Search

Ultrasound technology employs cavitation to generate high-pressure soundwaves to disrupt bacterial cells. This study reveals the effectiveness of a single frequency ultrasound device for bacterial cell inactivation. A low-cost ultrasound device having a single frequency, i.e. 22 kHz for lab-scale application, was developed first, and the prototype was mechanically designed and analyzed using the finite-element method to assure the targeted natural frequency could be achieved. The prototype was then tested inactivating bacterial cells, Escherichia coli (E. coli) and Bacillus subtilis (B. subtilis), in a simple medium and a food system, and the results were then compared to a commercial system. A treatment time of up to 15 minutes was able to reduce E. coli and B. subtilis cells by 3.3 log and 2.8 log, respectively, and these results were similar to those of the commercial system. The effectiveness of bacterial cell inactivation using the developed single-frequency ultrasound device is then discussed. The findings are useful for designing low-cost ultrasound devices for application in the food industry.

This study performs Stokesian dynamics simulations of suspensions of rigid spheres to determine the conditions under which swollen starch granules can be considered rigid for rheology measurements. The first part of the study benchmarks the numerical simulations to experimental measurements of storage modulus (G′) for monodisperse polystyrene suspensions. The second part of the study compares the simulations to experimental measurements of G′ for waxy maize and normal rice starch suspensions swollen to volume fractions 0.4 0.5. These results indicate that granule deformability plays an important role when φ > 0.5, and indicates the range where one can apply theories of rigid suspension rheology.

Granule size distribution of 8% w/w suspension of normal rice starch (NRS), waxy rice starch (WRS), modified potato starch (MPS), and normal potato starch (NPS) in water when subjected to heating at 60, 65, 70, 75, 80, and 85°C at different hold times (0–60 min) were characterized. The average starch granule diameter was larger at higher temperatures and hold times for NRS, WRS, and MPS indicating swelling, whereas for NPS it decreased indicating breakage. Swelling varied in the order: MPS > NRS > WRS. Earlier proposed pseudo first‐ and second‐order kinetic and Weibull models for swelling were evaluated. Swelling kinetics was also predicted using our previously developed mechanistic model (Desam et. al., 2018a Journal of Food Engineering 222:237–249) whose predictions agreed well with the experimental data of mean granule diameter and granule size distribution with time at different temperatures, and therefore can be employed to describe swelling at different processing conditions. PRACTICAL APPLICATIONS: Starches are incorporated in food products for a variety of reasons such as stabilizing, thickening, binding, and gelling. Starch occurs as discrete granules. Upon exposure to water, starch granules swell when heated. This results in thickening of starch suspension (known as pasting) due to an increase in volume fraction of swollen granules. Starch pasting results in an increase in its viscosity. Therefore, the texture of a variety of food products such as sauces, puddings, soups, batter mixes, and so forth are influenced by pasting. The rheology and texture of starch paste obtained by cooking of starch granules are governed by its swelling. It is, therefore, necessary to quantify swelling in order to predict the rheology of starch paste as well as to develop new food formulations. We developed a mechanistic model which predicts the swelling kinetics of rice and potato starch suspensions.

We present a methodology to predict the storage modulus ( G ’ ) of starch paste due to granule swelling, given the physical properties of the starch granule and temperature history. This was tested on experimental measurements of granule size distribution and G ’ for 8% w/w suspensions of waxy maize, normal maize, waxy rice, normal rice, and cross linked normal maize – all heated to different temperatures (65–90 °C) with holding times between 2 and 60 min. Experimental data of storage modulus G ′ vs volume fraction φ fall onto a master curve when G ′ is normalized by a multiple of γ / R ‾ , where γ is the granule-solvent interfacial energy, and R ‾ is the average granule size. We show that one can combine this master curve with starch swelling theories to forecast the time-dependent rheology of starches. This work also demonstrates that granule-solvent interfacial energy is a key physical parameter in controlling starch rheology.

