Mass transfer from a single gas bubble

Gases covering a wide solubility range were used to measure absorption rates from single bubbles rising freely in water. Absorption rates were not sensitive to any power of the diffusion coefficient and solubility alone proved to be an adequate correlating parameter. Experiments with bubbles containing inert and soluble gas mixtures yielded no evidence for a gas-film resistance, confirming published theory. Results for the absorption of CO₂ by NaOH solutions correlated well with the theory for pseudo-first-order fast reactions, provided allowance was made for a decreasing “physical” solubility of CO₂ with increasing ionic strength of the solutions.     

Elongated gas bubble dissolution under a turbulent liquid flow

Mass transfer between an elongated homogeneous gas bubble under a turbulent liquid flow in a duct is investigated experimentally. Elongated gas bubble dissolution is encountered in bioengineering tubular photobioreactors. Such reactors are interesting because they are compact, they have a low contamination risk and a low mechanical stress for a liquid phase containing fragile microalgae cells. It is demonstrated from experimental mass transfer measurements, that the interface of an immobilised elongated bubble can be approximated to a flat plane. Measured mass transfer experimental data, estimated using this simplification, appear to be well fitted by Sh_L = 1.76 × 10⁻⁵ × Re^1.506 × Sc^0.5, a correlation from Lamourelle and Sandall [8], given for a turbulent liquid flow in wetted-wall columns. A formula drawn from this hypothesis is proposed for mass transfer prediction in photobioreactors. For different applications, it is suggested that the results obtained for the studied geometry could be used to build mass transfer feedback control systems.     

Interphase mass transfer during drop or bubble formation

In derivation of all previous unsteady-state equations for prediction of mass transfer during formation of drops, it has been explicitly assumed that (i) the boundary layer around the drop is planar and, (ii) the concentration within the drop is reasonably constant. In the present work, it is shown that both these assumptions may be discarded by using the following expression for fractional approach to equilibrium, E, as a function of diffusivity, D, distribution coefficient, H, drop diameter, d, and formation time, t,:

where

However, the error introduced through assumption (ii) alone may be eliminated by using the equation:

where E_c is the fractional approach to equilibrium obtained by assuming constant concentration within the drop. These alongwith other existing equations are used to reevaluate the experimental data reported in the literature.     

Mass transfer from a spherical cap bubble in laminar flow

A theoretical account of mass transfer from a spherical cap bubble in laminar flow is given, based on the flow field derived by J.-Y. Parlange. The existence of concentration boundary layers on the bubble surface and on the surface of the spherical vortex wake is demonstrated, together with the presence of concentration wakes. The mass transfer process is described in qualitative terms. An approximate theory based on neglecting the thickness of the bubble is obtained, and the results compared with those given in various experimental accounts.     

Mass transfer between two turbulent liquid phases

The effect of forced turbulence on interfacial mass transfer between two liquid phases is investigated. A theoretical model is derived on the assumption that the mass transfer is controlled by unsteady diffusion into the vortices of the viscous subrange of the range of universal equilibrium. Mutual interaction of the turbulent fields in both phases is also accounted for. Experimental mass transfer rates for binary and ternary systems are presented; these were measured in a mixing cell of a new design. The model presented is shown to describe the process well, provided that the chosen liquid system is interfacially stable. The deviations due to interfacial instabilities are demonstrated for the case of the water—acetone—carbon tetrachloride system.     

Coalescence and fragmentation of drops in an isotropic turbulent flow

Coalescence and fragmentation of drops in an isotropic turbulent flow are considered. Equations for the minimum stable and maximum unstable sizes of drops were suggested. The coalescence frequency in liquid-gas and liquid-liquid systems was determined by analytically solving mass exchange equations. The drop fragmentation frequency in an isotropic turbulent flow was determined. The evolution of the size and time distribution function of drops was studied using the Fokker-Planck equation. A comparison with experimental data gave satisfactory agreement.     

Mass transfer in a recirculating bubble column

The mass transfer of oxygen between air and water in a recirculating bubble column has been studied, at gas and water superficial velocities of up to 0.23 m s^-1 and 0.68 m s^-1 respectively. Experiments show that the assumption of plug flow for the gas phase is reasonable, eliminating a possible source of error identified by other workers in calculating the mass transfer rates. The results obtained are consistent with other published work. It is also shown that for the air-water system breaking up the gas bubbles to increase the mass transfer does not have a large effect, due to rapid recoalescence of the bubbles.     

Mass transfer from a single rising bubble

The absorption rates of carbon dioxide, ethylene, and butene from single rising bubble of equivalent diameter 0.4–2.0 cm in water have been measured using an apparatus in which the bubble volume change with time of rise can be measured. The apparatus uses techniques previously reported but also is suitable for studies of mass transfer without and with chemical reaction at higher pressures (up to 4 atmospheres). The results have been compared with theoretical equations for rate of gas solution at the frontal surface of the bubble based upon potential flow theory and Higbie theory. The data are assessed together with those of others to show that they can be correlated well by This equation is valid for bubbles of equivalent diameter 0.6 < d < 4.0 cm and within the range 500 < N_Re < 20,000     

