Phenomena at the advancing ice-liquid interface: solutes, particles and biological cells

Ice formation in aqueous solutions and suspensions involves a number of significant changes and processes in the residual liquid. The resulting effects were described concerning the redistribution of dissolved salts, the behaviour of gaseous solutes and bubble formation, the rejection and entrapment of second-phase particles. This set of conditions is also experienced by biological cells subjected to freezing. The influences of ice formation in that respect and their relevance for cryopreservation were considered as well. A model of transient heat conduction and solute diffusion with a planar ice front, propagating through a system of finite length was found to be in good agreement with measured salt concentration profiles. The spacing of the subsequently developing columnar solidification pattern was of the same order of magnitude as the pertubation wavelengths predicted from the stability criterion. Non-planar solidification of binary salt solutions was described by a pure heat transfer model under the assumption of local thermodynamic equilibrium. The rejection of gaseous solutes and the resulting gas concentration profile ahead of a planar ice front has been estimated by means of a test bubble method, yielding a distribution coefficient of 0.05 for oxygen. The nucleation of gas bubbles has been observed to occur at slightly less than 20-fold supersaturation. The subsequent radial growth of the bubbles obeys a square-root time dependence as expected from a diffusion controlled model until the still expanding bubbles become engulfed by the advancing ice-liquid interface. The maximum bubble radii decrease for increasing ice front velocities. The transition between repulsion and entrapment of spherical latex particles by an advancing planar ice-front has been characterized by a critical value of the velocity of the solidification interface. The critical velocity is inversely proportional to the particle radius as suggested by models assuming an undisturbed ice front. The increase of the critical velocity for increasing thermal gradients shows good agreement with a theoretically predicted square-root type of dependence. Critical velocities have also been measured for yeast and red blood cells. The effect of freezing on biological cells has been analyzed for human lymphocytes and erythrocytes. The reduction of cell volume observed during non-planar freezing agrees reasonably well with shrinkage curves calculated from a water transport model. The probability of intracellular ice formation has been characterized by threshold cooling rates above which the amount of water remaining within the cell is sufficient for crystallization.(ABSTRACT TRUNCATED AT 400 WORDS)     

Generation of small bubbles and small bubble-liquid mass transfer in airlift reactors containing highly viscous liquids

The time-dependent gas hold-up is investigated during the aeration of the Saccharomyces cerevisiae suspension, the aqueous saccharose solutions and the glycerol solutions in the external loop airlift reactor. Due to the time-dependent bubble size distribution the fraction of the small bubble hold-up in the total gas hold-up decreases with an increase of the gas flow rate and with a decrease of the viscosity. The course of the accumulation process of the small bubbles is described by the first-order kinetic equation. The small bubble accumulation rate is investigated in the airlift reactor and the bubble column. It is showed that the small bubbles form and disappear exclusively in the riser of the airlift reactor. It is found that the small bubble-liquid mass transfer coefficient is several times larger than the overall oxygen transfer coefficient.     

Cavitation bubble- and gas bubble-induced fractional precipitation of paclitaxel from Taxus chinensis

In this study, a fractional precipitation technique of paclitaxel using ultrasonic cavitation bubbles and gas bubbles is presented. Precipitation efficiency has been dramatically improved, and the time required for precipitation has been reduced by 20–30 times compared to conventional methods. As a result of investigating the mechanism of fractional precipitation in which cavitation and gas bubbles were introduced, it was found that the bubble surface itself acts as a nucleation site, resulting in faster nucleation and thereby improving precipitation efficiency. In addition, compared to the conventional fractional precipitation, the particle size was reduced by 7.8–8.9 times and 4.7–4.9 times for cavitation bubbles and gas bubbles, respectively, and the diffusion coefficient was increased by 10.3–11.9 times (cavitation bubble) and 4.7–4.9 times (gas bubble).     

The influence of polymeric membrane gas spargers on hydrodynamics and mass transfer in bubble column bioreactors

Gas sparging performances of a flat sheet and tubular polymeric membranes were investigated in 3.1 m bubble column bioreactor operated in a semi batch mode. Air–water and air–CMC (Carboxymethyl cellulose) solutions of 0.5, 0.75 and 1.0 % w/w were used as interacting gas–liquid mediums. CMC solutions were employed in the study to simulate rheological properties of bioreactor broth. Gas holdup, bubble size distribution, interfacial area and gas–liquid mass transfer were studied in the homogeneous bubbly flow hydrodynamic regime with superficial gas velocity (U _G) range of 0.0004–0.0025 m/s. The study indicated that the tubular membrane sparger produced the highest gas holdup and densely populated fine bubbles with narrow size distribution. An increase in liquid viscosity promoted a shift in bubble size distribution to large stable bubbles and smaller specific interfacial area. The tubular membrane sparger achieved greater interfacial area and an enhanced overall mass transfer coefficient (K _La) by a factor of 1.2–1.9 compared to the flat sheet membrane.     