In this study we employed a layer-by-layer (LbL) deposition technique to produce fish oil in water emulsions encapsulated with a positively charged inner soy β-conglycinin (7S) layer by high shear mixing followed by deposition of a negatively charged outer high methoxyl pectin (HMP) layer using either high shear mixing or homogenization (500 or 3000 psi) and compared them with emulsions produced by 7S-HMP complex. The size, shape, morphology and wall structure of emulsion droplets were characterized by dynamic light scattering and microscopy. Emulsion produced by high shear mixing only were unstable with a droplet size of 7.48 μm. Stable emulsions were produced by high shear mixing followed by homogenization at 500 psi with significantly lower droplet size (3 μm) and uniform two layer shell thickness (80–170 nm) around the drops. The two layer shell thickness of emulsion drops produced by homogenization at 3000 psi was non uniform although it exhibited good long term storage stability. More diffuse distribution of 7S was observed in the adsorbed layer of emulsion droplets that were produced by 7S-HMP complex compared to LbL with a higher layer thickness and a lower ζ potential for the former thereby indicating a difference in morphology of adsorbed layers in the two cases. The results of this investigation seem to indicate that the mechanism of emulsion formation in the second homogenization step is closer to layer by layer deposition than stabilization by 7S-HMP complex and demonstrated a new method of LbL to utilize 7S as an emulsifier.

In this study, the effect of limited hydrolysis of soy β-conglycinin (7S) on the oxidative stability of 7S hydrolysate (7SH)-stabilized emulsions was investigated under different conditions of pH, ionic strength, degrees of hydrolysis (DH), and protein concentration in the continuous phase. The hydrolysis was performed using trypsinization and acid hydrolysis. Interfacial protein conformations were studied by thioflavin T fluorescence, scanning and transmission electron microscopy techniques, and Raman spectroscopy at oil-mimicking, functionalized silver surfaces. The antioxidant property was tested by the Trolox equivalent antioxidant capacity (TEAC) assay. At DH 0.7%, trypsinization improved emulsion oxidative stability at pH 7 under low ionic strength, as a result of an increase in protein antioxidant property and enhanced interfacial barrier property due to substantial increment of intermolecular β-sheets. The loose coil/helix to intermolecular β-sheet transition was deemed essential in the building of an effective interfacial barrier. At pH 3, however, the tryptic 7SH turned pro-oxidant, and interfacial coverage by the protein became uneven. As such, the emulsion oxidative stability was not better than that based on the native 7S at pH 7. The modification of the surface charge of the oil from non-polar to anionic led to increased formation of intermolecular β-sheet, but it did not improve the emulsion oxidative stability. Lastly, acid hydrolysis of 7S at a similar DH led to flocculation-induced destabilization of the emulsion at pH 3, which exacerbated the intrinsic oxidation of the encapsulated oil even further. Depletion flocculation and bridging were a result of fibril formation during acid hydrolysis.

A model for growth of bubbles during proofing of bread dough is presented for infinitely dilute as well as finite volume fraction gas dispersions. The model accounts for diffusion of CO2, produced by fermentation, along with the resistance to bubble expansion by the viscoelasticity of the dough as described by Oldroyd-B constitutive equation. The model predicts evolution of bubble size, bubble growth rate and the profiles of CO2 concentration and normal stresses in the vicinity of the gas bubble. The growth of bubbles exhibits a lag time followed by an exponential growth phase. The lag time is found to be smaller for larger dough relaxation time, larger surface tension, smaller dough viscosity, higher temperature, higher gas volume fraction and higher CO2 production rate. The bubble growth rate is larger for smaller bubbles resulting in crossover of bubble size at longer times.

A mutated variant of 20 amino acid miniprotein Trp-cage (TC5b), called TC5c (Asp9 replaced by Asn9), was designed to demonstrate the effect of a salt bridge. As a result of strong electrostatic interaction, the distance distribution between Asp9 and Arg16 exhibited a larger probability in the range of the salt bridge for TC5b compared to TC5c. The probability of α-helix formation for residues 3–8, as well as for residues 11–14, was high for TC5b. The salt bridge formation between Asp9 and Arg16 in TC5b was indicated by (a) a strong correlation of their distance of separation with the subtended angle with the centre and (b) a step decrease in the distance between Gly11O and Arg16H at 12 ns. Replica exchange molecular dynamics simulation at different temperatures in the range of 270–590 K indicated that the average distance between Asp9 and Arg16, end-to-end distance, root mean square deviation with respect to a reference NMR structure of TC5b did not change significantly with temperature below 370 K for TC...

