The background of this study is to develop a method to improve the ﬂuidity of highviscosity oil left in sunken ships. We focused on emulsiﬁcation to control the rheologicalproperties of the oil. As a ﬁrst step towards the goal, experiments and modeling wereconducted to understand the viscosity properties of oil-water emulsions. In theexperiments, oil-water emulsions were prepared using several surfactants to measureviscosity properties. The results showed a continuous change in viscosity withincreasing water content as well as a discontinuous change in viscosity due to phaseinversion that occurs at a certain water content. In the theoretical modelling, a newlayer-stacking model was developed and applied to the experimental results. Thismodel, though extremely simplifying the structure of the emulsion, was found to be ableto well explain the continuous and discontinuous viscosity characteristics of theemulsion.Key wordsEmulsion, Viscosity, Surfactant, Phase inversion, Model, Heavy fuel oilNomemclatureSymbols:shear strain ratio/fraction:shear strain:shear strain rate ():porosity/void fraction in particle-packed layer:volume fraction:viscosity:shear stress:normalized Layer ticknessSubscripts:of component which constitues bulk layer:of component which mainly constitues paticle-packed layer:of/in bulk layer:of/in entire system:of/in paticle-packed layer:of oilβγ˙γ=dγdtϵϕμτZBPbepo1 :of water1. IntroductionIn the ﬁeld of oil spill response, a counter measure to oil leakage from sunken shipsis one of the most crucial issues. Historically, many ships have sunk with oil left in theirfuel tanks. There were cases that a small amount of oil continued to leak for a longperiod of time, or leakage started after decades, which caused troublesome problemsthat could not be left unattended. It may be necessary to take measures by subsurfaceoil recovery from the sunken ship (Hansen,2014). In the deep sea or when the watertemperature is low, the oil to be extracted has a high viscosity, which may makes therecovery mission diﬀicult. To overcome this diﬀiculty, some counter measure is requiredto improve ﬂuidity of the high viscosity oil.There were many studies on the pipeline ﬂow so far. Among them, basic studies onmultiphase ﬂow of oil and water have been conducted for a long time (Russell,1959;Bunnwart,2004), and even in recent years, multiphase ﬂow for high-viscosity oil hasbeen attracting attention (Vuong,2009), reﬂecting the shift of oil production to high-viscosity oil. On the other hand, as a technology for dealing with spilled oil, severaltechnologies for in-pipe transportation of high-viscosity oil, including W/O emulsiﬁed byweathering, have been proposed. These include the technique of forming CAF (CoreAnnular Flow) by adding water (Drieu,2003; I.Fujita,2009) and the method of adding asmall amount of surfactant instead of water(I.Fujita,2011). These methods control thestructure of ﬂow in the pipe to reduce the pipe friction loss, however, are not suitablefor improving the ﬂuidity of a large mass of oil remaining inside the fuel tank of awreck.In oil recovery from the sunken ships, the ﬂuidity of the oil inside the tank isimportant as well as in in the pipeline. For this purpose, bulk heating is one of theoptions easy to conceive. It, however, has disadvantages such as requiring a largeamount of energy, poor heat transfer rate or heat dissipation into the cold water . Onoet al. tried to improve the ﬂowability by the bulk heating using induction heating(M.Ono(1),2015; M.Ono(2),2015), but found that it was diﬀicult to transfer heat deepinto the tank to enhance the ﬂuidity of the entire tank. Therefore, we needed to look foralternatives and focused on the improvement of ﬂuidity by emulsiﬁcation from arheological point of view. Our original idea was to use a vapor explosion tosimultaneously realize to disperse oil as ﬁne particulates into water and to reach theeﬀect deep in the tank (M.Ono,2018 ;Ono,2019). However, in order to achieve this,knowledge of emulsions composed of heavy fuel oil and water is not suﬀicient yet.In this