Fluid bridges exposed to a shear strain

As a first illustration we consider the model discussed in Section 1.3.3, namely a fluid of simple molecules confined between chemically striped solid surfaces (see Fig. 5.2). As before in Section 5.4 we treat the confined fluid as a thermodynamically open system. Hence, equilibrium states correspond to minima of the grand potential 11 introduced in Eqs. (1.66) and (1.67). The fluid fluid interaction is described by the intermolecular potential ug (r) introduced in Eq. (5.38) where the associated shifted-force potential is introduced in Eq. (5.39). The fluid substrate interaction is described by 1 1 (x, z) in the continuum representation [see Eq. (5.68)], where x replaces x because of the misaligmncnt of the sul)stratcs relative to each other [see Eq. (5.103)]. 

As a quantitative measure of the extent to which a confined phase is capable of resisting a shear deformation, we introduce in Section 5.6.2 the shear stress Txz. For a fluid bridge a typical shear-stress curve r (aSxo) is plotted in Fig. 5.18. Regardless of the thermodynamic state and the thickness (i.e., s ) of a bridge phase, a typical stress curve exhibits the following features  

Xx (qSxo) depends linearly on the shear strain asxo in the limit a —+ 0. That is to say, the response of the bridge phase to small shear strains follows Hooke s law. 

For larger shear strains, negative deviations from Hooke s law observed, eventually leading to a yield point ( , x x) defined by the constitutive equation 

As far as the current model is concerned, the degree of chemical corrugation of the substrate has significant consequences for the yield-point location (o, Plots of stress curves for various values of c, are shown in Fig. 5.19(a). For monolayer bridge phases and fixed s = 10 one c m see from Fig. 5.19(a) that both and are smallest for the smallest o, =. For c, only gas phases are thermodynamically stable because the strongly attractive portion of the substrate is too small to support formation of denser (bridge) phases. As Cr increases both and increase until they reach their maximum values (a sx,T ) (2.740,0.169) for For larger 

For larger shear strains, negative deviations from Hooke s law are 

One also notices from Fig. 5.19(a) that stress curves for c, = and 

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