Volume Fraction Of Dispersed Phase Research Articles

Turbulent convection in emulsions: the Rayleigh–Bénard configuration

This study explores heat and turbulent modulation in three-dimensional multiphase Rayleigh–Bénard convection using direct numerical simulations. Two immiscible fluids with identical reference density undergo systematic variations in dispersed-phase volume fractions, $0.0 \leq \varPhi \leq 0.5$ , and ratios of dynamic viscosity, $\lambda _{\mu }$ , and thermal diffusivity, $\lambda _{\alpha }$ , within the range $[0.1\unicode{x2013}10]$ . The Rayleigh, Prandtl, Weber and Froude numbers are held constant at $10^8$ , $4$ , $6000$ and $1$ , respectively. Initially, when both fluids share the same properties, a 10 % Nusselt number increase is observed at the highest volume fractions. In this case, despite a reduction in turbulent kinetic energy, droplets enhance energy transfer to smaller scales, smaller than those of single-phase flow, promoting local mixing. By varying viscosity ratios, while maintaining a constant Rayleigh number based on the average mixture properties, the global heat transfer rises by approximately 25 % at $\varPhi =0.2$ and $\lambda _{\mu }=10$ . This is attributed to increased small-scale mixing and turbulence in the less viscous carrier phase. In addition, a dispersed phase with higher thermal diffusivity results in a 50 % reduction in the Nusselt number compared with the single-phase counterpart, owing to faster heat conduction and reduced droplet presence near walls. The study also addresses droplet-size distributions, confirming two distinct ranges dominated by coalescence and breakup with different scaling laws.

Correlation study between structural parameters of droplets and rheological properties of O/W high internal phase Pickering emulsions above the closest packing density

The correlation between the structural parameters of droplets and rheological properties of O/W high internal phase Pickering emulsions (HIPPEs) stabilized by soy protein isolate (SPI) nanoparticles was elucidated, with a volume fraction of dispersed phase (ϕ) above the closest packing density (74%). The structural basis of SPI nanoparticles was confirmed to be spherical heat-induced protein aggregates, which had moderate wettability and excellent interfacial activity. The structural parameters of emulsion droplets (contact length L, diameter D, length d1, width d2, the number of adjacent contact droplets Z), and the stability and rheological properties of HIPPEs were characterized by the confocal laser scanning microscopy (CLSM), diffusing wave spectroscopy (DWS), and mechanical rheometer respectively. The results of CLSM indicated the transition of droplets from spherical to polyhedral shapes as increased ϕ, accompanied by an increased L and Z. The rheological and stability analysis confirmed the widened linear viscoelastic range, elevated gel point (εc), and the extended half−life of the intensity autocorrelation function of HIPPEs as ϕ increased. Moreover, the loss factor (tan δ) remained constant at 0.1 within the ϕ of 74%–86%, revealing the solid−like nature of HIPPEs. The correlation between ϕ, structural parameters of droplets, and rheological properties of HIPPEs was further analyzed. The nonlinear regression fitting between the L/D and G' (elastic modulus) yielded a better fitting effect than d1/d2 and Z, suggesting an intrinsic correlation between emulsion structure and rheology. In summary, this study elucidated the intricate relationship between ϕ, droplet structure, and rheological properties of HIPPEs, offering a research foundation and theoretical basis for the development and application of protein particle−stabilized HIPPEs.

