Session W15 - Fluids, Turbulence and Foams.
ORAL session, Thursday morning, March 15
Room 211, Washington State Convention Center

[W15.001] Stabilization of Capillary Bridges in Low Gravity With Acoustic Radiation Pressure

In the absence of gravity, cylindrical capillary bridges consisting of liquid between two circular supports of radius R naturally become unstable and break when the length L exceeds the circumference 2\pi R. This is the Rayleigh--Plateau limit where the slenderness S = L/2R is \pi. In experiments performed aboard NASA's low-gravity KC-135 aircraft, it was found that acoustic radiation pressure can be used to stabilize capillary bridges to lengths beyond the Rayleigh--Plateau limit. Capillary bridges composed of a water/glycerol mixture were deployed in a 29 kHz ultrasonic standing wave in air. The bridge radius R=1.62 mm is chosen such that the radiation pressure due to the sound field is a function of local bridge radius and squeezes more on regions of larger radius than on regions of smaller radius. Stabilization of bridges to S=4.5 was demonstrated, and stabilized bridges with S>\pi broke immediately upon deactivation of the sound field. In contrast with previous work [M. J. Marr--Lyon \textitet al., J. Fluid Mech.\ \textbf351, 345--357 (1997)] using active feedback control, this stabilization mechanism is a passive effect of the sound field.

[W15.002] Persistent Gravity-Induced Concentration Gradient in a Thermally Driven Liquid Mixture

At sufficiently large applied horizontal temperature gradients we expect thermal convection to readily stir away the vertical concentration gradient caused by earth's gravity in a binary liquid mixture. Earlier we found that for near-critical aniline + cyclohexane at an expected Peclet number (Pe, convection rate / diffusion rate) of 1.5 a concentration gradient remains. We used a modification of Hart's hydrodynamic theory to estimate velocity. Now, a scaling theory due to Hicks gives an alternative velocity prediction. And, we have been able to explore considerably larger horizontal temperature gradients. We find that at high Pe, 5.4 and 130 according to modified Hart and scaling theory, respectively, a vertical concentration gradient is still present. In fact we find that the magnitude of the gradient is increased 60relative to its equilibrium value. This observation contradicts both theories. The discrepancy is especially glaring for the scaling theory. Supported by the NSF through the Cornell Center for Materials Research.

[W15.003] Concept of New Air Spring applied to Safety Car Seat by using Fluid Dynamics

By using the Principle of Newton's Inertia law as well as Fluid Dynamics, we can control car seats. The basic conception of the experiment is to show how to remove the inertia law, which everything in the car depends on, in the moving car. Although an air spring reduces impact, it will rebound because particles in the air spring are in the isolated system and they do not lose their energy. However, since particles in our air spring interact on outside particles, there is no rebound. With the new fundamental concept of new air spring, safety car seat will be discussed how to be used by removing the natural law, Inertia Law.

[W15.004] The vortical flow of an ideal fluid for an arbitrary initial condition.

An analytic solution for the time derivative of the vorticity at the initial instant is presented. The solution is applicable to an ideal (incompressible and inviscid) fluid in three-dimensional space. Since no restrictions are imposed on the initial velocity field, this result can be used to reconstruct the time evolution of the vorticity field using a time series. The first terms of this time series are presented and analyzed. These results can be applied to calculate vorticity-induced lift forces on submerged bodies since they are mostly dominated by inviscid effects.

[W15.005] Modification of Turbulence by Polymers

It has long been known that the addition of a small quantity of a long chain polymer to a fluid can cause dramatic drag reduction in a turbulent pipe flow. The effect occurs for concentrations as low as 10 ppm by weight, for which the viscosity of the solution typically differs from that of pure water by only a few percent. The cause of the effect remains an open question, although models involving strain-induced anisotropic viscosity near the wall and visoelasticity have been put forward. We report measurements of particle trajectories in high Reynolds number bulk turbulence for dilute solutions of polyethylene oxide in water. The trajectories, measured with a temporal resolution of 70,000 frames per second, are used to compile Lagrangian statistics. We compare the rms acceleration of fluid particles in the polymer solution with those in pure water and find a decrease which appears to be in excess of that which would be caused by the nominal increase in viscosity. We also measure the acceleration autocorrelation function and find that several new features appear when the polymer is added which may reflect viscoelastic effects. This work is supported by NSF grant PHY9988755. http://milou.msc.cornell.edu/turbulence.html

[W15.006] Conditional Analysis of a Convective Internal Boundary Layer

A convective internal boundary layer (cibl) was formed as cool marine air was advected over a warm, sandy, flat beach. Seven sonic anemometers were deployed in a configuration that allowed both vertical and horizontal gradients to be approximated.

Two of the instruments were clearly at the top of the cibl. They yielded data alternating between conditions typical of the cibl and the overlying marine layer with a fairly sharp boundary between the two regimes. The data for each regime were separated from each other using a conditional analysis based on the standard deviation of the vertical component of the wind velocity. These conditional data and the data from the other instruments allowed analysis of turbulence energy budgets due to a step change in surface heating. Budget terms are evaluated both in the cibl and just above it.

