Bubble Growth In Liquid Research Articles

Growth of bubbles in liquid.

BackgroundEvolution of a gas injected in a liquid is analyzed using the example of the behavior of oxygen molecules in water in which bubbles of gas molecules grow slowly by attachment of gas molecules to bubbles, the bubbles then associate and finally flow up to the liquid–gas interface and pass into the gas phase.Results Two methods are considered for gas injection in a liquid, insertion of individual molecules and injection of small gas bubbles via gas penetration through a porous material. The behavior of oxygen bubbles in water and growth of those bubbles is analyzed. Subsequently, these grown bubbles float up and disappear, or reach the water boundary as a result of turbulent motion of the liquid.Conclusions It is shown that measurement of the size distribution function of micron-size bubbles in various regions of the water container allows one to establish the flow current lines on the basis of the theory of bubble growth.Graphical abstract:Schematic diagram of energies of molecules in the gas phase, in bubbles and bound to solvent

Energy dissipation and Ps bubble growth in liquids

Dissipative energy losses accompanying growth of the Ps bubble are calculated using the Navier–Stokes equation. This allows to demonstrate a fulfilling of the total energy balance in this process. It is in favor of the adopted approach.

Modeling Diffusion-Induced Bubble Growth in Polymer Liquids

Accurate modeling of diffusion-induced bubble growth is essential for the development of efficient polymer foaming processes. Consequently, a large number of transport models of this complex phenomena have been formulated. In most previous studies, one or more simplifying approximations have been invoked to reduce mathematical complexity. In this paper, we present and compare several models of bubble growth in liquids and examine the effects blowing agent concentration, liquid viscosity and elasticity on bubble growth dynamics. In addition, we compare predicted and measured bubble growth behavior in two polymer foaming systems.

Measurement of Heat Transfer Coefficient for Direct-Contact Condensation during Bubble Growth in Liquid.

A method to measure the heat transfer coefficient for direct-contact condensation during two-phase bubble formation is proposed. The growth behavior of a condensing vapor bubble at a single nozzle submerged in an immiscible liquid under constant-flow condition was taken by a high-speed video camera. By analyzing the recorded images of bubbles at the nozzle and calculating heat and mass balances at the bubble, the heat transfer coefficients for direct-contact condensation of a two-phase bubble of hexane or vinyl acetate are experimentally obtained. These coefficients depend on the temperature difference between vapor temperature and immiscible liquid temperature, and decrease with increasing temperature difference. The heat transfer coefficients for direct-contact condensation obtained experimentally are compared with those estimated theoretically. Under the present experimental conditions, in the range of the temperature difference less than 14 K, the experimental results correspond well to the theoretical values.

A note on the initial condition for the formation of foams

It is shown that the initial condition which is input into the model describing bubble growth in liquids needs to be re-examined for the case of rapid foam formation. The initial condition that is assumed in foam formation is the critical nucleus; it is from here that the expansion occurs. For a rapid foam formation the initial condition needs to be changed, the size adopted is that of a bubble which allows the onset of instability. This instability occurs when the pressure difference between the inside of the bubble and the outside is small and approaching a difference of the order of 1 to 2 atmospheres, this corresponds to bubble sizes of 10 −4 m. This is the value that should be used as the initial condition in the differential equations expressing the growth of bubbles in the formation of a liquid foam.

Mechanism of the initial stage of bubble growth in a liquid close to the superheat limit

The concept of the critical nucleus is the basis of the homogeneous nucleation theory which enables the upper limit of a superheat to be calculated. Only nucleus formation is considered. It is as if nuclei that reach the critical dimensions are removed from the system and replaced by an appropriate mass of liquid. The theory does not give any information concerning the dynamics of bubble growth either. Nevertheless, some researchers use the concept of the critical nucleus as the initial condition in a descritpion of the bubble growth in superheated liquid. A bubble begins to grow after the disturbance of the balance, when the pressure difference exceeds the surface tension. According to this scheme, the initial bubble growth results from the fact that the vapor pressure in the bubble is higher than that in the surrounding liquid.

Generalized quantitative criteria for predicting the rate-controlling mechanism for vapor bubble growth in superheated liquids

Criteria are presented for predicting the relative importance of the inertia of the liquid and heat transfer in the liquid as controlling effects for spherically symmetric vapor bubble growth in liquids. The coupled governing equations including both of the above effects are first cast in appropriate dimensionless forms. Then numerical solutions of the coupled equations are compared to the limiting solutions for solely liquid inertia and solely heat transfer controlled growth processes, in order to determine the respective regions of importance of these two mechanisms. The cases of growth initiated by a step decrease and a linear decrease in system pressure are both considered. The criteria are developed for the case of an idealized fluid having a constant vapor density and a linear vapor pressure curve, and then shown to be approximately independent of the vapor density and pressure relations of the particular fluid. The applicability and usefulness of the criteria are supported and illustrated by comparison of predictions based on them with previous theoretical and experimental results taken from the literature.

Bubble growth in liquids

Based on the first law of variable mass thermodynamics, a relation for the rate of bubble growth is obtained which is in good agreement with experimental data particularly for large Jakob numbers.