A coarse-grain (CG) algorithm is developed for molecular dynamics (MD) simulation of proteins in which the polypeptide backbone as well as side chains were mapped into spherical interaction centres. The force field parameters for non-bonded interaction between these centres (beads) were evaluated from the interaction of all atoms corresponding to these beads using pairwise additivity. The validity of CG algorithm was demonstrated by comparing the potential energy, radius of gyration (RG), end-to-end distance and root-mean-square deviation with those obtained by all-atom (AA) simulation for a small protein molecule Trp-cage as well as for lysozyme in solution. The CG simulation for lysozyme in solution requires less than 1/50 CPU-time compared to that for the AA method. Also, the CG method converges to equilibrium potential energy much faster than AA simulation. CG simulation for lysozyme adsorbed on silica surface showed that the molecule is more unfolded with a less compact tertiary structure compared to...

The effects of cooling rate, holding temperature, pH and polysaccharide concentration on gelation characteristics of gelatin and gelatin–polysaccharide mixtures were investigated using a mechanical rheometer which monitored the evolution of G ′ and G ″. At low holding temperatures of 0 and 4 °C, elastic gelatin gels were formed whereas a higher holding temperature of 10 °C produced less elastic gels. At slow cooling rates of 1 and 2 °C/min, gelling was observed during the cooling phase in which the temperature was decreased from room temperature to the holding temperature. On the other hand, at higher cooling rates of 4 and 8 °C/min, no gelation was observed during the cooling phase. Good gelling behavior similar to that of commercial Strawberry Jell-O ® Gelatin Dessert was observed for mixtures of 1.5 and 15 g sucrose in 100 ml 0.01 M citrate buffer containing 0.0029–0.0066 g low-acyl gellan. Also, these mixed gels were stronger than Strawberry Jell-O ® Gelatin Desserts as evidenced by higher G ′ and gel strength values. At a very low gellan content of 0.0029 g, increasing pH from 4.2 to 4.4 led to a decrease in the temperature at the onset of gelation, G ′ at the end of cooling, holding and melting as well as an increase in gel strength. The gelation time was found to decrease to about 40 min for gelatin/sucrose dispersions in the presence of 0.0029 g gellan at pH 4.2 whereas the corresponding time at pH 4.4 was higher (79 min). In general, the gelation time of gelatin/sucrose dispersions decreased by a factor of 2 to 3 in the presence of low-acyl gellan. The addition of low-acyl gellan resulted in an increase in the gelation rate constant from 157.4 to 291 Pa. There was an optimum low-acyl gellan content for minimum gelation time, this optimum being pH dependent. Addition of guar gum also led to a decrease in gelation time to 73 min with a corresponding increase in the gelation rate constant to 211 Pa/min though these values were not sensitive to guar gum content in the range of 0.008–0.05 g. The melting temperature of gelatin/sucrose/gellan as well as gelatin/sucrose/guar mixtures did not differ significantly from that of pure gelatin or Strawberry Jell-O ® Gelatin Desserts. At pH 4.2, the melting rate constant was highest at a low-acyl gellan content of 0.0029 g whereas the rate constant was insensitive to low-acyl gellan content at pH 4.4. Addition of guar did not seem to affect the melting temperature or the melting rate constant.

A model for Ostwald ripening of oil-in-water emulsion in the presence of small amount of surfactants is presented. It accounts for the transfer of oil from small to larger drops when the interfacial resistance is rate controlling. In this case, the continuous breakdown and reformation of the micellar structure during mass transfer through the interface, is assumed to be the rate-controlling step. A discretized population balance equation for the change in the number concentration of drops due to Ostwald ripening is solved using the method of characteristics. The third moment of the distribution (average volume) is found to increase linearly with time, consistent with available experimental observations, before reaching an abrupt equilibrium. The rate of change of drop volume is found to be strongly dependent on the solubility and is fairly insensitive to the volume fraction. The transients of the drop size distributions indicate an initial rapid decrease in the small droplets with a corresponding increase in the larger drops followed by a very slow change in the number distributions at longer times. The rate constants involved can be roughly correlated with the components of several experimental measurements, and allow comparison with the data of Kabalnov (Langmuir 10 (1994) 680), but only at small surfactant concentrations. The numerical agreement is not good but it is able to predict the anomalous direction of change with increased surfactant concentrations. The basis of the lack of numerical agreement is discussed.