Intracellular gas supersaturation tolerances of erythrocytes and resealed ghosts.

Intact mammalian, avian, and amphibian erythrocytes were saturated with up to 300 atm nitrogen or argon gas and rapidly decompressed. Despite the profuse nucleation of gas bubbles in the suspending fluid, no evidence of intracellular gas bubble nucleation was found; all or most of the cells remained intact and little or no hemoglobin escaped. Internal bubbles were similarly absent from resealed ghosts of human erythrocytes as shown by lack of disintegration and by retention of an entrapped fluorescent compound. The absence of bubbles may indicate that much of the internal water does not have the same nucleation properties as external water.     

Evolution of acoustically vaporized microdroplets in gas embolotherapy

Acoustic vaporization dynamics of a superheated dodecafluoropentane (DDFP) microdroplet inside a microtube and the resulting bubble evolution is investigated in the present work. This work is motivated by a developmental gas embolotherapy technique that is intended to treat cancers by infarcting tumors using gas bubbles. A combined theoretical and computational approach is utilized and compared with the experiments to understand the evolution process and to estimate the resulting stress distribution associated with vaporization event. The transient bubble growth is first studied by ultra-high speed imaging and then theoretical and computational modeling is used to predict the entire bubble evolution process. The evolution process consists of three regimes: an initial linear rapid spherical growth followed by a linear compressed oval shaped growth and finally a slow asymptotic nonlinear spherical bubble growth. Although the droplets are small compared to the tube diameter, the bubble evolution is influenced by the tube wall. The final bubble radius is found to scale linearly with the initial droplet radius and is approximately five times the initial droplet radius. A short pressure pulse with amplitude almost twice as that of ambient conditions is observed. The width of this pressure pulse increases with increasing droplet size whereas the amplitude is weakly dependent. Although the rise in shear stress along the tube wall is found to be under peak physiological limits, the shear stress amplitude is found to be more prominently influenced by the initial droplet size. The role of viscous dissipation along the tube wall and ambient bulk fluid pressure is found to be significant in bubble evolution dynamics.     

Probabilistic approach to lysozyme crystal nucleation kinetics

Nucleation of lysozyme crystals in quiescent solutions at a regime of progressive nucleation is investigated under an optical microscope at conditions of constant supersaturation. A method based on the stochastic nature of crystal nucleation and using discrete time sampling of small solution volumes for the presence or absence of detectable crystals is developed. It allows probabilities for crystal detection to be experimentally estimated. One hundred single samplings were used for each probability determination for 18 time intervals and six lysozyme concentrations. Fitting of a particular probability function to experimentally obtained data made possible the direct evaluation of stationary rates for lysozyme crystal nucleation, the time for growth of supernuclei to a detectable size and probability distribution of nucleation times. Obtained stationary nucleation rates were then used for the calculation of other nucleation parameters, such as the kinetic nucleation factor, nucleus size, work for nucleus formation and effective specific surface energy of the nucleus. The experimental method itself is simple and adaptable and can be used for crystal nucleation studies of arbitrary soluble substances with known solubility at particular solution conditions.     

Liquid-to-Gas Mass Transfer in Anaerobic Processes: Inevitable Transfer Limitations of Methane and Hydrogen in the Biomethanation Process

Liquid-to-gas mass transfer in anaerobic processes was investigated theoretically and experimentally. By using the classical definition of k(L)a, the global volumetric mass transfer coefficient, theoretical development of mass balances in such processes demonstrates that the mass transfer of highly soluble gases is not limited in the usual conditions occurring in anaerobic fermentors (low-intensity mixing). Conversely, the limitation is important for poorly soluble gases, such as methane and hydrogen. The latter could be overconcentrated to as much as 80 times the value at thermodynamic equilibrium. Such overconcentrations bring into question the biological interpretations that have been deduced solely from gaseous measurements. Experimental results obtained in three different methanogenic reactors for a wide range of conditions of mixing and gas production confirmed the general existence of low mass transfer coefficients and consequently of large overconcentrations of dissolved methane and hydrogen (up to 12 and 70 times the equilibrium values, respectively). Hydrogen mass transfer coefficients were obtained from the direct measurements of dissolved and gaseous concentrations, while carbon dioxide coefficients were calculated from gas phase composition and calculation of related dissolved concentration. Methane transfer coefficients were based on calculations from the carbon dioxide coefficients. From mass balances performed on a gas bubble during its simulated growth and ascent to the surface of the liquid, the methane and carbon dioxide contents in the gas bubble appeared to be controlled by the bubble growth process, while the bubble ascent was largely responsible for a slight enrichment in hydrogen.     

