Influence of Viscosity on Liquid Flow Inside Structured PackingsChristian Bradtmoller,† Anna Janzen,‡ Michel Crine,§ Dominique Toye,§ Eugeny Kenig,‡
and Stephan Scholl*,†
†Technische Universitat Braunschweig, Institute for Chemical and Thermal Process Engineering, Langer Kamp 7, D-38106Braunschweig, Germany‡University of Paderborn, Chair of Fluid Process Engineering, D-33098 Paderborn, Germany§Universite de Liege, Laboratoire de Genie Chimique, Allee de la chimie, B6C, Sart Tilman, 4000 Liege, Belgium
ABSTRACT: In this study, X-ray computer tomography and light-induced fluorescence were applied to investigate themorphology of liquid flow inside structured packings. Fluid dynamic parameters such as liquid holdup and wetted surface weredetermined to study the effect of the variation of viscosity and liquid load. Flow patterns inside the packing were identified andcategorized. Liquid film thickness and its distribution were analyzed on single sheets. For both methods, the measured holdupvalues are in good agreement, despite differences in the techniques of measurement. For the flow patterns and their relativecontribution, as well as mean liquid film thickness, a strong dependency on the varied parameters was found. Furthermore, thedensity function of film thickness distribution changed characteristically with liquid load and viscosity. The complementary use oftomography and optical assessment allowed an improved insight into flow phenomena and the observed interdependency ofphysical, geometric, and operational parameters.
1. INTRODUCTION
Corrugated-sheet structured packings are frequently used ascolumn internals in distillation and absorption processes. Theypromote a better flow distribution and provide a high gas−liquid interfacial area, resulting in both a low pressure drop andhigh separation efficiency. Physical properties of the liquidphase strongly influence fluid dynamics and performancecharacteristics of packed columns. Rising liquid viscosity isknown to increase liquid holdup and decrease the capacity, aswell as separation efficiency, of structured packings.1,2 Hence, itis necessary to understand the influence of liquid viscosity onflow phenomena inside structured packings to accuratelydescribe such dependencies in the modeling of separationprocesses.X-ray computer tomography (XCT) has been shown to act
as an efficient, noninvasive method to adequately display liquiddistribution in packed columns.3−10 However, it can deliveronly time-averaged cross-sectional images of the irrigatedpacking; hence, the dynamics of two-phase fluid flow cannot becaptured with this method. Moreover, water and air are usuallyused as working fluids in XCT studies. Hence, the appliedliquid has a rather low viscosity and deviates significantly fromthe surface tension of organic solvents. Sidi-Boumedine andRaynal11 investigated the influence of liquid viscosity ofaqueous polymer solutions in the range of 1−20 mPa s usingXCT, but in a co-current gas−liquid flow in a trickle bedreactor.Alternatively, flow patterns inside structured packings may be
investigated through the liquid flow on inclined planes andsingle sheets. Stoter12 studied the distribution of liquid betweentwo sheets, thus having no optical access, while otherauthors13−15 studied rivulet and film flow on inclined plates.They showed that rising viscosity can enhance spreading and,hence, influences the mass-transfer area. In most of these
studies, plane and smooth surfaces were investigated. Thisrepresents a strong simplification as the metal sheets ofstructured packings are corrugated and often have a structuredsurface (texture). The latter effect was considered byNicolaiewsky,14 who also studied embossed surfaces andshowed that higher viscosity can cause an increase of filmthickness and a decrease in the wetted surface. In contrast,Ataki16 conducted experiments with the corrugated surface ofthe structured packing Rombopak and observed an improve-ment of wetting. Subramanian and Wozny17 examined singlesheets with the characteristic corrugation of structured packingsand smooth and embossed surfaces. However, since differentworking fluids were used, the effect of viscosity cannot beassessed independently. Furthermore, the liquid was distributedfrom a single point source, resulting in a nonideal and unevendistribution perpendicular to the flow direction.Some recent studies focused on the improvement of mass
transfer through modifications of structured packing. For theabsorption of CO2 in industrial-scale processes, the reduction ofthe water content in the used solutions yields a large potentialfor the reduction of energy consumption. However, reducingthe water content will increase solution viscosity. Therefore,Hu18 and Sun19 studied the effect of macroscopic modificationsof the geometry of structured packings in absorptionexperiments with single sheets. Hu et al.18 performedabsorption experiments for aqueous diethanolamine solutionsand found that packing modification can increase mass transfer.Kohrt et al.20 evaluated the impact of different textured surfaceson the liquid-side mass transfer coefficient. They found a