CFD–PBM coupled modeling of liquid–liquid interphase mass transfer behaviors inside the Kenics static mixer

Kenics static mixers (KSM) are commonly used in various industries for its excellent mass transfer performance. It is essential to systematically analyze the relationship between fluid parameters and mass transfer parameters to better understand the mass transfer behaviors between liquid–liquid phases and optimize the mass transfer efficiency of the KSM. In this work, a computational fluid dynamic–population balance model coupled method is utilized and three mass transfer models are compared and analyzed. Further simulations investigate the mass transfer behaviors inside the KSM under different superficial velocities, dispersed phase volume fractions, and aspect ratios. The results show that the increase of superficial velocity leads to the 2.23–14.15–fold increase of volumetric mass transfer coefficient and the 1.71–4.56–fold increase of mass transfer rate. What's more, increasing the dispersed phase volume fraction leads to the significant increase of 15.51 times in volumetric mass transfer coefficient and 34.92 times in mass transfer rate. Moreover, the increase of aspect ratio could result in the reduction of 4.19–1.72 times in volumetric mass transfer coefficient and 1.81–1.17 times in mass transfer rate. This work provides valuable theoretical insights for the optimal design of the KSM and the enhancement of mass transfer performance.

Decoupling the rheological responses of a soft solid emulsion with liquid inclusions

Soft solid emulsions are liquid droplets encapsulated in a soft solid material. Typical of dispersed systems, they can combine properties from both the liquid inclusions and the soft solids. The relative importance of the two phases in the rheological response is captured through the elastocapillary number, which compares capillary forces in the liquid inclusions to the matrix rigidity. We work with solid emulsions formed of poly(ethylene glycol) droplets in a poly(dimethylsiloxane) (PDMS) continuous phase. We create three families of emulsions with varying elastocapillary numbers, and range of inclusion volume fractions from 0 to 0.5. Through oscillatory rheology we probe both the elastic response and the dissipative effects of liquid droplets. In the case of a dominant response from the continuous phase or the drops, the results can be described with Palierne’s model. However, for the intermediate elastocapillary series we show that the evolution of the storage and loss moduli decouple with dispersed phase volume fraction. We attribute the increase of loss factor with volume fraction to the high polydispersity in droplet size. We can further modulate the response of the materials by cooling to freeze the droplets. This approach allows us to compare these soft solid emulsions with theories related to solid dispersions.

High internal phase emulsions gel ink for direct-ink-writing 3D printing of liquid metal

3D printing of liquid metal remains a big challenge due to its low viscosity and large surface tension. In this study, we use Carbopol hydrogel and liquid gallium-indium alloy to prepare a liquid metal high internal phase emulsion gel ink, which can be used for direct-ink-writing 3D printing. The high volume fraction (up to 82.5%) of the liquid metal dispersed phase gives the ink excellent elastic properties, while the Carbopol hydrogel, as the continuous phase, provides lubrication for the liquid metal droplets, ensuring smooth flow of the ink during shear extrusion. These enable high-resolution and shape-stable 3D printing of three-dimensional structures. Moreover, the liquid metal droplets exhibit an electrocapillary phenomenon in the Carbopol hydrogel, which allows for demulsification by an electric field and enables electrical connectivity between droplets. We have also achieved the printing of ink on flexible, non-planar structures, and demonstrated the potential for alternating printing with various materials.

Atomization behavior of burning stable emulsion droplets

We investigate the atomization behavior of burning stable water-in-oil microemulsion droplets. The microemulsion compositions are prepared by altering the dispersed phase volume fraction (ϕ) and base oils (dodecane, xylene, and surrogate (90% dodecane and 10% xylene) by weight). The combustion of base oil follows classical droplet combustion, while two-stage combustion, i.e., classical droplet combustion and atomization-dominated combustion, is observed for emulsion droplets. We reveal that vapor bubble formation occurs primarily through heterogeneous nucleation, and the mechanisms leading to bubble formation can be accurately predicted and controlled for distinct, highly stable emulsions. During the initial phase of combustion, water vapor bubbles nucleate, while the nucleation of oil vapor is more prevalent in the later phase of combustion due to the depletion of water content. In both regimes, heterogeneous nucleation ensues due to the agglomeration of surfactant inside the burning droplet. The lower volatility and viscous nature of the oil inhibit the growth rate of the nucleated oil-vapor bubble within the oil–surfactant mixtures. On the contrary, the water vapor bubble exhibits a higher growth rate within the emulsion droplet, attributed to its higher volatility and low viscosity. We show that qualitatively, the global bubble dynamics associated with the emulsion droplets remain substantially consistent regardless of ϕ and the type of base oil. However, it is observed that the onset of nucleation, bubble growth and collapse cycles, and the size of secondary droplets display a strong dependence on the ϕ and the type of base oil. The normalized diameter at the onset of nucleation increases as ϕ increases, exhibiting a logarithmic trend. The optimal dispersed phase volume fraction for effective atomization is found to be ϕ=0.2, regardless of the type of microemulsion.