Formation of gas bubbles in biological tissues in decompression (a mathematical model)

A mathematical model simulating transport of gases between a bubble resulted from decompression and tissue around is presented. With the help of the model the influence of gas mixture and density of the bubble forming centres upon the growth rate was studied. An important part of CO2 in the bubble forming was found out. The bubbles with He have been shown to grow faster than those with N2. At a 5-10-fold decrease of the outer pressure during 1-2 seconds the bubbles can reach sizes which violate hemodynamics in the system of microcirculation.     

Mathematical model of gas bubble evolution in a straight tube.

Deep sea divers suffer from decompression sickness (DCS) when their rate of ascent to the surface is too rapid. When the ambient pressure drops, inert gas bubbles may form in blood vessels and tissues. The evolution of a gas bubble in a rigid tube filled with slowly moving fluid, intended to simulate a bubble in a blood vessel, is studied by solving a coupled system of fluid-flow and gas transport equations. The governing equations for the fluid motion are solved using two techniques: an analytical method appropriate for small nondeformable spherical bubbles, and the boundary element method for deformable bubbles of arbitrary size, given an applied steady flow rate. A steady convection-diffusion equation is then solved numerically to determine the concentration of gas. The bubble volume, or equivalently the gas mass inside the bubble for a constant bubble pressure, is adjusted over time according to the mass flux at the bubble surface. Using a quasi-steady approximation, the evolution of a gas bubble in a tube is obtained. Results show that convection increases the gas pressure gradient at the bubble surface, hence increasing the rate of bubble evolution. Comparing with the result for a single gas bubble in an infinite tissue, the rate of evolution in a tube is approximately twice as fast. Surface tension is also shown to have a significant effect. These findings may have important implications for our understanding of the mechanisms of inert gas bubbles in the circulation underlying decompression sickness.     

Observation and quantification of gas bubble formation on a mechanical heart valve

Clinical studies using transcranial Doppler ultrasonography in patients with mechanical heart valves (MHV) have detected gaseous emboli. The relationship of gaseous emboli release and cavitation on MHV has been a subject of debate in the literature. To study the influence of cavitation and gas content on the formation and growth of stable gas bubbles, a mock circulatory loop, which employed a Medtronic-Hall pyrolytic carbon disk valve in the mitral position, was used. A high-speed video camera allowed observation of cavitation and gas bubble release on the inflow valve surfaces as a function of cavitation intensity and carbon dioxide (CO2) concentration, while an ultrasonic monitoring system scanned the aortic outflow tract to quantify gas bubble production by calculating the gray scale levels of the images. In the absence of cavitation, no stable gas bubbles were formed. When gas bubbles were formed, they were first seen a few milliseconds after and in the vicinity of cavitation collapse. The volume of the gas bubbles detected in the aortic track increased with both increased CO2 and increased cavitation intensity. No correlation was observed between O2 concentration and bubble volume. We conclude that cavitation is an essential precursor to stable gas bubble formation, and CO2, the most soluble blood gas, is the major component of stable gas bubbles.     

Rates of Shrinkage and Growth of Air Bubbles Entrained in Wheat Flour Dough

The rates of shrinkage at constant temperature, and growth under a temperature rise below 100°C, of bubbles entrained in wheat flour dough were analyzed and compared with those of a bubble in water. The rate of shrinkage of bubbles in flour dough was controlled by the diffusion of dissolved air from the surface of bubbles to the bulk of flour dough. The apparent diffusion coefficient of the dissolved air in wheat flour dough with the water fraction of 0.49 calculated from the shrinkage of bubbles, was (3.2 ± 1.5) × 10^1?1 m²/sec (19°C), and (6.4 ± 2.0) × 10^?11 m²/sec (42°C). However, the growth behavior of bubbles in flour dough under a temperature rise was very different from that predicted from the diffusion theory. The critical radius of bubbles to grow was larger than that estimated from the diffusion theory. The mechanism of growth of bubbles in wheat flour dough, which was different from that of a bubble in water, is a subject that needs to be clarified.     

