Droplet Volume Fraction Research Articles

Numerical Study on the Impact of Cooling Rate on the Solidification of Al-Bi Hypermonotectic Alloys

A numerical model describing the liquid-liquid phase transformation of the nucleation, the diffusional growth, Ostwald coarsening and macro-transport phenomena was established based on Euler-Euler method. The microstructure development of Al-Bi alloys in different solidification rate has been simulated by coupling the calculated temperature and velocity fields with the kinetic equation which controls the microstructure evolution. The results showed that average diameter difference of L2 phase droplets between top and bottom of samples in low cooling rate increased by 151 % than in high cooling speed and the maximum volume fraction of the droplets at the bottom of the sample in low cooling rate much higher than in high cooling rate. Analysis that the bigger cooling rate can shorten the action time which caused by gravity settling and collisions coagulation of the droplets, and then improves the macrosegregation of solidification structure in favor of uniform distribution of the solidification structure.

Modeling of droplet dispersion in a turbulent Taylor–Couette flow

A process of dispersion of droplets in a developed turbulent Taylor-Couette flow is modeled. An apparatus, where the inner cylinder rotates whereas outer one is immobile, is considered. To exclude the effect of Taylor vorticities on a turbulent flow pattern, only flow regimes characterized by relatively high Reynolds numbers (>13,000) are investigated. Relatively dilute dispersions are modeled: the maximum droplet volume fraction does not exceed 10%. The time-dependent droplet size distribution in a Taylor-Couette device is described by an advection-diffusion equation containing a population balance term. Both breakup and coalescence of droplets are taken into account. An experimentally verified engineering model of a turbulent Taylor-Couette flow, based on the Prandtl mixing length theory, is used for calculating velocity, eddy diffusivity and turbulence energy dissipation rate distributions across a Taylor-Couette device gap. The known breakup and coalescence models of Coulaloglou and Tavlarides are employed for population balance modeling. However, the breakup model has been modified to account more accurately for turbulence – droplet interactions.The governing model equations are solved numerically. The computed droplet size distributions are compared with those obtained in the laboratory Taylor-Couette device in the presence of emulsion stabilizing surfactants for different rotation speeds and stirring durations. The dispersion process in a Taylor-Couette flow in both the presence and absence of surfactants is illustrated by numerical examples. The results of simulations and experiments are critically analyzed.

Development of the droplet-capable conductivity probe for measurement of liquid-dispersed two-phase flow

A new conductivity probe design has been developed in order to measure dispersed liquid particles in churn-turbulent and annular flows which cannot be detected by the conventional conductivity probes. The probe incorporates a common sensor near the measurement point to detect the local conductance signals between two sensor tips that are 150µm apart. Once fully developed, the probe is capable of measuring local two-phase parameters of various fields including small and large bubbles, large liquid droplets and a continuous liquid field. Preliminary benchmarking studies of the probe have been performed with a specially designed droplet dispensing setup. A high speed imaging system is used to provide benchmarking data such as droplet diameter, velocity, and chord length, for individual droplets, and the time-averaged data such as droplet volume fraction, volumetric flux and interfacial area concentration. Reasonable agreement has been obtained by comparing individual droplets with a diameter range of 1.4–4.0mm, and a velocity range of 1.6–4.8m/s. For time- and area-averaged parameters, the results from two test runs show that the maximum absolute relative errors are 6.42%, 7.43% and 5.72% for droplet volume fraction, interfacial area concentration and volumetric flux, respectively. The error is within 5% compared with the global droplet flow rate measurement.

