Interfaces ripple experiment

The ripple experiment works as follows In Fig. 6, HDH and DHD are depicted by open and filled circles where the filled circles represent the deuterium labeled portions of the molecule and the open circles are the normal (protonated) portions of the chains. Initially, the average concentration vs. depth of the labeled portions of the molecules is 0.5, as seen along the normal to the interface, unless chain-end segregation exists at / = 0. If the chains reptate, the chain ends diffuse across the interface before the chain centers. This will lead to a ripple or an excess of deuterium on the HDH side and a depletion on the DHD side of the interface as indicated in the concentration profile shown at the right in Fig. 6. However, when the molecules have diffused distances comparable to Rg, the ripple will vanish and a constant concentration profile at 0.5 will again be found. 

Fig. 6. The ripple experiment at the interface between a bilayer of HDH- and DHD-labeled polystyrene, showing the interdifussion behavior of matching chains. The protonated sections of the chain are marked by filled circles. The D concentration profiles are shown on the right. Top the initial interface at / = 0. The D concentration profile is flat, since there is 50% deuteration on each side of the interface. Middle the interface after the chain ends have diffused across (x < / g). The deuterated chains from Que side enrich the deuterated centers on the other side, vice ver.sa for the protonated sections, and the ripple in the depth profile of D results. A ripple of opposite sign occurs for the H profile. Bottom the interface when the molecules have fully diffused across. The D profile becomes flat [20,56].

Recently, Hanratty presented a comprehensive review of the attempts to account for the interfacial waviness in modelling the interfacial shear stress for the stability analysis of gas-liquid two-phase flows [53]. Basically, the approach taken was to implement the models obtained for the surface stresses in air flow over a solid wavy boundary as a boundary condition for the momentum equation of the liquid layer over its it mobile wavy interface. Craik [98] adopted the interfacial stresses components which evolve from the quasi-laminar model by Benjamin [84]. Jurman and McCready [99], Jurman et al. [100], and Asali and Hanratty [101] used correlated experimental values of shear stress components (phase and amplitude) based on turbulent models which consider relaxation effects in the Van Driest mixing length. Since the characteristics of the predicted surface stresses are dependent on the wave number, Asali and Hanratty picked the phase and amplitude values which correspond to the wave lengths of the capillary ripples observed in their experiments of thin liquid layers sheared by high gas velocities [101]. It was shown that the growth of these ripples is controlled by the interfacial shear stress component in phase with the wave slope. 

---