Hydraulic Conductivity Recovery versus Water Pressure in Xylem of Acer saccharum

Experiments were conducted to determine the influence of stem diameter, xylem pressure potential, and temperature on the rate of recovery of hydraulic conductivity in embolized stems of Acer saccharum Marsh. Recovery of conductivity was accompanied by an increase in stem water content as water replaced air bubbles and bubbles dissolved from vessels into the surrounding water. The time required for stems to go from less than 3 to 100% hydraulic conductivity increased approximately with the square of the stem diameter and increased with decreasing xylem pressure potential. Recovery was halted when xylem pressure potential decreased below −6 kPa. Increasing xylem pressure from 13 to 150 kPa reduced the time for recovery by a factor of 4. Temperature had little influence on the rate of recovery of hydraulic conductivity. All of these results are in accord with a theory of bubble dissolution in which it is assumed that: (a) the rate of bubble dissolution is rate limited by diffusion of air from the bubbles to the outer surface of the stems, (b) the equilibrium concentration of gases in liquid in stems is determined by Henry's law at all air-water interfaces, (c) the equilibrium solubility concentration is determined only by the partial pressure of the gas in the gas phase and not directly by the liquid-phase pressure, and (d) the gas pressure of an entrapped air bubble in the lumen of a cell can never be less than atmospheric pressure at equilibrium.     

Cell death from bursting bubbles: Role of cell attachment to rising bubbles in sparged reactors

Bursting bubbles are thought to be the dominant cause of cell death in sparged animal or insect cell cultures. Cells that die during the bubble burst can come from three sources: cells suspended near the bubble; cells trapped in the bubble lamella; and cells that attached to the rising bubble. This article examines cell attachment to rising bubbles using a model in which cell attachment depends on cell radius, bubble radius, and cell–bubble attachment time. For bubble columns over 1 m in height and without protective additives, the model predicts significant attachment for 0.5‐ to 3‐mm radius bubbles, but no significant attachment in the presence of protective additives. For bubble columns over 10 cm in height, and without protective additives, the model predicts significant attachment for 50‐ to 100‐μm radius bubbles, but not all protective additives prevent attachment for these bubbles. The model is consistent with three sets of published data and with our experimental results. Using hybridoma cells, serum‐free medium with antifoam, and 1.60 ± 0.05 mm (standard error) radius bubbles, we measured death rates consistent with cell attachment to rising bubbles, as predicted by the model. With 1.40 ± 0.05 mm (SE) radius bubbles and either 0.1% w/v Pluronic‐F68 or 0.1% w/v methylcellulose added to the medium, we measured death rates consistent with no significant cell attachment to rising bubbles, as predicted by the model. © 1999 John Wiley & Sons, Inc. Biotechnol Bioeng 62: 468–478, 1999.     

Effect of ventilation with soluble and diffusible gases on the size of air emboli

Pulmonary hypertension resulting from venous air embolism is known to increase after ventilation with highly soluble and diffusible gases. Exacerbation of the hypertension could be due to further blockage of the circulation if the bubbles enlarge as a result of ingress of gas by diffusion. This mechanism has been frequently cited but lacks direct proof. To determine directly whether intravascular air bubbles actually enlarge when highly soluble and diffusible gases are inspired, we used microscopy to measure the size of gas emboli in vivo. When air bubbles were injected into the right atrium, the bubbles that appeared in pulmonary arterioles were larger during ventilation with helium or nitrous oxide than with air. Air bubbles injected into the pulmonary artery enlarged when the inspired gas was changed to helium or nitrous oxide. The direction, magnitude, and timing of changes in bubble size were consistent with a net diffusion of gas into the bubbles. These data support the idea that venous air emboli enlarge during ventilation with soluble and diffusible gases and thereby cause further vascular obstruction.     

Interactions between animal cells and gas bubbles: The influence of serum and pluronic F68 on the physical properties of the bubble surface

We describe a method by which the degree of bubble saturation can be determined by measuring the velocity of single bubbles at different heights from the bubble source in pure water containing increasing concentrations of surfactants. The highest rising velocities were measured in pure water. Addition of surfactants caused a concentration-dependent and height-dependent decrease in bubble velocity; thus, bubbles are covered with surfactants as they rise, and the distance traveled until saturation is reached decreases with increased concentration of surfactant. Pluronic F68 is a potent effector of bubble saturation, 500 times more active than serum. At Pluronic F68 concentrations of 0.1% (w/v), bubbles are saturated essentially at their source. The effect of bubble saturation on the interactions between animal cells and gas bubbles was investigated by using light microscopy and a micromanipulator. In the absence of surfactants, bubbles had a killing effect on cells; hybridoma cells and Chinese hamster ovary (CHO) cells were ruptured when coming into contact with a bubble. Bubbles only partially covered by surfactants adsorbed the cells. The adsorbed cells were not damaged and they also could survive subsequent detachment. Saturated bubbles, on the other hand, did not show any interactions with cells. It is concluded that the protective effect of serum and Pluronic F68 in sparged cultivation systems is based on covering the medium-bubble interface with surfaceactive components and that cell death occurs either after contact of cells with an uncovered bubble or by adsorption of cells through partially saturated bubbles and subsequent transport of cells into the foam region. (c) 1994 John Wiley & Sons, Inc.     

