The Dynamics of Miscible Interfaces: A Space Flight Experiment
Experiments as well as accompanying simulations are described that serve in preparation of a space flight experiment to study the dynamics of miscible interfaces. The investigation specifically addresses the importance of both nonsolenoidal effects as well as nonconventional Korteweg stresses in flows that give rise to steep but finite concentration gradients. The investigation focuses on the flow in which a less viscous fluid displaces one of higher viscosity and different density within a narrow capillary tube. The fluids are miscible in all proportions. An intruding finger forms that occupies a fraction of the total tube diameter. Depending on the flow conditions, as expressed by the Peclet number, a dimensionless viscosity ratio, and a gravity parameter, this fraction can vary between approximately 0.9 and 0.2. For large Pe values, a quasi-steady finger forms, which persists for a time of O(Pe) before it starts to decay, and Poiseuille flow and Taylor dispersion are approached asymptotically. Depending on the specific flow conditions, we observe a variety of topologically different streamline patterns, among them some that leak fluid from the finger tip. For small Pe values, the flow decays from the start and asymptotically reaches Taylor dispersion after a time of O(Pe). Comparisons between experiments and numerical simulations based on the 'conventional' assumption of solenoidal velocity fields and without Korteweg stresses yield poor agreement as far as the Pe value is concerned that distinguishes these two regimes. As one possibility, we attribute this lack of agreement to the disregard of these terms. An attempt is made to use scaling arguments in order to evaluate the importance of the Korteweg stresses and of the assumption of solenoidality. While these effects should be strongest in absolute terms when steep concentration fronts exist, i.e., at large Pe, they may be relatively most important at lower values of Pe. We subsequently compare these conventional simulations to more complete simulations that account for nonvanishing divergence as well as Korteweg stresses. While the exact value of the relevant stress coefficients are not known, ballpark numbers do exist, and their use in the simulations indicates that these stresses may indeed be important. We plan to evaluate these issues in detail by means of comparing a space experiment with corresponding simulations, in order to extract more accurate Korteweg stress coefficients, and to confirm or deny the importance of such stresses.