Mark J. McCready

Study of waves on thin liquid films sheared by turbulent gas flows

Waves that occur at the interface of a thin, horizontal liquid film sheared by a concurrent turbulent gas flow are investigated. Observations using liquids in the range of 13–15 cP indicate that broad‐crested, steady, periodic waves appear as the gas velocity is increased above the point of neutral stability. For a sufficiently large gas Reynolds number, steady solitary waves appear. These travel at speeds significantly faster than the periodic waves. However, if the liquid flow rate is increased, solitary waves do not form. To quantitatively describe the waves, a weakly nonlinear wave equation is derived using boundary‐layer approximations. The equation is valid for liquid Reynolds numbers of O (1–100) and reveals the presence of both kinematic and dynamic processes, which may (i) act together or (ii) singularly dominate the wave field. For the latter case, reduced forms of the evolution equation are derived. Linear stability analysis of the complete equation and its reduced forms is used to determine the parameter ranges where either dynamic or kinematic processes dominate. The evolution equation in its nonlinear forms should be capable of describing and predicting the amplitudes, shapes, and interactions of finite amplitude waves.

Formation of waves on a horizontal erodible bed of particles

Abstract The mechanisms responsible for the initial growth of sand waves on the surface of a settled layer of particles are studied experimentally and theoretically. Experiments employ water-glycerin solutions of 1–14 cP and glass spheres (ϱs = 2.4 g/cm3) that are either 100 or 300 μm in diameter. The particle Reynolds number and Shields parameter are of order one and the flow Reynolds number is of order 1000 to 10,000. Experimentally obtained regime maps of sand wave behavior and data on the wavelengths of the sand waves that first appear on the surface of the settled bed are presented. Turbulence in the clear liquid is not necessary for formation of waves and there is no dramatic change in behavior as the flowrate is increased across the turbulent transition. The initial wavelength varies as the Fronde number to the first power. Because a flowing suspension phase is observed before waves form, linear stability analysis of the clear-layer—suspension-layer cocurrent two-phase flow is presented. The suspension phase is modeled as a continuum that has an either constant or exponentially increasing viscosity. Neither of the models correctly predicts the wavelength for the first observed waves, their growth rate or their speed. However, the initial wavelength is found to agree well with the trajectory length for a saltating particle obtained from a model for forces on individual particles.

Radial Model for Particle Formation from the rapid expansion of supercritical solutions

Abstract A numerical model for the rapid expansion of supercritical-fluid solutions (RESS) is presented. Considering the complete expansion of the fluid into a vacuum, the process is modeled as inviscid, radial flow. The particulate material is described by the moments of the particle size distribution by numerically integrating the moments with the equations describing an inviscid flow of a non-ideal solution. By varying the initial process conditions, we examine the trends due to changes in specific operational parameters for typical RESS solutions. These calculations show that in the limit of a very rapid expansion with no precipitation in the nozzle itself, an increase in solute concentration produces a large increase in the particle size of the solids produced. Increasing the initial temperature causes a decrease in the calculated mean particle size, while an increase in pressure produces larger particles. However, both temperature and pressure have a much smaller effect on the calculated particle sizes than does concentration. The calculations demonstrate that small particles with a narrow size distribution can be achieved by using as low a solute concentration as possible and operating at relatively low preexpansion pressures and high preexpansion temperatures.

Influence of mass transfer coefficient fluctuation frequency on performance of three-phase packed-bed reactors

Abstract In three-phase packed-bed reactors, different flow regimes exist due to intrinsic hydrodynamic instability. Among these, the pulsing-flow regime is characterized by fast alternating of “liquid-rich plug” (pulse) and “gas-rich plug” (base) along the column, which results in a periodically changing environment for the stationary catalyst. In this paper, the influence of pulsing frequency on several different reaction systems is explored based on models that describe a small local region within a multiphase packed-bed reactor. It is found that the time-averaged reactor performance indexes including conversion of key reactant, selectivity of desired product over waste and yield of desired product can be increased significantly over other flow regimes such as the trickling-flow regime. The extent of enhancement varies substantially with pulsing frequency, and it appears that by carefully tuning it, a great potential exists for enhancing reactor performance.

Linear stability of stratified channel flow

Abstract Linear stability of horizontal gas-liquid stratified flow was solved using a tau spectral method that is valid for all wavenumbers. Pressures of 0.1–10 atm and liquid viscosities of 1–600 cP were examined. Comparison of these results with Kelvin-Helmholtz, integral momentum and rigorous long wave expansion approaches indicates that the approximate models do not correctly predict the point of neutral stability. The discrepancies in the models are due to more than differences in the calculation of interfacial perturbation stress components and differences in the base states. Stability predictions that include gas phase turbulence, as modeled with either a polynomial velocity profile or with imposed boundary conditions obtained from measured pressure and shear stress variations, are similar to laminar results if the interfacial stress and liquid depth are the same. The long wave stability boundary is found to correlate well for different channel height, density ratio and viscosity ratio, using a gas superficial Froude number corrected with a square root of density ratio and a liquid superficial Froude number. For gas-liquid channel flow waves that grow fastest typically have dimensionless wavenumbers of order unity. Their growth rate scales as a corrected gas Reynolds number to the first power. If the gas-liquid depth ratio is less than approximately one, long waves can be unstable before moderate wavelength waves. Under conditions where unstable moderate wavelength waves appear within a couple of meters, it can take 20–50 times this length for slowly growing long wavelength waves, which can destroy regime stability, to appear.