Received: May 17, 2014Revised: August 31, 2014Accepted: December 22, 2014Published: December 22, 2014
significant increase that originated from the texturing comparedto a flat surface.Despite the undoubted relevance, no systematic conclusions
on the effect and interdependency of liquid load and viscositycan be drawn for corrugated sheets with embossed surfaces.Since, at higher liquid loads, a large portion of the surface iswetted,21 for the proper analysis of single sheets, a uniforminitial liquid distribution is essential. On the other hand, it isdifficult to draw conclusions about the liquid flow patternsinside the complex packing geometry, based on the undisturbedflow on a single sheet.In a previous study, images derived from the XCT
measurements showed three main flow patterns: film flow,contact point liquid and flooded areas.22 The total liquid flowcomprises these three patterns, while the contribution of eachpattern changes with physical properties (viscosity and surfacetension) and operating conditions. As a consequence, totalliquid holdup and gas/liquid interfacial area are affected. As anexample, with increasing liquid load, the holdup, which iscontributed by the contact point liquid, rises proportionally tothe total holdup, whereas the film-flow fraction decreases. Incontrast, the fraction contributed by flooded areas increases,this effect being more pronounced at higher viscosities.These findings are discussed in comparison to observations
made for the liquid flow on a single packing sheet by means oflight-induced fluorescence (LIF). The liquid holdup issuccessfully used to demonstrate that both methods can becompared, since the absolute values are in good agreement andshow the same dependencies on the varied parameters. Thefilm thickness on single sheets was also seen to increase withviscosity and liquid load. At low viscosities and liquid loads, themajor fraction of wetted surface is covered with very thin liquidfilms, while an increase of liquid load leads to more evendistributions.
2. EXPERIMENTAL SECTIONIn this work, two experimental methods were applied to studythe influence of viscosity on flow morphology and fluiddynamics in structured packings. XCT was used to gaininformation on liquid flow patterns inside structured packings.These studies were complemented with experiments on liquidflow on single packing sheets. Thus, optical access has beengiven and LIF was used to obtain a better spatial and temporalresolution of film thickness and its distribution on the surface.Different working liquids were applied for the two
experimental methods. In the experiments analyzed by XCT,water and water−glycerol mixtures were used as workingliquids to determine the influence of liquid viscosity. For thetests carried out with single sheets and analyzed by LIF,solutions of water, fluorescein, and the polymer Luviskol wereutilized. The polymer was added to adjust the viscosity withnegligible changes in density and surface tension. Furthermore,fluorescein was used as dye at a concentration of 50 mg/L todetermine the wetting behavior and film thickness by lightinduced fluorescence. Compositions and physical properties ofthe applied liquid mixtures are given in Table 1. Here, thesurface tension is given, since it is used in the models applied inthis study. Furthermore, the surface of the packing material isembossed, preventing a correct measurement of the contactangle. If values for the contact angle are needed, these can bedetermined from the surface tension, using experimental resultsfor different packing materials from Shi and Mersmann15 orapplying a correlation given by Rocha et al.23 In the applied
concentration range of the polymer, the solutions were testedand did not show a deviation from Newtonian behavior.The single sheets investigated by LIF are from the structured
packing Mellapak 500.Y. The results from these experimentswere compared with XCT measurements, in which the packingMellapakPlus 752.Y was studied. Both packings are manufac-tured by Sulzer Chemtech AG. MellapakPlus 752.Y is a high-capacity packing with almost the same corrugated sheetstructure and specific surface area as Mellapak 500.Y. Theonly difference with MellapakPlus 752.Y is in the smooth bendof the corrugation crimp at the packing edges up to an angle of90°. Whereas the corrugation angle, averaged over the height ofone packing element, is 45° for both packings, the bend on theedges of MellapakPlus 752.Y results in a slightly reducedcorrugation angle in the bulk of a packing element.24 Geometricparameters of the packings are given in Table 2. Results
presented by Suess1 show a negligible deviation in the liquidholdup, even for packings with corrugation angles of 45° and60°, but otherwise identical geometric features. Hence, thecomparison of MellaPak 500.Y and MellapakPlus 752.Y appearsreasonable, if the packing edges of the latter are not consideredin the analysis of the XCT data.