study, we investigate the viscosity properties of emulsions composed ofheavy fuel oil and water in a basic system without thermal phenomena such as vaporexplosion. In general, W/O emulsion is formed in nature, as is the case with spilledheavy oil, and viscosity increases, but in systems where surfactants are added,emulsions of various forms can be produced, which may lead to resolve the poorﬂowability problem.In the following sections, experiments are conducted to measure the viscosityproperties of oil-water emulsions with surfactants, and the results are analyzed using anewly proposed viscosity model and microscopic observations.2. Experiments2.1. Sample PreparationThis section describes the experimental procedure of viscosity measurement forwater-oil emulsions system we conducted in the study. For the test oil, an oil called Cfuel oil, which is widely distributed as fuel oil in Japan, was used. This oil is speciﬁed inthe Japanese Industrial Standard (JIS) K2205 and corresponds to MFO (marine fuel oil)as an international designation. Its viscosity characteristic is shown in Fig.1. Themeasurements were carried out using a Brookﬁeld B-type viscometer ( DV-III Ultra) at aw 2 temperature of 25°C.As shown in Fig.2, test samples were prepared using the agent-in-oil method,whose procedure is as follows:(1) Add chemical agent to the oil and stir for a while.(2) Weigh a certain amount (100 or 200g) from sample (1).(3) Weigh distilled water so that the desired water content is obtained, and add itto the sample (2).(4) Stir sample (3) at a constant rate for 3 minutes．(5) Deaerate sample (4) in a vacuum chamber for 3 minutes.A household juicer mixer of which power was 160W , was used for stirring in the step(4). Three types of chemicals, AB-3000, OTP-75 and MYL-10 were used as additivechemical agents. AB-3000 was selected as a representative of the general type oildispersant commercially available in Japan. OTP-75 is a 75% solution diluted with waterand ethanol containing diethylhexyl sodium sulfosuccinate as a surfactant component,and is used for wetting, permeation, and dispersion. MYL-10 is PEG-10 laurate oftenused as hydrophilic emulsiﬁer. The selection of these agents was based on Fujita's workon the decomposition of W/O emulsions(I.Fujita,2013). Test samples we prepared forthe test are summarized in Table 1. Figure 1 Viscosity of the test oil used for the experiment Figure 2 Schematic diagram of experimental procedure. 3 Table 1 Test sample conditionsCase#ChemicalagentDescriptionConc. ofC.A.1)OilWaterfraction1-Control sample without additive-Heavyfuel oil(Ref. toFig.1)0~50%2NEOSAB30002)Commercial oil dispersant10%3NIKKOLOPT-753)Diethylhexyl sodiumsulfosuccinate75% solution diluted by water andethanol(HLB>20)2%4NIKKOLMYL-104)PEG-10 laurate(HLB=12.5)1%52%64%1) Concentration of the chemical agent is deﬁned as weight ratio relative to the oil.2) https://www.epa.gov/emergency-response/neos-ab30003) https://www.chemical-navi.com/product-search/en_view3575.html4) https://www.chemical-navi.com/product-search/en_view282.html2.2. Viscosity MeasurementThe prepared test samples were measured for viscosity characteristics using theB-type viscometer described above. An example of the measurement is shown in Fig.3 ,which gives the relation between shear rate and shear stress at a certain water fraction. As seen in this ﬁgures, the emulsiﬁed sample becomes a non-Newtonian ﬂuid sothat the viscosity changes depending on the shear rate, thus the shear rate of 100.441/s is selected to deﬁne the representative viscosity in the following discussions. Figure 3 Example of viscosity measurementCase 2 and Experimental results of viscosity measurement in this study are given in Fig.4. Thehorizontal axis is the volume fraction of water added, and the vertical axis is theviscosity normalized by the initial viscosity without water addition. First, we look atCase 1, which does not contain any chemical agent. In this case, as the amount of wateradded is increased, the viscosity of the emulsion increases. This trend continues up tothe limit of water addition where the entire system can be treated as a uniformemulsion with no water separation phase.On the other hand, in the cases with additive (Case 2 to Case6), quite diﬀerentbehavior was observed. At the beginning when the water fraction was small, theviscosity increased with the addition of water as same as seen in Case 1. However, ifthe amount of water was further increased, the viscosity decreased suddenly andsharply at a certain point.