Session FK: Free Surface Flows III

Polygonal hydraulic jump on microdecorated surfaces

We report on the hydraulic jump resulting from the impact of a water jet onto topographically patterned surfaces, i.e. arrays of cylindrical micron-size posts arranged on square or hexagonal lattices. By varying the topographic features (height of the posts, lattice distance) and the jet properties (size of the nozzle, flow rate), we obtain a variety of stable shapes including hexagons, eight corner stars and circles. We rationalize our results by taking into account a fluid velocity that depends on the orientation of the lattice.   

Flow meandering and surface properties

We present a study of the behavior of a gravity-driven rivulet flowing down an inclined surface. Several surfaces with different wetting properties are investigated, with the objective to determine the influence of the contact angle on the statistical properties of rivulet meandering.   

Free surface capillary Stokes flow in an annulus

We present a numerical scheme, based on complex variable methods and conformal mapping techniques, for computing the free surface evolution of an annular region of very viscous fluid in the Stokes regime driven by surface tension, a model system relevant to certain design problems arising in the glass industry. Comparisons with related theoretical results will be given.   

A Study of Critical Wetting Condition of the CFE-Vane Gap Geometry

The Capillary Flow Experiment (CFE) Vane Gap experiments follow a line of experiments performed in low-g environments onboard International Space Station to observe critical wetting phenomena in large length scale capillary systems. In a cylindrical container in zero-g, single-valued finite height equilibrium capillary surfaces fail to exist if a critical wetting condition is satisfied. This nonexistence results in significant redistribution of the fluid in the container. The Vane Gap geometry consists of a right cylinder with elliptic cross section and a single central vane that does not contact the container walls. The vane is slightly asymmetric so that two gaps are not of the same size. In this study, we identify the critical wetting conditions of this geometry using the Concus-Finn method for both perfectly and partially wetting fluids as a function of container asymmetry. It will be shown that there are at least three critical geometric wetting conditions that include one for each gap region respectively and one for a global shift of bulk fluid which, among the three, is the most significant.   

The effect of flow field/geometry on the dynamic contact angle

A number of recent experiments suggest that, at a given wetting speed, the dynamic contact angle formed by an advancing liquid-gas interface with a solid substrate depends on the flow field/geometry near the moving contact line. In the present work, this effect is investigated in the framework of an earlier developed theory which was based on the fact that dynamic wetting is, by its very name, a process of formation of a new/fresh liquid-solid interface and hence should be considered not as a one-off problem but as a particular case from a general class of flows with forming or/and disappearing interfaces. The results demonstrate that in the flow configuration of curtain coating the actual dynamic contact angle indeed depends not only on the wetting speed and material constants of the contacting media, as in the so-called `slip models', but also on the inlet velocity of the curtain, its height and the angle between the falling curtain and the solid surface. In other words, for the same wetting speed the dynamic contact angle can be varied by manipulating the flow field/geometry near the moving contact line. The obtained results have important experimental implications: one can use the overall flow conditions and the contact angle as a macroscopic multiparametric `signal-response' pair that probes the dynamics of the liquid-solid interface. This approach would allow one to investigate experimentally such properties of the interface as, for example, its equation of state, the rheological properties involved in the interface's response to an external torque, and help to measure its parameters, such as the coefficient of sliding friction, etc.   

An investigation of surface wave rectification in a channel

Extracting energy from oscillatory flows, such as ocean waves, is an important engineering challenge in fluid dynamics. In this study, we investigate a wave rectifying channel that converts a periodic disturbance normal to the free surface to unidirectional flow around a suspended plate. The experiment was carried out in a long, narrow channel with a total liquid volume of 3.3 L. The channel was excited at frequencies of 1 Hz to 2.8 Hz and flow behavior was investigated using dye visualization and DPIV. The system shows robust and repeatable flow behavior that is highly sensitive to excitation profile and system geometry. Numerous flow regimes, from purely oscillatory to unidirectional pulsatile flow, can be achieved through manipulation of the excitation frequency alone. In the channel, we observed average flow rates as high as 50 mL/s at an excitation frequency of 2.2 Hz. An excitation frequency change of only 0.2 Hz is enough to change the flow from unidirectional clockwise to unidirectional counterclockwise. We discuss system parameters such as channel geometry and excitation profile as they relate to wave reflections, wave interactions, and overall system performance.   

Chocked flows in open capillary channels

Capillary systems provide a passive means to control fluids and are widely used for space craft fuel management. In the present study the forced liquid flow through an open capillary channel under low gravity conditions is investigated. Due to convective and viscous momentum transport the pressure along the flow path decreases and causes the free surface to bend inwards the open channel. Since the curvature of the free surface depends on the channel pressure the flow rate is limited. The maximum flow rate is achieved when the free surface collapses and gas ingestion occurs. This critical flow rate depends on channel geometry and liquid properties. The talk concludes analytical modeling and numerical computations to calculate pressure, free surface curvature and velocity parameters. The results predict the critical flow rate for different geometries and can be used to avoid greater design margins of capillary systems.   

Hydraulic jumps in a narrow channel

We present measured free surface profiles of stationary hydraulic jumps in a small open channel. We observe that the position of the jump depends linearly on the flow-rate and that the flow velocity immediately upstream of the jump has only a weak dependence on the flow-rate. We discuss these results and the conditions that determine the occurrence of the jump. We find a linear height profile upstream of the jump region with a slope that is independent of the flow-rate, and we compare our results with the solutions derived by Watson (1964) for laminar and turbulent channel flows.   

Capillary Flow in Weakly 3-Dimensional Conduits

A large literature exists for capillary driven flows along simple conduits of uniform cross section (i.e. right circular and regular polygonal cylinders, etc.). The work presented here extends the analysis to imbibing flows along conduits of increased geometric complexity with each possessing a slight taper along the primary flow path. Results are presented for transient flows in select conduits where power law time dependencies transition between regimes, depending on the time dependent boundary conditions. The experimental results of drop tower and spacecraft (ISS) tests support the analysis which is also compared with numerics. Such flows may be exploited for the passive manipulation of liquids in microfluidic systems on Earth as well as microgravity fluid systems aboard spacecraft.