CFD-PBM coupled modeling of the liquid-liquid dispersion characteristics and structure optimization for Kenics static mixer

Kenics static mixers (KSM) are extensively used in industrial mixing–reaction processes by virtue of high mixing efficiency, low power homogenization and easy continuous production. Resolving liquid droplet size and its distribution and thus revealing the dispersion characteristics are of great significance for structural optimization and process intensification in the KSM. In this work, a computational fluid dynamics–population balance model (CFD–PBM) coupled method is employed to systematically investigate the effects of operating conditions and structural parameters of KSM on droplet size and its distribution, to further reveal the liquid–liquid dispersion characteristics. Results indicate that higher Reynolds numbers or higher dispersed phase volume fractions increase energy dissipation, reducing Sauter mean diameter (SMD) of dispersed phase droplets and with a shift in droplet size distribution (DSD) towards smaller size. Smaller aspect ratios, greater blade twist and assembly angles amplify shear rate, leading to smaller droplet size and a narrower DSD in the smaller range. The degree of impact exerted by the aspect ratio is notably greater. Notably, mixing elements with different spin enhance shear and stretching efficiency. Compared to the same spin, SMD becomes 3.7–5.8 times smaller in the smaller size range with a significantly narrower distribution. Taking into account the pressure drop and efficiency in a comprehensive manner, optimized structural parameters for the mixing element encompass an aspect ratio of 1–1.5, a blade twist angle of 180°, an assembly angle of 90°, and interlaced assembly of adjacent elements with different spin. This work provides vital theoretical underpinning and future reference for enhancing KSM performance.

Predicting Human Dermal Drug Concentrations Using PBPK Modeling and Simulation: Clobetasol Propionate Case Study

Quantitative in silico tools may be leveraged to mechanistically predict the dermato-pharmacokinetics of compounds delivered from topical and transdermal formulations by integrating systems of rate equations that describe permeation through the formulation and layers of skin and pilo-sebaceous unit, and exchange with systemic circulation via local blood flow. Delivery of clobetasol-17 propionate (CP) from DermovateTM cream was simulated using the Transdermal Compartmental Absorption & Transit (TCATTM) Model in GastroPlus®. The cream was treated as an oil-in-water emulsion, with model input parameters estimated from publicly available information and quantitative structure-permeation relationships. From the ranges of values available for model input parameters, a set of parameters was selected by comparing model outputs to CP dermis concentration-time profiles measured by dermal open-flow microperfusion (Bodenlenz et al. Pharm Res. 33(9):2229–38, 2016). Predictions of unbound dermis CP concentrations were reasonably accurate with respect to time and skin depth. Parameter sensitivity analyses revealed considerable dependence of dermis CP concentration profiles on drug solubility in the emulsion, relatively less dependence on dispersed phase volume fraction and CP effective diffusivity in the continuous phase of the emulsion, and negligible dependence on dispersed phase droplet size. Effects of evaporative water loss from the cream and corticosteroid-induced vasoconstriction were also assessed. This work illustrates the applicability of computational modeling to predict sensitivity of dermato-pharmacokinetics to changes in thermodynamic and transport properties of a compound in a topical formulation, particularly in relation to rate-limiting steps in skin permeation. Where these properties can be related to formulation composition and processing, such a computational approach may support the design of topically applied formulations.