ϕw ϕw=0.154 4 This sudden drop in viscosity was a remarkable characteristic that was observedonly in the cases with additives as not seen in the case where additive absent (Case 1),and also seemed to imply that some rheological phase transition took place. Comparingthe case 2,3 and 5, the critical value of the water fraction at which the viscosity dropoccurred depended on the type of additive.The viscosity drop also depended on the concentration of the additive. Case 4 to 6with the same surfactant had the critical water fraction ranged from 0.18 to 0.28.Increasing the concentration of surfactant caused the drop with a smaller amount ofwater addition. When the water is added further after a discontinuous viscosity dropoccurs, the system still remains in an uniform emulsion state, and decreases itsviscosity as the water addition increases. Figure 4 Viscosity proﬁle of heavy fuel oil and water emulsion2.3. Microscope ObservationIn addition to the viscosity measurement, in order to understand the microscopicstructure of emulsion, visualization observations were carried out using a UVﬂuorescence microscope (OLYMPUS BX50 System Microscope). Since oil ﬂuoresceswhen exposed to ultraviolet rays, it is possible to determine whether the oil formsdispersed particles or a continuous phase. Figure 5 gives an example of Case 2. In thisexample, with a small amount of water added, water forms particlurate in thecontinuous oil media as shown on the left hand side. To the contrary, with a largeamount of water added, oil forms particlurate in the continuous water media as shownon the right hand side.The captured images were analyzed by image processing. The video data wasdecomposed into still images for subsequent image analysis. Each still image wasconverted to grayscale, and then binarized to calculate the ratio of the oil and waterconstituent areas. Since the particle distribution is not uniform, a small inspectionwindow traverses the entire picture as shown in Fig.6. For the image processing, a freesoftware named "OpenCV" was used (https://opencv.org/). The results of the imageanalysis were organized as a frequency distribution of oil fraction , then regressed to afollowing distribution function(Kanda J,1981 ):5 (1)This distribution function is bounded both on the lower and upper side and deﬁned inthe support [a,g], which is suitable for representing the distribution of oil fraction byletting a and g be 0 and 1, respectively. Parameters and , which deﬁne scale andshape of the distribution, respectively, were determined from the image processingresults by regression. An example is given in Fig.7. The results of the image processingwill be used in the discussion in Chapter 4 . (a) (b) Figure 5 Example of ﬂuorescence microscope observationCase 2, AB-3000 Figure 6 Image processingf(x)==[exp{−()κ}]dF(x)dxddxg−xν(x−a)νκ ϕw=0.08ϕw=0.35 6 Figure 7 Oil fraction distribution obtained from image analysis( Case 4: MYL-10 1% High viscosity region )3. Viscosity modelIn this chapter, we would like to develop a new viscosity model for oil-water (liquid-liquid) dispersed system. For solid-liquid dispersed system, namely suspension, therehave been many models proposed so far. Einstein theorized the viscosity equation ofsuspensions, which is known to agree well with the measured value under lowconcentration conditions (A.Einstein,1906). Brinkmann et al. developed a viscosityprediction equation using Darcy's law for ﬂuids ﬂowing in porous media(H.C.Brinkmann,1949). Mori and Ototake developed a simple viscosity equation usingthe thickness of the liquid ﬁlm between particles in a suspension (Y.Mori,1955). Theirformulas