On the interaction of Taylor length scale size droplets and isotropic turbulence

Droplets in turbulent flows behave differently from solid particles, e.g. droplets deform, break up, coalesce and have internal fluid circulation. Our objective is to gain a fundamental understanding of the physical mechanisms of droplet–turbulence interaction. We performed direct numerical simulations (DNS) of 3130 finite-size, non-evaporating droplets of diameter approximately equal to the Taylor length scale and with 5 % droplet volume fraction in decaying isotropic turbulence at initial Taylor-scale Reynolds number $\mathit{Re}_{\unicode[STIX]{x1D706}}=83$. In the droplet-laden cases, we varied one of the following three parameters: the droplet Weber number based on the r.m.s. velocity of turbulence ($0.1\leqslant \mathit{We}_{rms}\leqslant 5$), the droplet- to carrier-fluid density ratio ($1\leqslant \unicode[STIX]{x1D70C}_{d}/\unicode[STIX]{x1D70C}_{c}\leqslant 100$) or the droplet- to carrier-fluid viscosity ratio ($1\leqslant \unicode[STIX]{x1D707}_{d}/\unicode[STIX]{x1D707}_{c}\leqslant 100$). In this work, we derive the turbulence kinetic energy (TKE) equations for the two-fluid, carrier-fluid and droplet-fluid flow. These equations allow us to explain the pathways for TKE exchange between the carrier turbulent flow and the flow inside the droplet. We also explain the role of the interfacial surface energy in the two-fluid TKE equation through the power of the surface tension. Furthermore, we derive the relationship between the power of surface tension and the rate of change of total droplet surface area. This link allows us to explain how droplet deformation, breakup and coalescence play roles in the temporal evolution of TKE. Our DNS results show that increasing $\mathit{We}_{rms}$, $\unicode[STIX]{x1D70C}_{d}/\unicode[STIX]{x1D70C}_{c}$ and $\unicode[STIX]{x1D707}_{d}/\unicode[STIX]{x1D707}_{c}$ increases the decay rate of the two-fluid TKE. The droplets enhance the dissipation rate of TKE by enhancing the local velocity gradients near the droplet interface. The power of the surface tension is a source or sink of the two-fluid TKE depending on the sign of the rate of change of the total droplet surface area. Thus, we show that, through the power of the surface tension, droplet coalescence is a source of TKE and breakup is a sink of TKE. For short times, the power of the surface tension is less than $\pm 5\,\%$ of the dissipation rate. For later times, the power of the surface tension is always a source of TKE, and its magnitude can be up to 50 % of the dissipation rate.

Dynamical and structural signatures of the glass transition in emulsions

We investigate structural and dynamical properties of moderately polydisperse emulsions across an extended range of droplet volume fractions ϕ, encompassing fluid and glassy states up to jamming. Combining experiments and simulations, we show that when ϕ approaches the glass transition volume fraction , dynamical heterogeneities and amorphous order arise within the emulsion. In particular, we find an increasing number of clusters of particles having five-fold symmetry (i.e. the so-called locally favoured structures, LFS) as ϕ approaches , saturating to a roughly constant value in the glassy regime. However, contrary to previous studies, we do not observe a corresponding growth of medium-range crystalline order; instead, the emergence of LFS is decoupled from the appearance of more ordered regions in our system. We also find that the static correlation lengths associated with the LFS and with the fastest particles can be successfully related to the relaxation time of the system. By contrast, this does not hold for the length associated with the orientational order. Our study reveals the existence of a link between dynamics and structure close to the glass transition even in the absence of crystalline precursors or crystallization. Furthermore, the quantitative agreement between our confocal microscopy experiments and Brownian dynamics simulations indicates that emulsions are and will continue to be important model systems for the investigation of the glass transition and beyond.

Experimental investigation on spray and atomization characteristics of diesel/gasoline/ethanol blends in high pressure common rail injection system

The effects of gasoline and ethanol addition on the spray and atomization characteristics of diesel spray from a common rail injection system, was investigated in a constant volume chamber at different ambient and injection pressures. The fuel spray evolution process was recorded with high spatial and time resolution and the corresponding spray tip penetration (STP), the cone angle were extracted. The results show that increased gasoline proportion in the test blends causes decreased STP and increased spray cone angle. Additionally, the microscopic spray characteristics such as the local average droplet diameter and statistical size distributions were measured by particle/droplet image analysis (PDIA) technique. As gasoline blending ratio increases, significantly smaller droplet size was observed which indicates that the spray breakup and atomization processes were promoted. Further adding ethanol slightly increased the droplet size, but it is still much smaller than the droplet size of neat diesel spray. Moreover, the local droplet size increases along the radial direction but the local droplet volume fraction and normalized droplet number density decreases, indicating a reduced fuel concentration along the radial direction. Along the axial direction, the droplet size, the local droplet volume fraction and the normalized droplet number density were almost constant.