Periodic and solitary waves on thin, horizontal, gas-sheared liquid films

Abstract Measurements of wavelengths and speeds of periodic waves which occur at the interface of thin, horizontal, liquid films sheared by a cocurrent gas flow are compared with predictions of linear theory. In general, linear predictions accurately match the data near the point of neutral stability but begin to deviate as the gas velocity increases. The behavior away from neutral stability is explained by the examination of the dynamical system associated with steady solutions to a nonlinear wave equation based on boundary-layer approximations. Periodic waves are seen to occur in the neighborhood of the Hopf curve which serves as a boundary between periodic waves and a flat film. Solitary waves (which correspond under some circumstances to disturbance or roll waves) are observed to lie in another region of parameter space at gas velocities well above neutral stability. These results suggest that a complete nonlinear analysis of the boundary-layer (or associated wave) equations would be useful for predicting amplitudes and speeds for periodic waves and the region of occurrence for solitary waves.

Time varying behavior of cocurrent gas-liquid flows in packed beds

Abstract The time-varying fluid mechanics of the pulse flow regime are studied by the use of continuous pressure measurements. It is found that pulses can occur either or intermittently and the time period between pulses scales inversely with a modified Reynolds number. A simple physical basis for this scaling is suggested by a one-dimentional map. The results emphasize the importance of knowing the time scale of pulses and suggest that it is worthwhile to look for similar scalings for other intermittent flow phenomena such as slugs in horizontal gas-liquid flows.

Formation of solitary waves on gas-sheared liquid layers

Abstract The origin of solitary waves on gas-liquid sheared layers is studied by comparing the behavior of the wave field at sufficiently low liquid Reynolds number, R L , where solitary waves are observed to form, to measurements at higher R L where solitary waves do not occur. Observations of the wave field with high-speed video imaging suggest that solitary waves, which appear as a secondary transition of the stratified gas-liquid interface, emanate from existing dominant waves, but that not all dominant waves are transformed. From measurements of interface tracings it is found that for low R L , waves which have amplitude/substrate depth ( a / h ) ratios of 0.5–1 occur while for higher R L , no such waves are observed. A comparison of amplitude/wavelength ratios shows no distinction for different R L . Consequently, it is conjectured that solitary waves originate from waves with sufficiently large a / h ratios; this change of form being similar to wave breaking. The dimensionless wavenumber is found to be smaller at low R L , where solitary waves are observed. This suggests that perhaps, larger precursor (to solitary wave) waves are possible because the degree of dispersion, which acts to break waves into separate modes, is lower.

Uptake of calcium phosphate nanoshells by osteoblasts and their effect on growth and differentiation

The influence of calcium phosphate nanoshell materials on the uptake, viability, and mineralization of human fetal osteoblast cultures was evaluated. Proliferation rates and alkaline phosphatase activity of the cultures were unaffected by the addition of nanoshells to the growth media, but mineralization levels were enhanced by nearly 40%, in contrast to media prepared without nanoshells, or with other calcium phosphate nanomaterials. Nanoshells were internalized by macropinocytosis, and migrated toward the cell nucleus at a rate of 0.34 microm hr(-1). Dye-loaded nanoshells maintained high light emission intensity for over five days while inside the cells, where they could be used as intracellular markers for in vitro microscopic imaging. From these results, it appears that the CaP nanoshells could be developed into a safe sensor and delivery vehicle for osteoblast cell culture studies, whereas the carrier itself has intrinsic bioactivity and may itself upregulate the formation of new bone.

Stability of oscillatory two-phase Couette flow: Theory and experiment

The interfacial instability due to viscosity stratification is studied experimentally in a closed Couette geometry. A vertical interface is formed between two concentric cylinders with density-matched fluids of unequal viscosity. The outer cylinder is rotated with a time-harmonic motion, causing spatially periodic disturbances of the interface. The wavelengths and growth rates predicted by linear theory agree well with experimental results. Application of Fjo/rtoft’s inflection point theorem shows the neutral stability curves to be consistent with an internal instability occurring in the less viscous phase. Because the standard Floquet theory yields only time-averaged growth rates, the instantaneous behavior of the system is examined numerically. This reveals the flow to be unstable to a disturbance which has a maximum that oscillates between the interface and a location within the less viscous fluid. Surprisingly, it is found that interfacial wave amplification originates with the internal disturbance, a...