are given in Table 2.Table 2 Formulas of preceding worksNameEquationEq. #Einstein(2)Brinkmann(3)Mori and Otoktake(4)In the solid-liquid suspension, solid material always forms dispersed phase,however, the liquid-liquid dispersed system, namely suspension, is a bit morecomplicated so that it depends on various condition whether a certain component mayplay as a dispersed phase or a continuous phase. As seen in the previous chapters,drastic viscosity drop was observed in the oil-water dispersion system. This observationmay suggest that the structure of the dispersion system has changed signiﬁcantly.In this research, Fujita and Ma worked together to create an intuitive and concisemodel of the viscosity of a dispersed system that can include such a phenomenon. Inthis model, the dispersed system is hypothetically simpliﬁed as a stack of two layers , alayer densely packed with dispersed particles and a bulk layer without particles .Referring to a schematic shown in Fig.8, the mathematical formulation is derived asfollows. It is assumed that the two components, B and P , are mixed as a dispersedsystem as shown on the left side of the ﬁgure. Let us assume that component Pconstitutes particles. Our model considers the dispersed system to be equivalent to thestack of two layers as shown in the center of the ﬁgure.μe=μb(1+2.5ϕp)μe=μb(1−ϕp)−2.5μe=μb{1+}3−1ϕp10.52 7 Figure 8 Schematic of layer-stacking model for liquid-liquid emulsionIn this layer-stacking model, letting the volume fractions of component B andcomponent P be and , respectively, assuming that they are immiscible and thereis no volume change due to mixing, the volume conservation gives:(5)As for the layer thickness, letting and be the fractions of layer thickness of thepartilce-packed layer and the bulk layer, respectively, they satisfy:(6)It is assumed that all the P component is included in the particle-packed layer andpacked as densely as possible. A new parameter is introduced to deﬁne therelationship between the volume fraction, , and the particle-packed layer thickness, , which is:(7)The parameter physically means a porosity, or a void fraction that the componentsother than occupies in the particle-packed layer.Next, in order to consider the viscosity, we give a shear deformation to thedispersed system. As shown on the right side of Fig. 5, the shear deformation isdistributed to the bulk layer and the particle-packed layer.Let , and be theshear deformation of the entire layer, the bulk layer and the particle-packed layer,respectively, the shear deformation of the entire system should be the sum of the layersas follows:(8)Shear stress is common to all the layers and can be described using shear strain and viscosity of each layer as follows:(9), where dot means time derivative. Let us deﬁne as a ratio of bulk layer deformationto the entire shear, which is:(10)By applying Eqs.(10),(7) and (6) to Eq.(9), the viscosity of the entire dispersed systemcan be evaluated using only the viscosity of the bulk layer as follows:(11)ϕBϕPϕB+ϕP=1ZpZbZb+Zp=1ϵϕPZPZp(1−ϵ)=ϕPϵPγeγbγpγe=γb+γpτγZμτ=μe˙γe=μb=μp˙γbZb˙γpZpβbβb=γbγeμe=μb=μbβb=μbβb1Zb˙γb˙γe1Zb1−ϵ1−ϵ−ϕP8 When is small ( ), using the Taylor expansion, Eq.(11) can be linearized withrespect to the volume fraction , giving the following equation:(12)As for the deformation ratio , considering the particle-packed layer to be lessdeformable than the bulk layer, and also the limit where the approaches 0, isexpected to be a function that asymptotically approaches 1 like:(13), where is strain leakage to the particle-packed layer, and is amonotonically increasing function that takes 0 at and has an upper bound lessthan or equal to 1.In deriving this equation, we assume that the particle-packed layer has its deformationproportional to the layer thickness, but it is immobilized when the strain rate is smallwhile it can move to some extent as the stain rate increases. This model is hypothetical,but if accepted, it could explain the pseudoplasticity observed in W/O emulsions, asshown in Fig.9. This example is given for a