2.1. X-ray Tomography. 2.1.1. Experimental Setup. Ahigh-energy (420 kV) and large-scale (0.45 m diameter and 4 mhigh) X-ray tomograph was used in this study. The tomograph
Table 1. Physical Properties of Working Liquids Used inExperiments by XCT and LIFa
is equipped with a fan beam X-ray source and a linear detector,both fixed on a height-adjustable arm. The packed column isplaced on a rotating plate between the X-ray source and thedetector. The rotation time is 60 s, resulting in a circumferentialspeed of 5.5 mm/s. The column is made of transparent PVCand has an inner diameter of 0.105 m. Further details can befound in Toye et al.27
The column is filled with four MellapakPlus 752.Y structuredpacking elements, each rotated by 90°, with respect to eachother. The diameter of the packing elements is 0.1 m and theheight is 0.2 m. The packing elements used in this work aremade of embossed and perforated stainless-steel corrugatedsheets.The applied liquid load ranges from 4.6 m3/(m2 h) to 23.1
m3/(m2 h). The experiments are carried out without gas flow.Tomographic measurements are performed in both the dry andthe irrigated packed column in several packing cross sectionsdistanced by 10 mm. The total measuring range is 700 mm,beginning in the center of the first packing layer. To allow a
comparison with single sheets of Mellapak 500.Y, the crosssections at the packing edges, where the corrugation angle isreduced, are not considered. Altogether, 56 cross sections aretaken into account for this study.
2.1.2. Image Processing and Liquid Flow MorphologyAnalysis Method. Reconstructed “raw” images of the measuredcross sections are squares with dimensions of 499 × 499 pixels,the side length of which is 0.36 mm.27 In order to extractquantitative information about the liquid phase, the projectiondata obtained in the dry column are subtracted, beforereconstruction, from those obtained at the same height in theirrigated column. Furthermore, different numerical techniquesare applied to raw images in order to eliminate the backgroundnoise (for details, see refs 3 and 28). An example of theresulting gray scale images is given in Figure 1. Gray pixels areassociated with the liquid phase (“liquid pixels”), while whitepixels indicate the gas phase (“gas pixels”).The analysis of the tomographic images provides an insight
into the time-averaged liquid-flow morphology inside struc-
Figure 1. Images of liquid distribution in a column cross-section: (a) image before post-processing with the flow patterns exemplarily depicted(green rectangles, film flow; blue circles, C-P liquid; and red dashed oval, flooded region); (b) image after image post-processing with highlightedidentified flow patterns (colors correspond to those given for panel (a)).
Figure 2. (A) Schematic flow sheet of the test rig for single sheets of structured packings; (B) sectional drawing of the arrangement of the lightsource, sheet, and camera. (Legend: a, single packing sheet; b, CCD camera; c, scale for measurement of liquid holdup; d, liquid distributor; e, drippoints; and f, black light tube.)