The effect of conformation of α-lactalbumin on the dynamics of adsorption as well as on the properties of adsorbed layer at air–water interface were investigated. The surface hydrophobicity of molten globule conformation of α-lactalbumin (prepared by lowering pH to 2) was found to increase by 15-fold compared to the protein in its native form (pH 7) with increased flexibility as evidenced by a much smaller hysteresis area of spread surface pressure isotherms. This higher surface hydrophobicity resulted in (i) higher surface activity of α-lactalbumin in its molten globule conformation compared to the native form inspite of a much higher electrical energy barrier due to much higher net charge and (ii) diffusion controlled adsorption for much longer times and surface pressures than the native form. The diffusion coefficient of α-lactalbumin in molten globule state was lower than that for native form (2.22×10−10 m2 s−1 vs 4.65×10−10 m2 s−1) and increased for the former at higher ionic strength. The area per molecule during the dynamics of adsorption was found to be the same at a fixed surface pressure for both the conformations and lower than the corresponding value for fully denatured protein thus indicating that α-lactalbumin does not fully unfold at the interface in both the conformations. Even though α-lactalbumin adsorbed much more in its molten globule conformation, it gave poor interfacial rheological properties compared to the native form. Ionic strength did not influence the relationship between the interfacial elasticity and surface concentration for both the conformations.

A statistical thermodynamic model for the prediction of precipitation curves of globular proteins using nonionic polymers has been proposed. The model accounts for protein-polymer, polymer-solvent, electrostatic, and hydrophobic interactions as well as the entropy of mixing and employs simplifying assumptions such as spherical globular protein molecule with uniform surface properties and linear, homogeneous polymer uniform with respect to molecular weight. The proposed model can only be employed to predict precipitation curves of charged proteins at sufficiently high ionic strengths since it does not account for electrostatic protein-protein interactions due to overlap of electrical double layers. The model predictions of precipitation curves of human serum albumin (HSA) at the isoelectric point using polyethylene glycol (PEG) for different initial protein concentrations and molecular weights of PEG agreed well with the experimental data. Higher polymer concentrations were found to be required to...

Transient breakage drop-size distributions have been experimentally measured using an image analysis technique. The transient distributions show self-similar behavior. The breakage rate and daughter-drop distribution functions have been determined using an inverse-problem approach which takes advantage of this self-similarity. The inverse-problem results show that the breakage rate is not a power law function of the drop size. The breakage rate is found to increase sharply with the drop size and the stirrer speed while decreasing sharply with increase in the interfacial tension. It is also found to decrease with increase in the dispersed phase viscosity, though the dependence on the viscosity is weaker than on the other variables. The daughter drop distribution was found to be relatively insensitive to the stirrer speed and interfacial tension, but was found to depend on the dispersed phase viscosity. As the drop viscosity increases, the breakage becomes more erosive in nature, leading to a broader size distribution of daughter drops. Generalized correlations for the breakage rate and daughter-drop distribution which account for the effect of physical properties and experimental conditions are presented. These relations will be very useful in predicting the drop-size distributions in stirred dispersions. Models for the breakage functions are compared with those determined in this study and the model predictions of the transient-size distributions are compared with the experimental data.

Stored emulsions undergo various destabilizing processes including creaming and coalescence of drops. Many experimental studies have been carried out in the past to quantify drop coalescence; however, the presence of two distinct types of coalescence mechanismsone due to the relative motion between the drops and the other due to their permanent proximity to each other in the creamhas not been recognized. Furthermore, the effects of creaming in these investigations could not be eliminated in ways that do not introduce new modes of coalescence or alter the existing ones. The population balance equation for an emulsion in a column in which creaming, Brownian diffusion, and coalescence of drops occur simultaneously is analyzed. The analysis reveals the existence of a dynamic zone at the top of the column in which the net effect of creaming and Brownian diffusion of drops is eliminated. Thus, while the drops cream, diffuse, and coalesce as in an actual emulsion, the measurements from this zone allow the effect...

A mathematical and computational procedure called the inverse problem is developed to extract quantitative information from transient particle size distribution measurements The population balance framework describes the evolution of these transient size distributions. This paper describes an inverse problem for the determination of the size specific breakage rates and daugher drop distributions from transient size distribution measurements when these distributions evolve to a “self-preserving” or similarity distribution. The experimental time scaled with respect to the timescale of breakage is used as the similarity variable. A test for the existence of similarity is developed. This test uses only the available transient size distribution data. The result of this test is also used to determine breakage rate information The determination of the daughter drop distribution is an ill-posed problem. The ill-posedness is overcome by using the property that the distribution is a monotone function. Analysis shows that the asymptotic behavior of the daughter drop distribution can be determined from the experimental similarity distribution. Incorporating this additional information into the solution strategy has resulted in significantly improved solutions of the inverse problem. The optimum solution is chosen such that the similarity distribution predicted using this solution has error of the same order of magnitude as the error in the experimental similarity distribution. Several examples of the inverse problem are outlined

