J. Drahoš

Homogeneous–heterogeneous regime transition in bubble columns

A simple physical model for homogeneous–heterogeneous regime transition in bubble columns is developed. The model is based on hydrodynamic coupling between gas and liquid phases. For the homogeneous regime, the coupling is made via bubble drift concept (Darwin, Proc. Camb. Phil. Soc. 49 (1953) 342). As a byproduct, a novel non-empirical formula for bubble slip velocity results, u/w=1−ae/(1−e). For the heterogeneous regime, the coupling is obtained in a simple formal way, recovering the classical result of Zuber and Findlay. The regime transition is considered as a smooth and gradual process characterized by a transition function. The model has five parameters: two terminal bubble velocities, bubble drift coefficient, Zuber–Findlay constant, and intermittency factor. All have clear physical meaning and are extractable from experimental data. The model gives formulas for the voidage-gas flow rate dependence separately for the homogeneous regime, heterogeneous regime and transition regime. The model gives a kinematic stability condition for the homogeneous regime and predicts the critical gas flow rate where the transition begins. It also predicts the maximum possible gas holdup in bubble columns. The model is verified by experiments with four different air–water bubble columns. Good agreement is found. Our results are compared with results of other authors. The model agrees with the drift-flux concept developed by Wallis (One-dimensional Two-phase, Flow, McGraw-Hill, New York, 1969) and with the stability theory of Shnip et al. (Int. J. Multiphase Flow 18 (1992) 705).

Effect of bubble column dimensions on flow regime transition

Abstract For the first time, detailed and consistent experimental data are presented on the effect of column size on the homogeneous–heterogeneous regime transition in bubble columns. Systematic measurements were performed in air–water bubble columns of diameters 0.14, 0.29 and 0.4 m and heights between 0.1 and 1.2 m . The critical point where the homogeneous regime looses stability and the transition begins was evaluated from the drift-flux plot. The results show that both the column height and width destabilize the homogeneous regime and advance the transition. Our data were compared with predictions of two available stability theories. Both the theories agree with the data relatively well. Our results also suggest that the column aspect ratio alone cannot replace the simultaneous effect of the column height and width.

Diagnosis of chaotic dynamics of bubble motion in a bubble column

Abstract The motion of bubbles in a two-dimensional bubble column was characterized by the deterministic chaos analysis of time-series data of bubble frequency, measured locally by an optical transmittance probe with a narrowed He Ne laser beam. To diagnose the dynamics of bubble motion, three different methods were applied to the series of time intervals between two successive bubble passages: (i) the correlation dimensions were estimated from the reconstructed attractors, (ii) using the short-term predictability analysis, the deterministic and random features in the bubble motion were characterized in terms of Mann-Whitney statistic, and (iii) the value of the Hurst exponent was computed using the rescaled range ( R/S ) analysis. All three parameters were found to show consistent and significant changes at the transition between homogeneous bubble flow and heterogeneous churn-turbulent flow. These results indicate that at low velocity the motion of bubbles in the bubble column is deterministic chaotic whereas at high gas velocity the random-like motion of bubbles becomes significant.

Purification of Waste Waters Containing Low Concentrations of Heavy Metals

Abstract Two types of brown coal, oxyhumolite and peat were studied with respect to their ability to remove heavy metals from waste waters. The results showed that the calcium loaded form of these materials can be effectively used for metal extraction by ion exchange with calcium. The proposed method can be recommended for concentrations of metals less than 10 mM.

Intermittent transition from bubbling to jetting regime in gas-liquid two phase flows

Abstract The transition from bubbling to jetting regime in nitrogen-water system was studied experimentally. The gas was introduced into a pool of stagnant liquid through a single orifice plate above a gas chamber. Two quantities were measured: pressure fluctuations in the gas chamber and velocity of liquid circulations near the orifice. Individual bubbles were formed at low gas flow rates (bubbling regime) while a continuous jet of gas was formed at high rates (jetting regime). The transition from bubbling to jetting regime (transition regime) displayed intermittent character. Jetting bursts of various length appeared at random in originally periodic pressure signal. The distribution of bubbling portion in the pressure signal was hyperbolical with exponent −1.33 indicating type III intermittency. Similar characteristic time scales were found in power spectra of both signals. 1/ f noise was revealed in the velocity spectrum. This kind of noise usually accompanies intermittent transitions. These results implied that liquid circulations with 1/ f noise induced by bubbles affected the bubble dynamics itself as a feed-back and caused the intermittent regime transition. The point of the regime transition was indicated by a sudden drop of Kolmogorov entropy, correlation dimension of the attractor, and Mann-Whitney statistic calculated from pressure signal. An explanation for this drop is suggested on the base of combination of properties of two attractors coexisting/competing within the intermittency range.

The tortuosity concept in fixed and fluidized bed

Abstract A new concept was suggested for the tortuosity of beds of particles based on the parallel-cappilary model. The resulting relation between the tortuosity and bed voidage is applicable over a wide range of conditions (from fixed to highly expanded bed). Even the simplified limiting form of eq. (6) seems to be fixed and fluidized bed.

Structure of gas pressure signal at two-orifice bubbling from a common plenum

Bubble formation at two orifices with a common plenum was studied experimentally. Different modes of bubble formation were identified by means of analysis of gas pressure fluctuations measured in the plenum. Two synchronous regimes were found at low and high gas flow rates, separated by a wide range of asynchronous regimes. The effect of important operational parameters (barrier in the plenum and in the liquid, orifice spacing, water height, and column diameter) on the stability threshold of the lower synchronous regime was investigated.

Natural modes of multi-orifice bubbling from a common plenum

Abstract Bubble formation at multiple orifices with a common gas plenum was studied experimentally. Gas pressure fluctuations in the plenum were measured and different modes of bubble formation were identified. Main attention was paid to regular synchronous modes because of their importance in formation of uniform gas–liquid mixtures. Factors affecting the interactions among orifices on both the gas and liquid sides were identified.

Analysis of wave modes in liquid film falling down a vertical oscillating plate

Abstract The stability of periodic two-dimensional waves on a liquid film falling down a vertical oscillating plate was studied experimentally using the aqueous solutions of carboxy-methylcellulose. A set of capacitance probes was used to measure the instantaneous film thickness. Artificial flow fluctuations induced by the plate oscillations caused distinct intensification of the wavy flow. We use the methods of phase space reconstruction and deterministic chaos analysis to show that the dynamics can be understood within the framework of deterministic chaos. We find that regions of relatively ordered and more complex chaotic dynamics alternate as the frequency of oscillations is varied. There are particular oscillating frequencies at which the system is close to a three-frequency quasiperiodic motion with the spectrum of Lyapunov exponents of type (0,0,0, −, …), elsewhere the system is either in a simple chaotic mode with the spectrum of type (+, 0, 0, −, …) or in a hyperchaotic mode with spectrum of type (+, +, 0, −, …).

Entropy of fluidized bed—a measure of particles mixing

The paper presents an attempt to define the physical entropy of the dense phase of a fluidized bed, based on liquid-like properties of fluidized systems. The quantity U was used as the analogy of temperature in classical thermodynamics. The obtained expression for physical entropy was compared to the correlation suggested for the Kolmogorov entropy in bubbling bed.