ﬂuid of by letting be a expressionfor the ﬁrst-order relaxation phenomenon as:(14), which makes you see the model has good representation for the pseudoplasticity. Itshould be noted that, in the following chapter, we neglect the eﬀect of shear strain rateand let , since the main discussion is developed at the ﬁxed strain rate. Figure 9 Example of layer-stacking model applied to pseudoplasticﬂuidOn the other hand, , the parameter related to the porosity in the particle-packedlayer, may change variously depending on the conditions. In special case when theparticle size is constant, Kepler conjecture, a mathematical theorem about spherepacking in three-dimensional Euclidean space, gives an upper limit for , which is about0.26. Einstein's model (2) has its coeﬀicient 2.5 which can be interpreted as of 0.6 inthe layer-stacking model. For example, viscosity change predicted by the layer-stackingmodel is given by Fig.10. Two typical cases are plotted which are for theKepler limit and for Einstein model.ϕPϕP→0ϕPμe=μbβb(1+ϕP)11−ϵβbϕPβbβb=1−βp=1−=1−Zpf(˙γe)=1−f(˙γe)γpγeϕp1−ϵβp=γpγpf(x)x=0τ∝˙γe0.8ff(˙γe)=f0{1−exp(−)}˙γe˙γ0βb=1 ϵϵϵϵ=0.26ϵ=0.69 Figure 10 Viscosity change predicted by layer-stacking modelIn the above derivation, the component P was treated as forming particles in theparticle-packed layer, however, in case of multiple emulsion as shown in Fig.11, thecomponent P may become a liquid that ﬁlls the void in the particle-packed layer. Evenin this case, Eqs. (11) and (12) are still valid by changing the interpretation of theporosity, ε, to the volume fraction of particles constituted by component B. The layer-stacking model asserts that the viscosity of the entire system depends on the thicknessand properties of the bulk layer, and ε can be interpreted as a parameter thatrepresents the amount of bulk layer components taken up by the particle-packed layer. is alwasys ﬁlled with bulk component. In that sense, from here on, should be writtenas or . Figure 11 Schematic of layer-stacking model for multiple emulsionTo summarize this chapter, we introduced a simple layer-stacking model, whichdivides the dispersed system into a particle-packed layer and a bulk layer. In thismodel, the entire viscosity of the dispersed system is determined by the attributes ofthe bulk layer of its viscosity and thickness.4. DiscussionsIn this chapter, we discuss the viscosity characteristics of oil-water emulsion systemobserved in the experiment results described in Section 2.2In particular, we focus onthe continuous viscosity change and discontinuous and sudden viscosity drop. For thediscussion, we will use the layer-stacking model introduced in Chapter 3 and the resultsof image analysis of microscopic observation introduced in Section 2.3.ϵϵϵbϵB 10 When the water addition, , is small, the oil component constitutes the bulk layer.In this case, the layer-stacking model, Eq.11, assuming that , gives the viscosityof the entire system( ) normalized by the oil viscosity() as:(15), where is a volume fraction of water added to the entire system, and is a volumefraction that oil component occupies in the particle-packed layer which is determinedby a least square curve ﬁtting with the experimental data. Curve ﬁtting results aregiven in Fig.12 for the case 1 to 6. In the ﬁgures, other models by Einstein (Eq.2),Brinkmann (Eq.3) and Mori and Otokake (Eq.4) are also plotted. Adjusting theparameter, , to the appropriate values, the layer-stacking model has betterrepresentation of the experimental data than the other models. In this experiment,values of 0.34 to 0.58 were obtained as depending on each case. The larger the ε, thelarger the increase rate of viscosity, but in the cases of 2 to 6 containing the surfactant,it was found that the larger the , the faster the system jumps to the low viscosityregion with respect to the water addition as shown in Fig.13. This seems to suggest arelationship between and the stability of the system, which will become clearer in thefollowing discussion on the region where water addition is large.To the contrary, when is