Crystallization kinetics from mixture Na2SO4/glycerol droplets of Na2SO4 by FTIR-ATR

The efflorescence of mixed Na2SO4/glycerol aerosols on the ZnSe substrate with various mole ratios (Na2SO4/glycerol=1:1, 1:2, 1:4) has been studied in the relative humidity (RH) linearly decline process, using a situ Fourier transform infrared attenuated total reflection (FTIR-ATR) technique. The crystal ratio at a given RH can be gained by the absorbance of the band at 1132cm−1, which shows the incomplete nucleation for mixed Na2SO4/glycerol aerosols and the decreased amount of the droplets crystallized at the lowest RH with the glycerol increase. Using the volume fraction of droplets that have yet to crystallize, the heterogeneous nucleation kinetics has been gained. By the Extended Aerosol Inorganics Model (E-AIM), the nucleation rate as the function of solute saturation degree has been gained for various mixed Na2SO4/glycerol aerosols.

Augmenting regional and targeted delivery in the pulmonary acinus using magnetic particles.

BackgroundIt has been hypothesized that by coupling magnetic particles to inhaled therapeutics, the ability to target specific lung regions (eg, only acinar deposition), or even more so specific points in the lung (eg, tumor targeting), can be substantially improved. Although this method has been proven feasible in seminal in vivo studies, there is still a wide gap in our basic understanding of the transport phenomena of magnetic particles in the pulmonary acinar regions of the lungs, including particle dynamics and deposition characteristics.MethodsHere, we present computational fluid dynamics-discrete element method simulations of magnetically loaded microdroplet carriers in an anatomically inspired, space-filling, multi-generation acinar airway tree. Breathing motion is modeled by kinematic sinusoidal displacements of the acinar walls, during which droplets are inhaled and exhaled. Particle dynamics are governed by viscous drag, gravity, and Brownian motion as well as the external magnetic force. In particular, we examined the roles of droplet diameter and volume fraction of magnetic material within the droplets under two different breathing maneuvers.Results and discussionOur results indicate that by using magnetic-loaded droplets, 100% of the particles that enter are deposited in the acinar region. This is consistent across all particle sizes investigated (ie, 0.5–3.0 µm). This is best achieved through a deep inhalation maneuver combined with a breath-hold. Particles are found to penetrate deep into the acinus and disperse well, while the required amount of magnetic material is maintained low (<2.5%). Although particles in the size range of ~90–500 nm typically show the lowest deposition fractions, our results suggest that this feature could be leveraged to augment targeted delivery.

Heat transfer in droplet-laden turbulent channel flow with phase transition in the presence of a thin film of water

We present results of a numerical study of turbulent droplet-laden channel flow with phase transition. Previous studies of the same system did not take into account the presence of gravity. Here, we do so introducing a thin film of water at the bottom wall and permitting droplets to fall into and merge with it. We treat the carrier phase with the Eulerian approach. Each droplet is considered separately in the Lagrangian formulation, adopting the point–particle approximation. We maintain the film thickness constant by draining water from the bottom wall to compensate for (a) the droplets that fall onto the film and (b) evaporation/condensation. We also maintain on average the total mass of water in the channel by inserting new droplets at the top wall to compensate for the water that has been drained from the bottom wall. We analyze the behavior of the statistically averaged gas and droplet quantities focusing on the heat exchange between the two phases. We increase (a) the initial droplet diameter keeping the same initial droplet volume fraction and (b) the initial number of droplets in the channel keeping their diameter the same. In both parameter studies we find that droplets grow less than in the reference case. In case (a) this is explained by the larger velocity with which they travel to the bottom wall and in case (b) by the lower rate of condensation of vapor due to the presence of neighboring droplets.