Single drop breakup in turbulent flow

The breakup process of a single drop in homogeneous isotropic turbulence was studied using direct numerical simulations. A diffuse interface free energy lattice Boltzmann method was applied. The detailed visualization of the breakup process confirmed breakup mechanisms previously outlined such as initial, independent, and cascade breakups. High‐resolution simulations allowed to visualize another drop breakup mechanism, burst breakup, which occurs when the mother drop has a large volume, and the flow is highly turbulent. The simulations indicate that the type of the breakup mechanism is a strong function of mother drop size and energy input. Large mother drops in highly turbulent flow fields are more likely to burst, producing a large number of drops of the size close to the Kolmogorov length scale. Small drops in moderate turbulence tend to break only once (initial breakup). The interfacial energy of a drop was tracked as a function of time during drop deformation and breakage. The maximum energy level of the deformed mother drop was compared to commonly used estimates of critical energy necessary to break a drop. Our results show that these reference levels of critical energy are usually underestimated. Moreover, in some cases even if the critical energy level was exceeded, the drop did not break because the time of the interaction between the drop and the eddies was not enough to finish the breakup. The numerical insight presented here can be used as a guideline for the selection of assumptions and simplifications behind breakup kernels.     

Mass transfer from single gas bubble — a comparative study on experimental methods

A comparative study on the experimental techniques which have been used for the study of mass transfer from single gas bubble was made. The instantaneous mass transfer rates from a single carbon dioxide bubble rising through quiescent liquid medium (water) were measured using two different methods. For the first method, two movie cameras were placed on a moving platform along perpendicular directions and were used to record the position and size change of the bubble. The second method measured the mass transfer rates by recording the pressure changes in the free space at top of the bubble column, which was caused by the change of bubble size. The instantaneous mass transfer coefficients determined by either method exhibited wide scattering which is typical of work of this kind. Discussions are given on the relative merits of these two methods.     

Mass transfer in a turbulent radial wall jet

Experimental and theoretical coefficients are reported for mass transfer in a turbulent radial wall jet initiated by an impinging free jet. The hydrodynamic solution was obtained by the momentum integral technique, and mass transfer was predicted by analogy. Point mass transfer data were obtained for air-naphthalene and cinnamic acid-water systems. At low Schmidt numbers, experimental coefficients were slightly above the theoretical prediction, and followed the theoretical trend with radial distance and nozzle Reynolds number from 10,000 to 60,000. Coefficients at high Schmidt numbers showed large positive deviations from theory, which decreased with radial distance and increased with Schmidt number. These discrepancies were attributed to surface roughness effects.     

Mass transfer from outer surface of thin tubes in parallel turbulent flow

The mass transfer coefficients from the outer surface of tubes or cylinders held in parallel turbulent steams have been calculated using integral momentum and mass transfer equations. The solution uses a hydrodynamics independent constant, λ _c which depends only upon Schmidt number. The results exhibit significant effect of curvature. For Schmidt number less than 108, Sherwood number can be predicted by $Sh_d Sc^{ - 1/3} = 0.039Sc^{0.208} times left( {frac{L} {d}} right)^alpha operatorname{Re} _d^{0.8}$Sh_d Sc^{ - 1/3} = 0.039Sc^{0.208} times left( {frac{L} {d}} right)^alpha operatorname{Re} _d^{0.8}, where α = −0.169Sc^−0.0103. The effect of the curvature is insignificant where $frac{L} {d}operatorname{Re} _L^{ - 0.2} - 0.033 times ln (Sc) leqslant 0.214$frac{L} {d}operatorname{Re} _L^{ - 0.2} - 0.033 times ln (Sc) leqslant 0.214.     

Mass transfer between a liquid and an array of discs in a cylindrical container. Part I: Pumped flow or rotation alone

This paper deals with average mass transfer between a liquid and both sides of discs arranged as baffles in a cylindrical container. The case of pumped flow alone through the stationary arrangement is first considered; the radial flow between the pairs of stationary discs is divergent and convergent successively. In other experiments, there is no pumped flow, but the discs are rotated between the stationary annular discs. The mass transfer coefficients are measured electrochemically for different geometrical and hydrodynamic conditions and the results are empirically correlated. The behaviour of corresponding surfaces involving a convergent or a divergent radial flow is discussed.     

Mass transfer to a drop stream from a field liquid

Mass transfer from a stream of drops falling freely in a stagnant liquid was investigated. Drop streams were produced by a dripping method and by a jet breakup method. Water and isobutanol, mutually saturated, were used as the dispersed and the continuous phases. Sodium hydroxide was transferred from isobutanol to water drops which were initially free of solute. The mass transfer resistance is on the continuous phase side. The mass transfer coefficient and terminal velocity of drop streams were measured experimentally. The experimental results show that the mass transfer coefficient in the drop stream is affected by the shielding effect of the previous drops. The experimental data have been correlated as K_t/U_t^0.5 versus interdrop distance l, a relationship describing the effect of the interdrop distance on the mass transfer coefficient in the continuous phase.     

Unsteady mass transfer between a slender bubble and a viscous liquid in a simple extensional flow

Unsteady mass transfer between a slender bubble and a viscous Newtonian liquid in a simple extensional and creeping flow has been studied. The exact analytical solution, at large Peclet numbers, has been obtained using similarity transformations and by the method of characteristics. It was determined that when a dimensionless time (the strength of the flow multiplied by the time) is greater than 2, then steady state is, in practice, obtained.