[W15.007] Energy Transport during Turbulent Electroconvection

We report measurements of the energy dissipation during electroconvection of a nematic liquid crystal in the fully turbulent regime. The energy dissipation is quantitified by measuring the electric current at constant potential difference. In certain cases, we observe the surprising result that the dimensionless energy dissipation ceases to increase with increasing potential difference. In some circumstances, a power law scaling relationship between the dimensionless excess energy dissipation and the reduced voltage is observed. This is similar to the well known Nusselt number scaling in turbulent Rayleigh-Benard convection. However the scaling exponent varies dramatically with both the time scale of the driving electric field and the separation between the electrodes.

[W15.008] Instantaneous Vorticity Measurements using Fiber-Optic Couplers

A novel fiber-optic technique is developed to measure one component of the time and space resolved vorticity vector ømega (r,t). In the technique, two single-mode, polarization-maintaining fibers and a fiber-optic coupler are used to measure an instantaneous velocity difference. The two input fibers collect the scattered light by seed particles with the same polarization and scattering wavevector but from two spatially separated regions in a flow. The obtained signals interfere when combined via the fiber-optic coupler and the resultant light contains a beat frequency proportional to the velocity difference between the two measuring points. With the new technique, a compact vorticity probe consisting of two sets of optical fibers and couplers can be built, which would simultaneously measure two velocity gradient components at four closely spaced locations. The new vorticity probe is capable of measuring ømega (r,t) with a spatial resolution down to 50 micron. The operation of the probe is similar to laser Doppler velocimetry and can be used widely in the general area of fluid dynamics.

[W15.009] Power fluctuation in a closed turbulent system and the 2D-XY model

It has recently been observed that the probability distribution of turbulent power fluctuations in closed flows is the same as that of the harmonic 2D-XY model. We propose an explanation for this phenomena by postulating the existance of a coherent structure in the system. The fluctuations relevant to the power dissipation is the frictional loss at the interface of the turbulent flow and the coherent structure. These can be mapped to the 2D-XY model in the harmonic limit. This not only accounts for the form of the probability distribution but also the Reynolds number dependence of the ratio of the mean and the variance.

[W15.010] Boundary effects on forced drainage through aqueous foam

The flow of liquid through foam confined in vertical tubes was investigated by measuring the velocity v_f of the liquid front forced down by gravity for various flow rates Q. The power law relating the velocity to flow rate of the incoming liquid (v_f\sim Q^\alpha) was observed for tubes of various cross-sectional areas, A. The exponent \alpha was found to vary linearly with the reciprocal of the area: \alpha= 0.325 + 13.7 mm^2/A . This further supports the node-dominated foam drainage model, which predicts \alpha= 1/3 in the limit of infinite cross-sectional area. This relation appears to be independent of bubble size, suggesting that using smaller foam bubbles may not alleviate boundary effects. The results of these experiments also partially explain the discrepancies in measurements of \alpha reported in previous works.

[W15.011] Soap froths and crystal structures

We propose a physical mechanism to explain the crystal symmetries found in macromolecular and supramolecular micellar materials. We argue that the packing entropy of the hard micellar cores is frustrated by the entropic interaction of their brush-like coronas. The latter interaction is treated as a surface effect between neighboring Voronoi cells. The observed crystal structures correspond to the Kelvin and Weaire-Phelan minimal foams. We show that these structures are stable for reasonable areal entropy densities.

[W15.012] A non-linear von Neumann law for three-dimensional foam coarsening

About 50 years ago, John von Neumann proved that the coarsening rate of individual bubbles in a 2-D dry foam is a linear function of the number of edges of the polygonal bubble. Soon afterwards it was conjectured that a statistical analog holds in three dimensions: polyhedral bubbles with a given number F of faces have an average growth rate that scales linearly in F. Using a theorem by Minkowski, we derive a parameter-free analytical expression for the average growth rates and show that it is non-linear, asymptoting to a square-root power in F. Experimental data and detailed foam simulations are in exceptionally good agreement with the analytical results. A refined model incorporates foam disorder to further improve the predictive power of the theory.

[W15.013] Effective Tempertures in Foam Simulations

Foam, a dense packing of bubbles in a small amount of liquid, is a disordered zero-temperature system because the thermal energy is much smaller than the typical energy barrier required for bubbles to change their relative positions. If a foam is steadily sheared, however, it flows as bubbles change their relative positions in rearrangement events. Our aim is to determine whether the effects of steady shear on bubble motion can be characterized by an effective temperature. We study several possible definitions of temperature, all of which reduce to the true temperature in an equilibrium system. Two definitions arise from linear response relations between fluctuations in diagonal components of the stress tensor and compressibilities. One arises from the fluctuation-dissipation relation, connecting the viscosity to fluctuations in shear stress. A fourth definition arises from the distribution of interparticle normal forces. We find that all of these definitions yield effective temperatures with the same shear-rate dependence over four orders of magnitude of shear rate. This suggests that the concept of an effective temperature may be useful for describing driven athermal systems.

[W15.014] Stress Distribution in Fluid Foams

In two-dimensional foams we define the mesoscopic stress and strain, which we measure directly from foam images. We evaluate the local stress in foams from both experiments and simulations. In flowing foams and foams under shear, we never observe force-chain like distribution as those found in granular materials. Instead, stress distribution is smooth and homogeneous in foams. Comparing the shear flow of monodispersed and polydispersed foams, we discuss the stress-strain relationship and foam's transition between the elastic and viscous regimes.

Part W of program listing