Entropic, electrostatic, and interfacial regimes in concentrated disordered ionic emulsions

We develop a free energy model that describes two key thermodynamic properties, the osmotic pressure Π and the linear elastic shear modulus G′p (i.e. plateau storage modulus), of concentrated monodisperse emulsions which have isotropic, disordered, droplet structures, and are stabilized using ionic surfactants. This model effectively incorporates the concept of random close packing or jamming of repulsive spheres into a free energy F that depends on droplet volume fraction ϕ and shear strain γ both below and above the a critical jamming point ϕ c ≈ 0.646. This free energy has three terms: entropic, electrostatic, and interfacial (EEI). By minimizing F with respect to an average droplet deformation parameter that links all three terms, we show that the entropic term is dominant for ϕ well below ϕ c, the electrostatic term is dominant for ϕ near but below ϕ c, and the interfacial term dominates for larger ϕ. This EEI model describes measurements of G′p(ϕ) for charge-stabilized uniform emulsions having a wide range of droplet sizes, ranging from nanoscale to microscale, and it also is consistent with measurements of Π(ϕ). Moreover, it describes G′p(ϕ) for similar nanoemulsions after adding non-amphiphilic salt, when changes in the interfacial tension and the Debye screening length are properly taken into account. By unifying existing approaches, the EEI model predicts constitutive properties of concentrated ionic emulsions that have disordered, out-of-equilibrium structures through near-equilibrium free energy minimization, consistent with random driving Brownian excitations.

Confined tube flow of low viscosity emulsions: Effect of matrix elasticity

This study is addressed to the effect of the elasticity of the continuous phase on confined flow of low viscosity emulsions, a topic of interest in several applications. A Newtonian silicone oil was used as the dispersed phase, while three different water-based fluids, a Newtonian and two Boger fluids, were used as the continuous phase. All the fluids have the same viscosity (ca. 0.05 Pa s). Emulsions were prepared by feeding the two phases to a T-junction followed by a membrane. When the continuous phase was a Boger fluid, the average drop size of the so obtained emulsions was higher (as compared to the Newtonian continuous phase) and a bimodal distribution was observed. Such lower mixing efficiency for a Boger continuous phase is in line with the result for an isolated droplet that breakup is hindered by matrix elasticity. High-speed microscopy visualization of the emulsions flowing through a microcapillary allowed one to determine the velocity profiles and the droplet spatial distribution as a function of the shear rate. In all the experiments, the formation of a droplet-rich core and of a droplet-devoid wall region Δ was observed, with a significant enhancement when the continuous phase was a Boger fluid (where values of Δ as high as 37% of capillary radius were found). So, confinement here refers to the fact that, although the droplets are much smaller than capillary radius, the droplet-free layer takes up a significant fraction of the capillary radius. The observed nonhomogeneous droplet spatial distribution was not due to a transient entry effect, as shown by imaging the emulsions flow at different sections from the capillary inlet, but can be explained by a balance between collision-induced drop diffusion and wall lift force. The former acts to homogenize droplet spatial distribution, while the latter tends to push droplets away from the wall and is enhanced by matrix elasticity. These effects lead to the accumulation of larger droplets around the center of the channel, while smaller droplets are pushed toward the periphery. The velocity profiles for the Boger continuous phase were flat in the droplet-rich core, thus suggesting that the confined emulsions behave as a Bingham fluid. The corresponding yield stress was determined by data fitting of the velocity profiles and rather large values were so obtained. This result is consistent with the high values, close to the maximum packing for spherical particles in binary dispersions, of the droplet volume fraction in the core, which were estimated by measuring the thickness of the droplet-devoid annular region as a function of the applied flow rate and making a volume balance. Overall, the results of this work bear strong analogies with the confined flow of other concentrated suspensions of deformable particles, such as red blood cells in microcirculation, where the formation of a cell-free layer at the wall, which is referred to as margination, has important pathophysiological implications. These findings suggest that low viscosity emulsions with an elastic matrix under confined flow can be used as a tunable model system of biomedical relevance.