Development and rheological modeling of dietary fiber and policosanol plant-based bigels for potential food applications

Bigels are composite materials made by two phases with different polarities (i.e., an oleogel and a hydrogel) mixed between them without the addition of emulsifiers. Owing to their versatile rheological properties, they can be used for designing new products for food industry, or for cosmetics and pharmaceutical applications. In the past, different models have been proposed to relate their rheological properties to single phases characteristics and volume fraction. This paper proposes the rheological characterization and modeling of bigels prepared with citrus fiber particle gels (as the aqueous phase) and policosanol-based oleogels by investigating the effects of the ratio between rheological properties of phases and of the dispersed phase volume fraction. Both components (i.e., citrus fiber and policosanol) exhibit interesting properties for preparing plant-based healthy foodstuffs. Rheological characterization was carried out revealing that O/W bigels were formed at low fractions of oleogel added to gelled suspension whereas, at higher fractions, a transition through a matrix-in-matrix systems and, finally, a phase inversion occurred. The trend of phase angle at 1 Hz with oleogel volume fraction was used as a criterion to highlight the phase transition, as confirmed by confocal microscopy. Two models were proposed for predicting the rheological behavior of samples with both phase arrangements.

EXPERIMENTAL STUDY OF TWO-PHASE TURBULENT WAKE USING PIV TECHNIQUE

Near-wake regions of the turbulent wake flows behind a long cylinder at two Reynolds numbers (Re<sub>d</sub> = 3860 and 9650) and laden with the particles with mean size of 55 μm are studied using a two-phase particle image velocimetry (PIV) technique. Four mass-loading ratios (α) of 0 (equivalent to the single-phase case), 1, 3, and 5% corresponding to the dispersed-phase volume fractions of 1.248 × 10<sup>-6</sup>, 3.743 × 10<sup>-6</sup>, and 6.241 × 10<sup>-5</sup> for the last three cases, respectively, are investigated. In the particle-laden cases, complex variations of turbulence intensity are discovered; in the near-wake regions, turbulent intensity is either suppressed or enhanced locally compared with the single-phase case. No correlation between the turbulence-intensity modulation and the parameter of either α or Re<sub>d</sub> is found to exist. However, the turbulent mixing capability is attenuated for the cases with particles laden in the wakes. This attenuation is increased with α in both Re<sub>d</sub> cases. In contrast to the turbulence modulation, the turbulent dispersion of the laden particles increases as either α or Re<sub>d</sub> is increased.

Creation of Next-Generation Plant-Based Seafood Using Emulsion Gel Technology: Omega-3-Enriched Sea Foie Gras Analogs

Plant-based seafood analogs are gaining increasing popularity as replacements for traditional fish and other seafood products due to environmental (stock depletion, pollution, and bycatch issues) and health (bioaccumulated toxins, norovirus, and allergies) concerns associated with them. Several companies have launched plant-based fish products, but the market still lacks alternatives to shellfish and other sea delicacies. In this study, a plant-based sea foie gras (monkfish liver product) analog was developed using duckweed RuBisCO protein and omega-3-rich flaxseed oil to form emulsion gels. These gels consisted of a high concentration of flaxseed oil droplets dispersed within a gelled RuBisCO protein network. It was hypothesized that the high disperse phase volume fraction of the oil droplets and the heat-set gelation properties of the RuBisCO proteins would enable us to create emulsion gels that mimicked the properties of sea foie gras. A natural pigment (β-carotene) was incorporated into the oil phase of the emulsions to mimic the red-orange color of conventional sea foie gras. The structural, textural, and optical properties of real and plant-based sea foie gras analogs were characterized using scanning electron microscopy, confocal microscopy, dynamic shear rheology, texture profile analysis, and colorimetry. Emulsion gels prepared using 40% flaxseed oil and 10% RuBisCO proteins produced plant-based products that closely simulated the texture and color of the real products. Rheological analysis suggested that the oil droplets acted as active fillers within the protein gels. Our results suggest that emulsion gels may be used to create more sustainable and healthier plant-based seafood products.