Foam fractionation of globular proteins

Foam fractionation of bovine serum albumin (BSA) was studied as a model system for potato wastewater. The effects of feed concentration, superficial gas velocity, feed flow rate, bubble size, pH, and ionic strength on the enrichment and recovery of BSA were investigated in a single-stage continuous foam fractionation column. Enrichments ranged from 1.5 to 6.0 and recoveries from 5 to 85%. The feed concentrations were varied from 0.01 to 0.2 wt %, and enrichments were found to increase with lower feed concentrations. Enrichments also increased with lower superficial gas velocities and larger bubble sizes. At sufficiently low feed flow rates, enrichment was found to increase with an increase in the flow rate, eventually becoming insensitive to the feed flow rate at higher values. The pH was varied from 3.5 to 7.0 and ionic strength from 0.001M to 0.2M. The effects of pH and ionic strength were found to be coupled with bubble size. A minimum bubble size was found at pH 4.8, the isoelectric point of BSA, resulting in a minimum in the enrichment. Bubble size, and thus enrichment, was found to increase as the ionic strength decreased from 0.2M to 0.01M. Previous models(1,2) for the hydrodynamics of foam column were extended for a singlestage continuous foam fractionation column for the prediction of enrichment and recovery. The model assumed adsorption equilibrium, infinite surface viscosity, and bubbles of the same size. Though coalescence was formally accounted for in the model by considering bubble size as a function of foam height, calculations for the experimental runs were performed only for the case of no coalescence. Quantitative predictions of enrichment and recovery could not be made with a single representative bubble size because of the broad inlet bubble size distribution as well as broadening of the distribution as a result of coalescence. The experimental enrichments were higher and recoveries were lower than the model predictions, the discrepancy being more pronounced at lower feed concentrations because of increased coalescence. The higher enrichments are due to the predominant effect of internal reflux as a result of coalescence whereas the lower recoveries are a result of detrimental effects of broadening bubble size distributions.     

Promotion of oxygen transfer in three-phase fluidized-bed bioreactors by floating bubble breakers

The objective of the present study was to investigate a method to enhance the volumetric rate of oxygen transfer in three-phase fluidized-bed bioreactors. The rates of oxygen transfer from air bubbles to viscous liquid media were promoted by floating bubble breakers in three-phase fluidized beds operated in the bubble coalescing regime. The liquid-phase volumetric oxygen transfer coefficient has been recovered by fitting the axial dispersion model to the resultant data, and its dependence on the experimental variables, such as the gas and liquid flow rates, particle size, concentration of bubble breakers, and liquid viscosity, has been examined. The results indicate that the liquid-phase volumetric oxygen transfer coefficient can be enhanced up to 20-25%. The coefficient exhibits a maximum with respect to the volume ratio of the floating bubble breakers to the fluidized solid particles; it increases with increases in the gas and liquid flow rates and size of fluidized particles, while it decreases with an increase in the liquid viscosity. An expression has been developed to correlate the liquid-phase volumetric oxygen transfer coefficient with the experimental variables.     

Absorption of oxygen in highly viscous newtonian and non-Newtonian fermentation model media in bubble column bioreactors

Summary Mean relative gas holdup, slip velocity, bubble size distribution, mean specific interfacial area, and volumetric mass transfer coefficient of oxygen were estimated in sparged columns 14 cm in diameter and 380 and/or 390 cm high with two different aerator types (porous plate and injector nozzle) in highly viscous Newtonian (glycerol solutions) and non-Newtonian (CMC solutions) fluids.For the Newtonian liquids the above properties were estimated as function of the viscosity of the liquid. For the non-Newtonian liquids they were determined as function of the fluid consistency index and flow behavior index. Significant differences between Newtonian and non-Newtonian systems appear. In Newtonian medium k_L a drops with increasing viscosity and already approaches a constant value at =40 cP. In pseudoplastic medium k_L a varies with the fluid consistency and flow behavior indexes in the entire investigated range.In both of these systems the primary bubble population changes into two or three populations along the reactor: the medium bubbles gradually disappear and small and large bubbles are formed.