Interfaeial pressure

The presence of surfactants at the water/oil interface will lower the interfaeial tension between the two phases. The interfaeial pressure (n) is defined as... 

Example 3 (Shoek Refleetion from a Higher Z Interfaee). If material B is replaeed by material C, with a higher shoek impedanee than A, the same interfaeial boundary eonditions ean be applied. In this ease, however (Fig. 2.18), this resulting state ( 2 ), is at higher pressure than state 1. The wave refleeted baek into material A is a shoek. If the right-hand bloek of material is replaeed by another bloek of material A, there are no refleeted waves, and the transmitted shoek is identieal to the ineident wave. 

Most simulations have been performed in the mieroeanonieal, eanonieal, or NPT ensemble with a fixed number of moleeules. These systems typieally require an iterative adjustment proeess until one part of the system exhibits the required properties, like, eg., the bulk density of water under ambient eonditions. Systems whieh are equilibrated earefully in sueh a fashion yield valuable insight into the physieal and, in some eases, ehemieal properties of the materials under study. However, the speeifieation of volume or pressure is at varianee with the usual experimental eonditions where eontrol over the eomposition of the interfaeial region is usually exerted through the ehemieal potential, i.e., the interfaeial system is in thermodynamie and ehemieal equilibrium with an extended bulk phase. Sueh systems are best simulated in the grand eanonieal ensemble where partiele numbers are allowed to fluetuate. Only a few simulations of aqueous interfaees have been performed to date in this ensemble, but this teehnique will undoubtedly beeome more important in the future. Partieularly the amount of solvent and/or solute in random disordered or in ordered porous media ean hardly be estimated by a judieious equilibration proeedure. Chemieal potential eontrol is mandatory for the simulation of these systems. We will eertainly see many applieations in the near future. 

Hgure 15 13 Comparison between experimentally obtained droplet sizes and deseriptions by the model (data from Schrrider et al. 1998, 1999). The membrane used was a eeramic membrane with average pore size of 0.4 pm, and with transmembrane pressure of 3 bar sunflower oil was emulsified in water with different surfaetants. One only obtains a good quantitative fit with the data when one assumes that the interfaeial tensions are 18 mN/m with 0.05% Tween-20 11 mN/m with 0.5% Tween-20 and 1.7 mN.m with 2% SDS. These values are not physically realistic therefore, the model does not quantitatively deseribe the data. 

The oil phase containing only 0.01 wt % asphaltene gives rise to a less rigid interfacial film than observed at the water surface (Fig. 8). This is most likely due to the possibility of the hydrocarbon tails of the asphaltenes to orient toward the highly aliphatie oil phase, making the interactions between the film material and, hence, the pressure increase during film compression, less extensive. In general, interactions between the bulk phase and interfaeial components are different fi om the water/air ease. 

All the relevant interfaeial quantities can be expressed as integrals over the three-dimensional pressure tensor P of the interface regarded as a three-dimensional body. The pressure tensor is simply the negative of the three-dimensional mechanical stress tensor tr (to be distinguished from the two-... 

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