An evaluation of a mass transfer rate at the boundary of different release mechanisms in complex liquid dispersion

The paper focuses on the development of the criteria for modelling mass transfer during release process at the boundary of diffusion and fragmentation in complex liquid dispersion, such as double emulsions. The proposed model for predicting release rates accounts for the effect of mass transfer resistance coupled with the emulsion structure and external release environment. The criteria of the applicability of the proposed model were formulated after verification by studies of drug release from O1/W/O2 emulsions, prepared in a Taylor–Couette flow bioreactor. It has been found that one or more mechanisms may dominate at different release stages, depending on the mixing intensity of the release medium and internal structure of double emulsions. The experimental analysis of release rates and the changes in the emulsion structure during the release process, revealed the existence of three mechanisms: (i) diffusion, (ii) diffusion and fragmentation—loss of the original structure from double emulsions to single emulsions and (iii) fragmentation. The criteria covering the diffusion release model have been formulated, as the shear rate ranges at the boundary of different mechanisms, and correspond to the values of the critical capillary numbers, which seemed to depend on the volume fraction of internal droplets of multiple emulsions.

Numerical simulation of coalescence phenomena of oil-in-water emulsions permeating through straight membrane pore

Abstract We numerically investigated the demulsification phenomena of oil-in-water (O/W) emulsions using a membrane coalescence process. We simulated the permeation of O/W emulsions through a membrane with a single straight pore using our numerical framework based on the coupled level set and volume-of-fluid (CLSVOF) method. With a low droplet volume fraction, small droplets, and a large pore size, the oil droplets frequently passed through the membrane without attaching to its surface. After the steady coalescence of the droplets on the membrane surface at the permeation side, large oil droplets could be obtained. With a higher droplet volume fraction, larger oil droplets, and smaller membrane pores, the oil droplets easily blocked the membrane pores and were thus forced away by the permeating flow, which yielded relatively small oil droplets. Our numerical work revealed the fundamental dynamics of the coalescence of oil droplets in an O/W emulsion using a simple membrane model.

Effect of droplet interaction on droplet-laden turbulent channel flow

We present results of direct numerical simulation of heat transfer and droplet concentration in turbulent flow of a mixture of dry air, water vapor, and water droplets in a differentially heated channel. In particular, we study the effects of droplet collisions by comparing results of simulations with and without droplet collision model for several overall droplet volume fractions. The results show that droplet collisions have a large influence on droplet concentration. Maximum local concentrations, which occur close to the walls of the channel, are reduced by almost an order of magnitude for the case with the highest overall volume fraction. In addition, the positive skewness of the local volume fraction is reduced by a factor of two near the walls. These findings show the importance of including four-way coupling, even in cases where the overall droplet volume fraction is only on the order of 10−4 and the Stokes number in wall units is only about 10. In spite of this large effect of droplet collisions on droplet concentration, the effect on the overall heat transfer between the walls of the channel is not more than approximately 17%. That the effect on the overall heat transfer is relatively small can be explained by the lower heat exchange area between droplets and gas in the near-wall areas, which results in a higher temperature difference between droplets and surrounding gas.

Preparation of Pickering double emulsions using block copolymer worms.

