Hydrodynamic forces resulting from liquid motion in capillary tubes

The wetting kinetics of model tubes of different geometrical shape has been investigated theoretically and experimentally under conditions of simulated zero-gravity (earthbound laboratory experiments) and low gravity (sounding rocket experiments within the TEXUS-programme). The present note deals with the hydrodynamic forces (capillary-, friction-, inertia forces, etc.) resulting from capillary rise in cylindrical, conical and sinusoidal tubes. The rôle of these forces is studied numerically in some detail.     

LONG-TERM RIGOROUS NUMERICAL INTEGRATION OF NAVIER-STOKES EQUATION BY NEWTON-GMRES ITERATION

The recent result of an orbit continuation algorithm has provided a rigorous method for long-term numer- ical integration of an orbit on the unstable manifold of a periodic solution. This algorithm is matrix-free and em- ploys a combination of the Newton-Raphson method and the Krylov subspace method. Moreover, the algorithm adopts a multiple shooting method to address the problem of orbital instability due to long-term numerical integra- tion. The algorithm is described through computing the extension of unstable manifold of a recomputed Nagata~s lower-branch steady solution of plane Couette flow, which is an example of an exact coherent state that has recently been studied in subcritical transition to turbulence.     

Fluid transport in capillary systems under microgravity

The wetting kinetics of model tubes of different geometries has been investigated experimentally and theoretically under conditions of simulated zero-gravity and microgravity. Numerical calculations of meniscus configurations and the rise of the menisci in tubes of different shape are compared with photographic pictures obtained from sounding rocket experiments (TEXUS-Programme). It is demonstrated that menisci under microgravity conditions are essentially different from those of simulated zero-g-experiments. These results, together with observed streamline patterns, yield valuable information with respect to the hydrodynamic deformation of phase interfaces and dynamic contact angles.