Non-linear seepage law and a characterization model of heavy oil-in-water emulsion in porous media

Stable emulsions with different continuous-phase viscosities, dispersed-phase volume fractions, and dispersed droplet sizes were prepared. Seepage experiments using heavy oil-in-water (O/W) emulsion were then conducted in sand packs to analyze the effects of different injection rates, permeabilities, and emulsion characteristics on the seepage law. Finally, an evaluation method for the seepage law was established, and a regression model that considered the factors influencing the non-linear seepage laws was developed using the 1stop software to quantitatively reveal the seepage mechanism. The matching relationship between droplet size and permeability determined the seepage behavior of the O/W emulsion. Emulsions with droplet sizes matched with permeability behaved as a pseudoplastic fluid, with a non-linear flow. With an increase in the dispersed-phase volume fraction, the emulsions displayed a more non-linear behavior due to the accumulated retention and disordered plugging of dispersed droplets. With an increase in the injection rate, the emulsion with a low continuous-phase viscosity had more significant non-linear characteristics than the emulsion with a high continuous-phase viscosity. The correlation of the characterization model was relatively strong under the experimental conditions, with a correlation coefficient of 93.28%. Therefore, the characterization model accurately predicted the effects of the non-linear seepage law for all factors studied.

A comparative study on emulsification in the presence of a nanoclay (Pickering emulsion) or a surfactant using high intensity mixing

The study explored the potential of using a nanoclay, Laponite RD, as a stabilizing agent in comparison to a surfactant, Tergitol TMN6, at dispersed phase volume fractions of 10–50% vol. An ultrasonicator was employed as an energy intensive device; covering a specific power input range of ∼ 36–52 W kg− 1. In both cases, final dispersions obtained could be considered stable over the period of ageing tests for 3 months as comparable drop size distributions were obtained although there were some differences in the rheology at the highest dispersed phase concentration. Whilst surfactant stabilized emulsions were of Newtonian behavior, Pickering emulsions stabilized with the nanoclay exhibited non-Newtonian behavior, which may be a desirable feature of the final product- certainly one that requires attention in design and scale up. Kinetics of breakup studied through the evolution of the Sauter mean diameter prior to reaching an equilibrium value on the basis of energy density have shown the breakup process being faster with the Pickering emulsions although the equilibrium drop diameters were larger. Overall, with emulsions stabilized using a surfactant, Sauter mean drop diameters could be as low as 240 nm, regardless of the dispersed phase volume fraction, drop sizes were larger with Pickering emulsions which depended on the dispersed phase concentration.

High internal phase emulsion stabilized by sodium caseinate:quercetin complex as antioxidant emulsifier

High internal phase emulsion (HIPE) was produced and stabilized using a novel antioxidant emulsifier formed by the complexation between sodium caseinate (SC) and quercetin (Q). Colloidal complexes, produced via an alkaline process, showed great ability to reduce the interfacial tension between oil–water phases, promoting stabilization of the HIPEs even at low concentrations (1.5% w/v in the aqueous fraction). HIPEs at 0.80 volume fraction of dispersed phase presented remarkable viscosity due to the high-packing network of oil droplets surrounded by a thin liquid layer. Moreover, the emulsions showed a gel-like behavior and kinetic stability for 45-days at 25 °C. The approach of SC:Q complexes on HIPEs development is promising to reduce lipid oxidation, translated by the formation of hydroperoxides and malondialdehyde during storage, especially for the complex formed with the highest amount of the phenolic compound. In this study, the development of HIPEs with outstanding kinetic and oxidative stability is reported as a potential alternative for the development of healthier products with reduced saturated and trans-fat content.