A model for concentration of proteins from dilute solutions in a continuous foam fractionation column is proposed. This model accounts for (1) kinetics of adsorption of proteins in the liquid pool as well as in the foam, (2) liquid drainage from thin films due to Plateau border suction and disjoining pressure, (3) gravity drainage of liquid from Plateau borders, and (4) bubble coalescence in the foam. Protein enrichment and recovery were found to increase as the liquid pool height increased, eventually attaining constant values (corresponding to adsorption equilibrium), thus demonstrating the strong dependence of protein separation on adsorption kinetics. Higher enrichments and lower recoveries were obtained for smaller gas velocities, larger bubble sizes, and higher feed flow rates. Enrichments as well as recoveries were higher at lower feed concentrations. Coalescence was found to lead to higher enrichments and lower recoveries, this dependence being stronger for larger inlet bubble sizes.

Dispersed-phase systems are analyzed with a fresh perspective where the volume fraction of the dispersed phase is emphasized, not particle numbers as in population balance. Such volume fraction balances are more pertinent to engineering because they deal with the amount of the dispersed phase relative to that of the continuous phase. Although it is easy to make detailed volume fraction balances directly or from population balance, many interesting features are identified here with balance equations in terms of volume fraction, which simply characterize the dispersion process and structure the resulting equation. They lead to equivalent “single-particle” (comprising the entire dispersed phase) processes which can be simulated with great simplicity allowing rapid calculation of quantities associated with the dispersed phase and dispersion. The techniques can solve an inverse problem for mass-transfer coefficients of individual droplets from (simulated) measurements of the bivariate distribution of drop size and concentration of a transferring solute. Such inverse problem method is important in developing experimental techniques techniques to measure multivariate population distributions such as those of Bae and Tavlarides (1989) and of flow cytometry.

A model for the hydrodynamics of coalescing foam bed is proposed which accounts for liquid drainage through thin films and plateau borders, bubble coalescence, and mixing of liquid between thin films and plateau borders. Foam bed is assumed to consist of equal sized dodecahedral bubbles at any cross section, and the variation of bubble size with foam height due to coalescence is described through phenomenological models. This model is employed to investigate the effect of coalescence on enrichment and recovery for the nonanol-water system in a continuous foam fractionation column for different inlet bubble sizes, superficial gas velocities, and inlet concentrations. Coalescence is found to yield higher enrichments and lower recoveries, possibly because of the predominant effect of increased liquid drainage due to larger bubble sizes resulting in a significant decrease in liquid holdup with foam height. Larger bubble sizes and lower superficial gas velocities were found to result in higher enrichm...

A model for transitional breakage probability of droplets in agitated lean fiquid-liquid dispersions is proposed based on the mechanism of breakage of droplets due to their oscillations resulting from relative velocity fluctuations. A universal transitional breakage probability in terms of non-dimensionalized drop diameter is derived for all dispersed phases whose density and viscosity are almost the same as that of continuous phase. The maximum stable drop diameter ds derived from the model, shows a dependence of NWe−0.6. It is shown that a “power law” approximation Kvn is valid for transitional breakage probability for d/ds up to 2. The exponent 2.67, predicted by this model corresponds rather well with an estimate of 2, obtained from experimental observations. A functional relation for the rate constant K in terms of the parameters and physical properties of the system is derived. A universal non-dimensionalized equilibrium drop-size distribution for agitated lean liquid-liquid dispersions is derived by analytical solution of a population balance equation simplified by order of magnitude estimates. Interestingly enough, this analytical solution is the same as the Gaussian distribution suggested empirically by Chen and Middleman.

A generalized isothermal effectiveness factor correlation has been proposed for catalytic reactions whose intrinsic kinetics are based on the redox model. In this correlation which is exact for asymptotic values of the Thiele parameter the effect of the parameters appearing in the model, the order of the reaction and particle geometry are incorporated in a modified form of Thiele parameter. The relationship takes the usual form: and predicts effectiveness factor with an error of less than 2% in a range of Thiele parameter that accommodates both the kinetic and diffusion control regimes.