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tured packings. In the frame of this work, the three main flowpatterns, identified in Janzen et al.,22 are considered. Theimages reveal that film flow is the predominant flow pattern(green rectangles in Figure 1a). Moreover, liquid is observed tobe retained at the contact points between two facing sheets, dueto adhesion forces and surface tension (blue circles). We callthis flow pattern “contact-point liquid” (C-P liquid). Thedynamics of this flow pattern cannot be captured with thetomography technique; hence, it is not clear whether the C-Pliquid is continuously renewed by the liquid flow or onlysporadically. Nevertheless, it is obvious that liquid mixing ispromoted at these locations. At locations with high liquid loads,the entire space between two packing sheets is filled with liquid.These “flooded regions” (red dashed oval) represent the thirdflow pattern. Figure 1b shows the result of the image processingprocess and the distribution of the detected liquid to the threeflow patterns.The image analysis method was used to obtain quantitative
information about the contribution of each flow pattern to theoverall liquid holdup as a function of both operating conditionsand liquid properties.22 In this method, the liquid flowstructures are analyzed on the basis of their size and shape toidentify the above flow patterns. Therefore, the size and shapeof liquid structures are characterized as functions of themaximum and minimum Feret diameters. The minimum Feretdiameter is equivalent to the thickness of the structure, whilethe ratio of maximum to minimum Feret diameters indicateswhether the shape of the structure is rounded or elongated.Basic correlations concerning the size and shape of theidentified flow patterns, can be described as follows:
• Film flow: thin and elongated structures• C-P liquid: relatively small and rounded structures• Flooded regions: large and rather rounded structures
A flow structure can be composed of more than one flowpattern, since two liquid patterns can be connected by film flow.In this case, flow structures are subdivided until the ratio ofliquid pixel area to the area of the Feret parallelogram is above50%.22 Otherwise, it is assumed that the fit is insufficient, sincea lower ratio implies a higher amount of enclosed gas pixels,and hence, several flow patterns are (or can be) comprisedwithin the analyzed cross-sectional area. The applied imageanalysis method is implemented in MatLab. From this analysis,the contribution of each flow pattern to the overall liquidholdup is quantified.2.2. Wetting Behavior and Liquid Holdup on Single
Sheets. 2.2.1. Experimental Setup. The experiments werecarried out with a single sheet of structured packing. This sheetwas freely suspended in a frame as shown in Figure 2, providingoptical access of the wetting and the possibility to determinethe liquid holdup gravimetrically.Mellapak 500.Y single sheets were used in this work. The
sheets are made of embossed and perforated stainless steel.They have a width (w) of 142 mm, a height (h) of 102 mm, anda depth (d) of 6.5 mm, resulting in a sheet volume (w × h × d)of 94 146 mm3. The volumetric liquid holdup is given by theratio of the liquid volume (which is determined throughindividually measured liquid mass and density) and the sheetvolume.The wetting was investigated for liquid loads varying between
1 m3/(m2 h) and 40 m3/(m2 h). The mass flow was measuredby means of a coriolis flowmeter. The temperature of the liquidwas held constant at 20 °C to avoid changes in physical
properties during the experiment. As depicted in Figure 2, thedistributor has 21 metal strips, serving as drip points, to provideliquid to each flow channel on the front and rear side of thepacking sheet. Hence, no droplets have to be released, but arivulet flow to the packing sheet is enabled. Thereby, especiallyfor low liquid loads and the given high surface tension of theaqueous solutions, a much higher distribution quality ascompared to droplet flow is achieved. Nevertheless, for liquidloads (wL) of <10 m
3/(m2 h) and low viscosities, uneven liquiddistribution is observed, resulting in higher loads in somechannels.To measure the holdup gravimetrically, the sheet was
suspended freely in a frame, which was connected to a scale.The resolution for the weighing was 0.1 g. The sheet wassuspended to avoid wetting of the frame and the distributor wascarefully positioned to leave a small gap to the packing sheet.The light source was positioned above the sheet as depicted inFigure 2B. The fluorescence was excited by a black light tube(Sylvania, 6W, 188 mm in length). The images were taken witha digital camera (Canon, Model EOS 500D) in front of thepacking sheet with an exposure time of 0.1 s. No additionalfilters were used. To facilitate the subsequent processing of theimages and increase the accuracy, the entire setup wasprotected against ambient light.
2.2.2. Image Processing and Film Thickness Determina-tion. The images are processed to determine the fraction of thewetted surface, the mean film thickness and the frequencydistribution of the film thickness. For these calculations, aMatLab algorithm is used. The film thicknesses are determinedby applying the Lambert−Beer law to the light intensitiesderiving the needed empiric parameters for this equation inconjunction with the mass of the liquid holdup.A digital camera is used to provide images for the relevant
image section of the packing sheet (3200 pixels × 2300 pixels).This leads to a spatial resolution of >22 pixels/mm. Sincefluorescein emits green light with a wavelength of 525 nm, allpixels outside this color range are set to black. In this way,ambient light, as well as reflections of the black light used forthe excitement, can be removed from an image. Since theintensity of emitted light varies with the incoming light,depending on the distance from the light source, the measuredvalues are corrected. Namely, they are normalized with theincoming intensity in the center of the sheet. Therefore, thelight is considered to originate from the center of the appliedblack light tube and the light intensity decreases according tothe circumference given by this center and the position on thesurface of the packing. Finally, the conversion to a grayscaleimage (Figure 3) enables determination of the fraction of drysurface (black pixels) and a classification of the gray levels,which correspond to the light intensities of former green pixels,into a frequency distribution. This distribution subdivides thelight intensities into 72 classes, ranging from 0 (black pixel) to1 (white pixel).Based on the measured mass of the liquid holdup (mhL,exp),
the liquid density (ρL), and the ratio of the wetted surface(rwet), the mean liquid film thickness can be calculated using eq1 below. Since the images represent the two-dimensional (2D)projection area of the packing surface, the area (Ap), which isderived from the outer dimension of the sheet, is used.