larger than the critical value, water constitutes the bulklayer. In this case, the layer-stacking model can be written as:(16)This equation has a singularity at , and diverges to inﬁninty when approaches , which seems to provide physical insight into the stability of the system.The emulsion which has water as a bulk layer is only stable when the water fraction isin the range , and when the water fraction falls below , the system becomesunstable so as to trigger phase inversion.This hypothesis will be tested using experimental data. As shown in Fig. 8, theintersection of the line obtained by regressing the data in which the viscosity drop tookplace by Eq. (12) and the regression line in which the viscosity drop did not occurseems to coincide with the critical point where the viscosity drop takes place.If we draw the lines of equations (14) and (15), we obtain a region that overlaps theallowable water content, as shown in Fig.14. Within this region, it seems that bothstates can exist. However, in our experiments, emulsions with water as the continuousphase were generated in the overlapping region. This may depend on thethermodynamic free energy, and in this region, it is conceivable that the state in whichwater forms a continuous phase has a smaller energy than the state in which oil forms acontinuous phase, although we cannot say for sure because emulsions are notthermodynamically stable systems.As a guideline for future development, in order to reduce the viscosity with as littlewater as possible, it is important to make the as small as possible, that is, to formthe particle-packed layer as densely as possible as the structure of the emulsion.However, when the diameter of the dispersed particles is constant, is limited byKepler conjecture. If the particle size is various so that small particles ﬁll the gapsbetween large particles, or if the particles are not spherical, it may be possible toovercome the Kepler conjecture limit. In this experiment as well, in cases 3, 5 and 6, was obtained to be lower than Kepler's conjecture.Next, we discuss the microscopic structure of emulsions. When no chemical agentis added, the structure of emulsions formed in an oil-water system is relatively simpleto be an water-in-oil (W/O) emulsion, while emulsions formed in a system with chemicalagent can have a complex structure. Figure 15 shows the ﬂuorescence microscopeobservation of the structure of oil and water in a particle-packed layer. The ﬁgureincludes two cases, Case 3 and 5. For each case, series of images with diﬀerent waterfraction are given. Images with a picture frame are the observation in the high-viscosityregion, and images without a picture frame were taken in the low-viscosity region. Inϕwβ=1.0μeμo=μeμo1−ϵo1−ϵo−ϕwϕwϵoϵoϵoϵϵϕw=μeμw1−ϵwϕw−ϵwϕw=ϵwϕwϵw[ϵw,1]ϵw ϵwϵwϵw 11 Case 3, it was observed that particulates were formed by oil in the low-viscosity regionand water in the high-viscosity region, respectively. This means that in Case 3, theemulsion system changes its form from W/O emulsion to O/W emulsion with increase ofwater addition. On the other hand, in Case 5, particulates were formed by oil in both ofthe low-viscosity region and the high-viscosity region, which means that the system hasO/W/O multiple emulsion in the low-viscosity region and changes its form to O/Wemulsion. Although the structure of the emulsions changes depending on the type ofchemical agent, the layer-stacking model can explain them comprehensively.Finally, we examined the agreement between the area of oil or water obtained fromthe image processing and the obtained from the model ﬁtting. Case 3 is shown inFig.16 as an example. The image on the left is the one taken in the high viscosityregion, giving of 0.68, and the image on the right is taken in the low-viscosity region,giving of 0.13. These values obtained from image analysis do not necessarily have tomatch those obtained from model ﬁtting. In fact, in the high viscosity region, the valuesobtained from model ﬁtting and image processing has some discrepancy: 0.58 formodel ﬁtting and 0.68 for