The rational formulation of Pickering double emulsions is described using a judicious combination of hydrophilic and hydrophobic block copolymer worms as highly anisotropic emulsifiers. More specifically, RAFT dispersion polymerization was utilized to prepare poly(lauryl methacrylate)–poly(benzyl methacrylate) worms at 20% w/w solids in n-dodecane and poly(glycerol monomethacrylate)–poly(2-hydroxypropyl methacrylate)–poly(benzyl methacrylate) worms at 13% w/w solids in water by polymerization-induced self-assembly (PISA). Water-in-oil-in-water (w/o/w) double emulsions can be readily prepared with mean droplet diameters ranging from 30 to 80 μm using a two-stage approach. First, a w/o precursor emulsion comprising 25 μm aqueous droplets is prepared using the hydrophobic worms, followed by encapsulation within oil droplets stabilized by the hydrophilic worms. The double emulsion droplet diameter and number of encapsulated water droplets can be readily varied by adjusting the stirring rate employed during the second stage. For each stage, the droplet volume fraction is relatively high at 0.50. The double emulsion nature of the final formulation was confirmed by optical and fluorescence microscopy studies. Such double emulsions are highly stable to coalescence, with little or no change in droplet diameter being detected over storage at 20 °C for 10 weeks as judged by laser diffraction. Preliminary experiments indicate that the complementary o/w/o emulsions can also be prepared using the same pair of worms by changing the order of homogenization, although somewhat lower droplet volume fractions were required in this case. Finally, we demonstrate that triple and even quadruple emulsions can be formulated using these new highly anisotropic Pickering emulsifiers.

Cellular ceramics by gelatin gelcasting of emulsified suspensions with sunflower oil

Highly porous cellular ceramics were prepared by a versatile method combining emulsification of sunflower oil in alumina suspension, using collagen as surfactant, stabilizer and gelcasting additive. Emulsified suspensions show shear thinning behavior at emulsification temperatures, and their rheology was related to the volume fraction of dispersed oil droplets, collagen contents and stirring rate, based on a suitable Taguchi plan. This provides guidelines for the dependence of microstructural features on these processing parameters. The robustness of the method was demonstrated by the ability to perform early stages of burnout at relatively high heating rates, without risks of collapse or onset of factures in the resulting cellular ceramics. Combined DTG/DTA/FTIR studies were used to analyse the burnout stages, and provide guidelines to minimize emissions of gases with safety or environmental risks.

Affine and nonaffine motions in sheared polydisperse emulsions.

We study dense and highly polydisperse emulsions at droplet volume fractions ϕ≥0.65. We apply oscillatory shear and observe droplet motion using confocal microscopy. The presence of droplets with sizes several times the mean size dramatically changes the motion of smaller droplets. Both affine and nonaffine droplet motions are observed, with the more nonaffine motion exhibited by the smaller droplets which are pushed around by the larger droplets. Droplet motions are correlated over length scales from one to four times the mean droplet diameter, with larger length scales corresponding to higher strain amplitudes (up to strains of about 6%).

Formation of stable hydrocarbon oil-in-water nanoemulsions by phase inversion composition method at elevated temperature

Stable hydrocarbon oil (hexadecane, C16)/nonionic surfactant (HCO-60, Span 80)/water system oil-in-water nanoemulsions were prepared by the phase inversion composition method at elevated temperature. To minimize droplet size, the composition ratio for stable nanoemulsions, we experimented by changing the HLB value, oil/surfactant ratio, and droplet volume fraction. When the HLBmix value 11, the nanoemulsions show a minimal sample droplet size of 360.3 nm. By varying the oil/surfactant ratio from 0.6 to 1.4, we found the optimum oil/surfactant ratio to be approximately 0.6, which corresponds to the minimum droplet size of 71.8 nm. We also varied the droplet volume fraction; when the droplet volume fraction is 0.06, the droplet size is very small. For the emulsion with the minimal droplet size, the polydispersity index is less than 0.3, which reflects a good monodispersity of the nanoemulsion. Viscosity and electrical conductivity measurements were carried out for determining the internal structure of the bicontinuous phase during the emulsification. When the water content ranges from 4 to 6 w/w%, the systems may have a bicontinuous or lamellar phase. Oil-in-water nanoemulsion stability assessment was performed by observing the droplet size as a function of storage time; we did not observe any change in droplet size over the course of a month.

Crossover between entropic and interfacial elasticity and osmotic pressure in uniform disordered emulsions.

