Stability Of Plane Poiseuille Flow: Effects Of Micro-scale, Viscosity Stratification And Wavy Wall

Three important problems, such as the micro scale, viscous stratification andwavy plane boundary, on the stability of plane Poiseuille flow are discussed in thisdissertation. For micro scale length between the two planes, the flow called microflow,often behaviors differently from the prediction of the conventional form of theNavier-Stokes (N-S) equations. New model based on molecules motion is required toinvestigate microflow. When the Knusen number is about 0.01, the N-S equations canbe modified to study microflow.The stability of microflow with a not-too-large Knusen number (Knusen numberaround 0.01) is discussed in the first part of this dissertation. Apparent viscosity isemployed in the N-S equations to predict flow stability. It is found out that the criticaltransition Reynolds number can be much smaller than the conventional one. A theorybased on the molecular theory is presented to calculate the apparent viscosity. It isfound that the apparent viscosity is much higher than the bulk viscosity in the vicinityof the plane (wall) under certain conditions, and it is going to reach its bulk valuerapidly with the increase of the distance away from the wall. The numerical resultsshow that the higher apparent viscosity only stretches out in several nanometers.The stability of normal scale flows is investigated in the second part of thedissertation. For the viscosity-stratified plane Poiseuille flow, three models, calledbreak interface model, single film model and double film model, are proposed tosimulate the structure of liquid-liquid interface. The results of different models arecompared in detailed. The critical Reynolds number predicted by the break interfacemodel is the smallest, and that predicted by the single film model is the largest amongthe three models. For periodically wavy plane case, the distribution of the meanvelocity and its flow stability are computed with the help of coordinate transformation.The results show that the flow instability is greatly enhanced by the wavy walls. Inall studies, the Chebyshev collocation method is adopted.The above studies lay a solid foundation for further research on the extraction inmicrochannels.