Interfacial Wave Transitions in Liquid-liquid Flows and Insight into Flow Regime Transition

Measurements of developing interfacial waves on oil-water channel flows show that long wave modes form and grow to large amplitude even though they have much smaller linear grow rates than shorter waves. There is evidence for a "triggering" of these long waves by interaction with much shorter waves, although most of the energy for wave growth comes from the mean flow. Thus linear instability of these long waves is a necessary condition for their formation and consequently, for flow regime transitions from a stratified state. However, experiments in a rotating Couette flow show regimes of no wave growth, even when long waves are unstable. The apparent reason for this is given by numerical integration of the equations that describe weaklynonlinear wave modes at the interface. The simulations show a cascade of energy from long to short waves and no preferred wavenumber in the spectrum. INTRODUCTION Multifluid flows exist in oil wells, oil production and transportation pipelines, heat exchangers, gas-liquid reactors with solid catalyst and various other process piping and vessels. An important emerging issue for multifluid flow research will be how to best solve the contacting/mass and heat transfer problems that will greatly increase, as a new generation of "molecularly-engineered" catalysts developed with much higher dispersion of active metal and more elaborate possibilities of interconnection of pores on different scales. However, given the current uncertainty that exists in the simplest case, gas-liquid flow in pipe, these new problems may be difficult to solve. Even in light of the need to understand multifluid flow on small scales, their defining characteristic, in channels, pipes and even packed beds is the strength of the largest scale disturbances present. For gas-liquid pipe flows, where 6 different flow regimes are possible, slug flow [1] is the regime with large coherent disturbances cause large pressure fluctuations [2] and variations in the gas and liquid flow rates that can affect process equipment. For gas liquid packed bed flows, the corresponding region is the pulsing flow regime[3], for which the large disturbances have been shown to have the beneficial effect of increased mass transfer rates that can favorably affect the reaction outcome[4]. The existing problem in the prediction of large disturbances leading to slug formation is there are multiple mechanisms that are at work [5] and slugs can form directly from growth of waves on flat layers or by coalescence of several large rollwaves. The standard techniques for the prediction of slugs are various linear stability theories, based on different assumptions and some work that addresses the stability of a slug once it forms. Figure 1 shows several such models. It is readily seen that significant disagreement exists between the different procedures for slug prediction -even those that are based on the same premise of unstable long waves. If these models are plotted for a model oil-gas flow at 100 ATM in a larger pipe, even bigger disagreement exists. From these results it can be concluded that considerable uncertainty exists in the prediction of slug flow for engineering purposes.