We develop a simple predictive model of the osmotic pressure Π and linear shear elastic modulus G of uniform disordered emulsions that includes energetic contributions from entropy and interfacial deformation. This model yields a smooth crossover between an entropically dominated G ∼ kBT/a(3) for droplet volume fractions ϕ below a jamming threshold for spheres, ϕc, and an interfacially dominated G ∼ σ/a for ϕ above ϕc, where a and σ are the undeformed radius and interfacial tension, respectively, of a droplet and T is the temperature. We show that this model reduces to the known ϕ-dependent jamming behavior G(ϕ) ∼ (σ/a)ϕ(ϕ - ϕc) as T → 0 for ϕ > ϕc of disordered uniform emulsions, and it also produces the known divergence for disordered hard spheres G(ϕ) ∼ (kBT/a(3))ϕ/(ϕc - ϕ) for ϕ < ϕc when σ → ∞. We compare predictions of this model to data for disordered uniform microscale emulsion droplets, corrected for electrostatic repulsions. The smooth crossover captures the observed trends in G and Π below ϕc better than existing analytic models of disordered emulsions, which do not make predictions below ϕc. Moreover, the model predicts that entropic contributions to the shear modulus can become more significant for nanoemulsions as compared to microscale emulsions.

조성 상전이 방법으로 제조된 안정한 액상 파라핀-물 나노에멀젼

물/Span 80-Tween 80/긴 사슬 파라핀 오일 계에서 PIC (조성 상전이) 방법을 이용하여 O/W 나노에멀젼을 제조하였다. 제조 온도를 <TEX>$30^{\circ}C$</TEX>에서 <TEX>$80^{\circ}C$</TEX>로 상승시킴에 따라 제조된 나노에멀젼의 입경은 120 nm에서 40 nm로 감소하여 나노에멀젼을 형성하였다. 혼합 계면활성제의 HLB를 변화시킴에 따라 12.0 ~ 13.0 부근에서 가장 작은 입경을 형성하는 최적 HLB가 존재하였다. 나노에멀젼의 점도는 액적의 부피 분율(<TEX>${\phi}$</TEX>)에 따라 현격하게 증가하였으나, 입경의 크기는 약간 증가하였다. 그리고, <TEX>${\phi}{\leq}0.3$</TEX> 조건에서 나노에멀젼의 크기 분포는 2개월 이상 일정하게 유지 되었다. 이러한 결과는 점성 파라핀 오일의 경우 <TEX>$30^{\circ}C$</TEX>에서는 PIC 방식으로 거의 분산할 수 없음을 보여주지만, 제조 온도가 증가할 경우 단 분산 나노에멀젼의 제조가 가능하다는 것을 보여준다. 나노에멀젼이 생성되면, Ostwald ripening에 대한 안정성은 연속 상에서 액상 파라핀 오일의 매우 낮은 용해도로 인해 안정하게 되며, 이는 화장품 응용에서 매우 중요하다. Oil-in-water nanoemulsions were prepared in the system of water/Span 80-Tween 80/long-chain paraffin oil via the PIC (phase inversion composition) method. With the increase of preparation temperature from <TEX>$30^{\circ}C$</TEX> to <TEX>$80^{\circ}C$</TEX>, the diameter of emulsion droplets decreased from 120 nm to 40 nm, proving the formation of nanoemulsions. By varying the HLB (hydrophilic lipophilic balance) of mixed surfactants, we found that there was an optimum HLB around 12.0 ~ 13.0 corresponding to the minimum droplet size. The viscosity of nanoemulsions clearly increased with droplet volume fraction, f, but the droplet size slightly increased. Significantly, at <TEX>${\phi}{\leq}0.3$</TEX>, the size distribution of nanoemulsions kept constant more than 2 months. These results proved that the viscous paraffin oil can hardly be dispersed by the PIC method at <TEX>$30^{\circ}C$</TEX>, but the increase in preparation temperature makes it possible for producing monodisperse nanoemulsions. Once the nanoemulsion is produced, the stability against Ostwald ripening is outstanding due to the extremely low solubility of the liquid paraffin oil in the continuous phase. The highly stable nanoemulsions are of great importance in cosmetic applications.