image processing. On the other hand, in the low-viscosityregion, the model ﬁtting and image processing gave values of 0.13 and 0.13,respectively. As for the other cases, results are summarized in Table 3. Observing othercases as well, there is a quantitative discrepancy between the ε obtained by imageprocessing and that of model ﬁtting. However, comparing cases 4-6, where MYL-10 wasused as the surfactant, as the surfactant concentration increases, increases in thehigh viscosity region, while decreases in the low viscosity region. This trend iscommon to both image processing and model ﬁtting. This ﬁnding implies that theparameter, , in the model, even though having been introduced hypothetically at ﬁrst,may represent the actual physical structure qualitatively.ϵϵoϵwϵoϵwϵ 12 (a) Case1: C heavy oil(b) Case2: AB3000, 10% (c) Case3: OTP75, 2%(d) Case4: MYL10, 1% (e) Case5: MYL10, 2%(f) Case6: MYL10, 4%Figure 12 Measured viscosities and Layer-stacking model ﬁtting 13 Figure 13 Relation between and the criticalwater addition ratio Figure 14 Schematic diagram of phase inversionϵo 14 = 0.089 = 0.164 = 0.227 = 0.282 = 0.329 = 0.370 = 0.408 = 0.440 = 0.469(a) Case3: OTP75-2%, x20. = 0.000 = 0.047 = 0.089 = 0.164 = 0.227 = 0.242 = 0.255 = 0.282 = 0.395(b) Case 5: MYL10-2%, x20.Figure 15 Observed results by ﬂuorescence microscope.(Images with picture frame are in high-viscosity region,and others are in low-viscosity region)ϕwϕwϕw ϕwϕwϕw ϕwϕwϕw ϕwϕwϕw ϕwϕwϕw ϕwϕwϕw 15 (a) In high-viscosity region(b) In low-viscosity regionFigure 16 Microscope image used for image processing(Case 3, OTP-75 2%)Table 3 Comparison of Case #Chemical agentHigh viscoisty regionLow viscoisty regionImage proc.(Min./Median/Max.)*Model ﬁt.(Eq.15 )Image proc.(Min./Median/Max.)*Model ﬁt.(Eq.16 )1none0.491 / 0.814 / 0.9930.358N/AN/A2AB30000.753 / 0.891 / 0.9830.3410.010 / 0.052 / 0.1140.4313OTP-750.559 / 0.884 / 0.9960.580.009 / 0.107 / 0.3040.1294MYL-10 (1%)0.772 / 0.878 / 0.9700.3780.001 / 0.047 / 0.2360.3745MYL-10 (2%)0.723 / 0.914 / 0.9940.4180.003 / 0.033 / 0.090.2306MYL-10 (4%)0.846 / 0.965 / 0.9980.5110.000 / 0.013 / 0.0730.199* Min./max. are deﬁned as values that covers 95% (2 coverage in normal distribution) with themedian value in the middle.5. ConclusionsIn this paper, emulsions of heavy fuel oil and water were investigated. In theexperiments, oil/water emulsions with surface active agents were prepared to measuretheir viscosity characteristic and observe their microscopic structure usingﬂuorescence microscope. In the theoretical analysis, a new layer-stacking model wasproposed to compare and interpret the experimental results. The following ﬁndingswere obtained:In the region of low water content, the viscosity of oil-water emulsions increaseswith increasing water content.In the system with surfactant, the viscosity suddenly decreases when the watercontent reaches a certain critical value caused by phase inversion.The newly introduced layer-stacking model can well represent the increasingviscosity characteristics of emulsions.The layer stacking model introduced a new parameter deﬁned as a fraction ofthe continuous phase component in the particle-packed layer. This parameter isrelated to the stability of the emulsion system and can explain the viscosity droptriggered by the phase inversion.Microscopic observations corroborate the above results.AcknowledgmentsThis work was funded by JSPS KAKENHI Grant Number JP19K04870. NikkoChemicals Co., Ltd. kindly provided us with a sample of surfactant. Dr. Kuwae, groupleader of Coastal and Estuaries Environment Research Group of Port and AirportResearch Inst. , kindly let us use the expensive ﬂuorescence microsope with nocompensation. Dr. Taku Ogura, a visiting Associate Professor of Tokyo University ofScience gave us valuable advices. We would like to express our gratitude by writinghere. Last but not least, we will present this paper as a sincere condolence andacknowledgement to our long-time colleague, Dr. Shoichi Hara, who led us to this topicϵo=0.68ϵw=0.13ϵo/wϵoϵw σ 16 in the beginning of this research.