CFD-PBE Simulation of Flow Dynamics and Mass Transfer in Two-Stage Countercurrent Mixer-Settler

Flow condition and mass transfer behavior of liquid–liquid extraction in a two-stage countercurrent extractor are investigated experimentally and numerically. CFD-PBE simulation is adopted to analyze the impact of operating parameters, including impeller speed, residence time, and organic-aqueous ratio of feed flow on volume fraction and droplet size of dispersed phase and volumetric mass transfer coefficient. Droplet size distribution is calculated by considering breakage and coalescence of dispersed phase. The allocation of dispersed phase between stages is found to be determined by impeller speed. Meanwhile, the allocation of dispersed phase between mixers and settlers is governed by residence time and organic-aqueous ratio of feed flow. Turbulence intensity, volume fraction, and droplet size distribution are revealed to be dominating parameters that affect the spatial nonuniform distribution of volumetric mass transfer coefficient. The mass transfer rate can be improved by increasing impeller speed in two stages. Higher residence time and organic-aqueous ratio of feed flow, however, have opposite effects on mass transfer rate in stage-1 and stage-2.

Preparation and application of natural protein polymer-based Pickering emulsions

Abstract Emulsification is the effect of a liquid being uniformly dispersed as tiny droplets in another liquid that is immiscible. Traditional emulsification requires the addition of suitable surfactant to stabilize the emulsion. When the surfactant molecules are replaced by solid particles, the emulsion is known as Pickering emulsions (PEs). PEs with dispersed phase volume fraction above 74% are also named high internal phase Pickering emulsions (HIPPEs). The use of solid particles of natural origin allows PEs to be highly physically stable, environmentally compatible, and biodegradable compared to traditional emulsions. Among them, protein-based solid particles are well suited to stabilize PEs for their great emulsification properties and nutritional value. In this article, we reviewed the preparation of different forms of proteins and their emulsion stabilization properties and summarized the applications of protein-based PEs in various fields, including food, biomedicine, porous materials, biodegradable packaging films, sewage treatment, 3D printing, etc.

Rheological characterization and shear viscosity prediction of heavy oil-in-water emulsions

The rheology of oil-in-water emulsion is a key issues in heavy oil development, storage, transport, and processing. Based on single-factor experiments, the effect of shear rate (γ), dispersed-phase volume fraction (φ), continuous-phase viscosity (ηc), and droplet size (D50) on the rheological properties of heavy oil-in-water emulsions were evaluated through microscopic observation and rheological experiments. Furthermore, a 10-factor/3-level experiment was designed to investigate the sensitive factors affecting shear viscosity. The experimental results indicated that, when the volume fraction of dispersed-phase was higher than 0.3, the rheological characteristics of the prepared emulsions exhibited an obvious shear-thinning behavior, and the droplet size had a significant influence on shear viscosity at shear rates between 0.3 and 100 s−1. When the volume fraction of the dispersed-phase was less than 0.3, the emulsions behaved as Newtonian liquids. As the shear rates increase, the droplets disperse to a greater extent, leading a reduction in viscosity, and ultimately causing the emulsion to exhibit the characteristics of a Newtonian fluid. Owing to the strong hydration effect of small droplets, the viscosity of small droplet-size emulsions increases at a constant dispersed-phase volume fraction. Emulsions exhibit obvious shear-thinning behavior with an increase in shear rate, as a result of a low effective dispersed-phase volume fraction under a high shear rate. Finally, the volume coefficient of the Sibree model was corrected by considering correlation factors from the experiments, and the Sibree model was improved. The improved shear viscosity model better fits the experimental data for all the studied heavy oil-in-water emulsion, with the mean relative error of 9.3%. Therefore, the improved model can predict the effects of all factors affecting shear viscosity.