Boundary value problems involving oblique or mixed second derivative boundary conditions[1,3] arise in the description of heat (or mass) transfer in stationary media which are peripherally cooled (or leached) by a fluid in which the temperature (or concentration) is varying significantly in the direction of flow. By decomposing the energy equation into a pair of first order systems Ramkrishna and Amundson have shown[1] how the originally non-selfadjoint boundary value problems can be reduced to selfadjoint problems. The foregoing decomposition allows for an elegant analytical solution of the boundary value problems which is also numerically efficient. This paper relaxes certain redundant constraints imposed earlier on the method of solutions[1] and demonstrates the power of the method by actual numerical calculations for a constant heat source function.

Photographic measurements of transient drop-size distributions from stirred liquid-liquid systems of low dispersed phase fraction in a batch vessel confirm consistency with a similarity behavior from population balance established earlier by Narsimhan et al. (1980). Moreover, breakage functions are presented in generalized dimensionless form accounting for dependence on physical properties of the system and power input through stirring. This information is essential for predicting drop-size distributions in stirred liquid-liquid systems. Experimental measurements of steady-state drip-size distributions obtained from stirred, continuous flow systems with known inlet drop sizes compare very favorably with theoretical predictions based on population balance analysis using the breakage functions obtained from batch experiments.

Based on the generalized treatment of isothermal mean effectiveness factor presented by Aris, an experimental factor Φ exp has been obtained, the numerical value of which could be ascertained from experimental measurements of reaction rate and other pertinent properties of the fluid-particle system. It is shown that if Φ exp ⩽ 0·03, the experimental data reflect solely the influence of intrinsic kinetics of the system. Based on available kinetic information pertaining to a phthalic anhydride process, the variation of Φ exp with temperature, catalyst activity and external diffusion has been presented. Finally a plot of Φ exp against generalized Thiele parameter for low orders of reaction, has been used to check the consistency and absence or otherwise of pore diffusion limitation in experimental data reported in existing literature.

The process of thermal decomposition of calcium carbonate has been treated as one governed by simultaneous heat and mass transfer, under quasi steady state conditions, to the decomposition interface. It is believed that the surface chemical reaction is very fast and as such does not interfere in the determination of the overall decomposition rate. Rigorous expressions, based on heat transfer rate, have been derived, based on the system properties, for the prediction of decomposition times for definite geometric shapes such as spheres and cylinders. The good agreement observed between the actual and predicted values bears out the soundness of the decomposition scheme assumed for the process. The expression derived are: Based on an analysis of simultaneous heat and mass transfer rates the following correlation is obtaiend: This equation bears very close resemblance to the theoretical expression for the evaporation of small spheres into quiet air. This equation may be rearranged to provide: which is a modified form of the usual correlation for simultaneous heat and mass transfer based on Chilton-Colburn analogy. The mathematical treatment has been extended to a two-phase solid system (Mg CO 3 -Ca CO 3 ) characterized by finite but different equilibrium decomposition temperatures. The mathematical analysis involves the solution of simultaneous differential equations. This has been done numerically by the modified Runge-Kutta method with the help of an IRM computer. The confirmation of the proposed equation must await future experimental data for the two-phase system.

The cell model developed by Amundson and co-worker has been applied to compute the bulk and particle temperatures and partial pressure along the length of a packed bed reactor where an exothermic non-catalytic solid-gas reaction, viz. proceeds under adiabatic conditions. The kinetic data previously obtained have been used in the numerical computation procedure adopted in programming on a CDC 3200 computer. By linearizing the transient equations around the steadystate, the stability problem has been investigated by examination of the Lienard-Chipart criterion. The condition of sectional stability has been obtained as: which is a more conservative condition that the usual van Heerden's slope conditions, at the specified cell. An approximate but safe stability condition applicable over the entire bed at any stage of conversion has been obtained as Experimental work is in progress.

is not available.

is not available.

Experimental measurements of transient drop size distributions in a stirred liquid-liquid dispersion (with low dispersed phase fraction) have been used concomitantly with population balance theory to recover the transition probability of droplet breakage, based on a similarity concept. The data remarkably uphold the proposed similarity hypothesis, and the estimated probability function displays the same qualitative trend as the model due to Narsimhan et al. (1979).

In an earlier communication[l] we have indicated a general graphical design procedure for a sequence of sparger reactors in which a second order liquid phase reaction proceeds in a stagewise fashion. The prediction of the reactant concentration in each stage and hence the conversion depended on a search procedure initiated along a straight line representing the mass balance equation at the given stage and drawn from the known feed stage located on the abscissa in a E-IU diagram for the given system.