δρ
=m
A rL,mh ,exp
L p wet
L
(1)
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The measurements of the liquid hold-up mass and thefraction of wetted surface mainly determine the accuracy of thecalculated mean liquid film thickness. For low liquid loads andlow viscosity, the liquid mass is small and a large portion of thesurface is wetted with thin films, resulting in low lightintensities. Therefore, the wetted surface value is more sensitiveto the threshold used to distinguish between wetted and drysurface than for high liquid loads. Hence, an overall uncertaintyof ±9% can be assumed for δL,m. For higher liquid loads andviscosities, the uncertainty reduces to ±4% of the mean filmthickness.To determine the local film thicknessesand, based on that,
a frequency distributionthe film thickness has to bedetermined for the individual pixels of an image. Therefore,the linear correlation between the gray level of a pixel and theintensity of the fluorescence, which is proportional to the filmthickness at this position, is used. The nonlinear relationshipbetween the intensity of the exciting light and the film thicknesscan be described by the Lambert−Beer law:
δε
=−
−I I I
clog[( )/ ]
L0 0
fluor (2)
where I0 is the intensity of the black light, ε the extinctioncoefficient, and cfluor the concentration of fluorescein. Thisrelationship can be used, as described by Al-Sibai,29 to generate
a calibration curve, correlating light intensity to a sample withknown film thickness. Al-Sibai measured the film thickness ontwo points with focused laser beams and stated that it is criticalto hold all parameters constant between calibration andmeasurement. Since not only two points, but the entire imagesare to be analyzed, this method was not applied here. Instead,the experimentally measured mass of the liquid is comparedwith the mass calculated according to eq 3. Here, the frequencydistribution H(I) of gray levels from the image processing isused to calculate the liquid volume represented by each class oflight intensity. Considering the liquid to be distributed equallyto front and back of the sheet, the summation of all classes givesthe liquid mass for each image.
∑ρ δ==
m A H I I2 ( ( ) ( ))I
calc p L0
1
L(3)
On that basis, the parameters I0 and ε from eq 2 aredetermined by minimizing the differences of measured andcalculated masses by the least-squares method, according to eq4.
∑ − ==
m m( ) mini
n
1h ,exp h ,calc
2L L
(4)
Because of possible changes in the concentration offluorescein between two subsequent experimental series, eq 4is applied to all images taken for the same viscosity and thedenominator from eq 2 is adjusted, instead of determiningindividual values for I0 and ε. With these parameters, eq 2allows calculating the film thickness for each pixel of an imageand thus provides a high spatial resolution in the plane of thepacking sheet.Because of the corrugation, the liquid films are not observed
perpendicular to the surface, but the projection plane of thepacking is considered instead. Hence, the film thicknessespresented here, both local and mean, represent an apparent filmthickness. Therefore, they can be compared nevertheless. Theaccuracy of the local film thickness is determined by two effects:(i) the effect of corrugation and refraction on the observed lightintensity and (ii) an uncertainty in the relation between lightintensity and film thickness. To determine the relation betweenlight intensity and film thickness, the parameter εcfluor wasregressed along with I0 for an entire series of pictures, thusreducing the effect of individual measuring errors. Theuncertainty in the film thickness resulting from this is below±5%. Because of the angle under which the surface wasobserved, resulting from the corrugation of the sheet, as well as
Figure 3. Resulting image of wetted sheet after image processing.Actual viscosity is 1.0 mPa s and liquid load is 4.3 m3/(m2 h). Forcomparison with XCT results, the fraction of wetted surface isdetermined between the dashed lines.
