalized balance reduces to the Young-Laplace equation (5). Let us assume that an OBM or BPT experiment is performed in such a way that in-plane inertial stresses, and viscous stresses exerted on the interface by the adjoining bulk phases are negligible.…”

“…Moreover, we assume the deformation is small and uniform. Under these conditions the momentum balance of the interface reduces to [6] P (2) − P (1)…”

Dynamics of complex fluid-fluid interfaces

“…One of the issues raised by Javadi et al [35] at the end of their contribution is the proper generalisation of the Young-Laplace equation typically used for the analysis of tensiometry experiments, to dynamic conditions. The contribution by Sagis [36] discusses how such generalisations can be derived within the framework of nonequilibrium thermodynamics.…”