Emulsification mechanism in an ultrasonic microreactor: Influence of surface roughness and ultrasound frequency

An ultrasonic microreactor with rough microchannels is presented in this study for oil-in-water (O/W) emulsion generation. Previous accounts have shown that surface pits or imperfections localize and enhance cavitation activity. In this study cavitation bubbles are localized on the rough microchannels of a borosilicate glass microreactor. The cavitation bubbles in the microchannel are primarily responsible for emulsification in the ultrasonic microreactor. We investigate the emulsification mechanism in the rough microchannels employing high-speed imaging to reveal the different emulsification modes influenced by the size and oscillation intensity of the cavitation bubbles. The effect of emulsification modes on the O/W emulsion droplet size distribution for different surface roughness and frequency is demonstrated. The positive effect of the frequency on minimizing the droplet size utilizing a reactor with large pits is presented. We also demonstrate microreactor systems for a successful generation of miniemulsions with high dispersed phase volume fractions up to 20%. The observed emulsification mechanism in the rough microchannel offers new insights into the utility and scale-up of ultrasonic microreactors for emulsification.

Effect of Continuous and Discontinuous Droplet-Size Distributions on the Viscosity of Concentrated Emulsions in Premix Membrane Emulsification

The dispersed phase volume fraction of concentrated emulsions can be substantially increased without a considerable increase in viscosity by optimizing the droplet-size distribution (DSD) of emulsion mixtures. However, due to the limitations of the traditional methods to control the DSD, the study of its effect on the viscosity of emulsion mixtures is usually limited. The premix membrane emulsification method was used to prepare a droplet-size-controlled concentrated emulsion, and the DSD’s effect on the viscous behavior of emulsion mixtures was investigated. It was observed that widening the DSD led to a decrease of the viscosity at lower shear rates, while at higher shear rates, a shear-thickening behavior was observed. In a discontinuous DSD, there was a tendency for the viscosity to decrease to a minimum value at about 75% mixing fraction of larger-droplet-size emulsions beyond which the viscosity increased until the monomodal packing limit. The viscosity could be decreased by more than 20-fold in bimodal emulsions depending on the droplet-size ratio. Mixing emulsions of different DSDs enabled attaining a viscosity lower than that of the monodispersed parent emulsions.

Liquid–liquid dispersion system in a moving baffle OBC: a numerical and theoretical study

Liquid-liquid dispersion is prevalent in the chemical industries to create a larger interface between the phases that can intensify the chemical processes, such as liquid extractions and heterogeneous reactions. Oscillatory baffled columns (OBCs) have emerged as alternatives to conventional commercial columns in which external components apply an oscillating flow. A computational fluid dynamics (CFD) approach coupled with the factorial design of the experiment method was employed to study the effect of main geometrical and operational factors, including free baffle area (known as amplitude, and frequency along with their interactions on minimum droplet diameter (), maximum droplet diameter (), and Sauter mean diameter (). The ANOVA p-values showed that the interaction between frequency and all the other main factors was insignificant for all responses. In addition, did not have a significant impact on the in the system, and amplitude had the most substantial impact on all the responses (i.e., and ) among all the factors. It was found that the higher amplitude, higher frequency, and smaller resulted in smaller which can provide higher interfacial area, higher mass transfer, and higher reaction rate for the processes such as suspension polymerization and liquid-liquid extractions. In addition, the larger provided a narrower range of droplets ( which is of significance for polymerization processes. Mathematical models were also developed for and using regression analysis with a reasonable level of accuracy. For the first time, semi-theoretical models were proposed for and in an OBC by combining the models existing in the literature for and and a quasi-steady-state model for energy dissipation rate in an OBC. The proposed models can be used to predict the parameters mentioned above by having geometrical and operational parameters, which help design suitable OBCs for a desired liquid-liquid dispersion system. A visual assessment of the and the dispersed phase volume fraction was also accomplished, showing larger droplets tended to be closer to the wall. Besides, a very uniform dispersed phase volume fraction throughout the OBC indicated the suitability of the column for such processes.