Figure 4. Influence of viscosity on liquid flow morphology. Feret rectangles are superimposed on images of irrigated cross-section (H = 110 mm,liquid load = 17 m3/(m2 h)). [Legend: green, film flow; blue, C-P liquid; red, flooded regions.]22
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the refraction of light, the apparent film thickness is <28%higher than the actual film thickness. It must be emphasizedthat this maximum deviation is not to be applied to all localvalues, because a portion of liquid flows on surfaces that areobserved perpendicular.To visualize the influence of viscosity on film thickness and
compare the distributions from different operating conditions,the frequency function H(I) is transformed into the probabilitydensity function f 2,wet(δL,i). Here, the indices indicate that thedensity function refers to a 2D surface and the surface fractionwhich is wetted with liquid. The mean film thickness isdetermined from the density function scaled with the wettedsurface. This facilitates the comparison of different experiments.Furthermore, to account for the nonlinear relationship of lightintensity and film thickness, the individual width of a class i isconsidered in eq 5:
δδ δ
=Δ
fH I
r( )
( )( )ii
i2,wet L,
wet L L, (5)
3. RESULTS AND DISCUSSION3.1. Morphology Analysis and Influence of Viscosity
on Flow Patterns. 3.1.1. Morphology Analysis of FlowPatterns in Structured Packing. First, computer tomography isused to provide a view on the liquid distribution in the packingelements and the occurring flow patterns. Figure 4 showsimages of the classified liquid flow structures with super-imposed Feret rectangles. All images are related to the samecolumn cross-section and a liquid load of 17 m3/(m2 h), but todifferent liquid viscosities. The increase of both the total liquidholdup and the fraction of flooded regions with growingviscosity is obvious. Furthermore, it can be seen that, while thenumber of flow structures recognized as C-P liquid is constant,the cross-sectional area of these structures increases. Hence, theamount of liquid retained at contact points between adjacentpacking sheets increases almost proportionally to the totalliquid holdup, while the fraction of this flow pattern is constant.Thus, it can be assumed that the packing geometry largelydetermines the number of contact points, whereas physicalproperties and operational parameters influence the amount ofthe accumulated liquid.In Janzen et al.,22 it was shown that the fraction of holdup,
identified as film flow, decreases in favor of the flooded regionsat higher viscosities. Since the film flow is most important forthe interfacial area, the impact of liquid load and viscosity onthe absolute values of flow patterns is investigated. To enable acomparison with the observations for a single sheet, averagevalues over the total packing height without the packing edgesare calculated. Figure 5 shows the influence of liquid load onthe contributions of the different flow patterns to the totalliquid holdup at different viscosities. Film flow liquid increaseswith liquid viscosity and liquid load, whereby the influence ofload is reduced for wL > 12 m3/(m2 h). The absolute amount ofC-P liquid increases slightly with wL and ηL, but seems to levelout for wL > 12 m3/(m2 h) at constant viscosity. In contrast, thecontribution of the flooded regions exhibits a negligibleincrease with liquid load at 1 mPa s, but a drastic increase athigher viscosities. In summary, a complex inter-relation ofliquid load and viscosity on liquid holdup, wetted surface, andgas/liquid interfacial area is observed. Proper quantification ofthe different flow patterns and their relative development mayserve as the key link between the two.
3.1.2. Morphology Analysis of Flow Patterns on SingleSheets. The liquid on single sheets can be assumed tocorrespond to film flow. Since XCT shows that film flow is thepredominant flow pattern within the packing, this is studied indetail on a single sheet. Here, flooding and C-P liquid cannotbe observed, but the optical accessibility enables a directevaluation of the film characteristics. For a qualitative analysis,Figure 6 shows images for selected values of liquid load andviscosity. Figures 6a, 6b, and 6c illustrate the influence ofincreasing liquid load for a constant viscosity of 1 mPa s. Theincrease in the wetted surface area and light intensity can beseen. In comparison, Figures 6d, 6e, and 6f display the effect ofdynamic liquid viscosity (ηL = 16.1 mPa s) for the same liquidloads. For both viscosities, the light intensity and, correspond-ingly, film thickness increase with liquid load. In all images,fluctuations in light intensity can be observed along the flowchannels formed by the corrugation of the sheets. Those areinduced by the embossed surface. If the liquid surface ispresumed not to follow the surface of the sheets exactly, thefilm thickness will change due to the uneven surface below thefilm.In Figure 6a, it can be seen, that, at a low liquid load and
viscosity, only one flow channel is wetted with a continuous-film-like structure. The wetting in the other channels isdiscontinuous. Here, only the dimples of the embossed sheetare filled with stagnant liquid. This results from an intermittentwetting by droplets running through the channels. For lowloads, and especially for liquids with high surface tension, it isnot possible to maintain a continuous distribution of liquid toevery channel on the front and back of the packing. This causesan initial distribution of droplets to the channels. Hence, thechannels are wetted intermittently and the liquid in the dimplesis renewed periodically. Upstream of holes, and on the bottomof the sheet, liquid accumulates until the critical mass for therelease of a droplet is reached. Thus, the initial distribution ofliquid in this setup is equal to the distribution in a packing layer.A rise of the liquid load results in an increase of dropletfrequency until continuous flow is reached. In Figure 6b, thetransition from the regime of periodic wetting to continuous
Figure 5. Influence of liquid load and viscosity on holdup in packingelements contributed by each flow pattern. [Legend: filled symbols,film flow; empty symbols, C-P liquid; and crossed symbols, floodedregions.]
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films can be observed. Here, some channels are alreadypermanently wetted.The viscosity has a pronounced influence on this transition.
If Figures 6a and 6d are compared, changes in light intensityalong the flow channels can be observed in Figure 6d. Thisindicates that droplet flow also occurs here. Because of thehigher viscosity, compared to Figure 6a, the droplets arestretched and a lower velocity was observed in the experiments.Figure 6e presents an almost-complete transition to film flow.At high liquid loads, all channels are continuously wetted for
both viscosities. This state is reached above 20 m3/(m2 h) for 1mPa s and at 15 m3/(m2 h) for 16.1 mPa s. If all channels arewetted, an increase of viscosity causes a rise of film thickness,obvious from the higher light intensity.
In the experiments, the bottom right corner of the sheet wastypically not wetted, because the liquid predominantly followsthe flow channels. Although the trespass from one channel overthe corrugation to the channel below is unusual for the aqueoussystem investigated here, liquid passing through the perforationcan be observed frequently. Thus, liquid changes from the frontside to the back and reaches a lower channel resulting in aneffective flow angle that is steeper than the corrugation angle.In summary, significant changes in the morphology of the
liquid flow are observed, depending on liquid load andviscosity. Especially in the identified regime of droplet flow, apronounced influence of viscosity can be shown. In this regime,the embossed surface prevents a strong dewetting. Thephenomenon of droplet flow does not seem to be limited tothe wetting of single sheets. Additional fluid dynamic tests were
carried out in a glass column with di = 150 mm. Here, dropletsoriginating at the interface between two packing elements andrunning down the flow channels also were observed.As compared to XCT, optical access offers a good spatial and
temporal resolution of the flow patterns, enabling theinvestigation of dynamic liquid flow phenomena.3.2. Influence of Viscosity on Fluid Dynamic Param-
eters. 3.2.1. Method Comparison and Influence of Viscosityon Liquid Holdup. In order to show that the results for a singlesheet and the XCT measurements of the packing arecomparable, despite the differences in the condition for liquidflow, the liquid hold-up values are compared. The measure-ments on the single sheet cover a wider range of viscosities. Toprevent a major alteration of density and surface tension, awater−polymer solution was used in these experiments. Thus,the values for viscosity do not match exactly. The holdup forsingle sheets is measured gravimetrically. As both sides of thesheet are irrigated, the volumetric holdup is calculated based onthe volume of the sheet and the density of the liquid. In case ofthe packing, the liquid holdup is calculated from tomographicimages, averaged over the axial profile, excluding the edgesbetween the packing elements.Figure 7 shows an increase of the holdup with liquid load and
viscosity for both the single sheet and packing. Since water is
used in the experiments at a viscosity of 1 mPa s, there is nosignificant difference in density and surface tension at thisviscosity. Despite the different geometries, the experiments arein very good agreement for viscosities up to 10 mPa s. Atviscosities of ≥16 mPa s, the experimental values of bothmethods deviate, with XCT experiments with the packingshowing higher values for liquid holdup. The values of Aferka etal.5 are slightly lower, because they are obtained underconsideration of the regions at the top and bottom of Mellapak752.Y. This packing exhibits a higher inclination of thecorrugation in these regions, resulting in a lower local andoverall liquid holdup. Furthermore, experimental results fromSuess and Spiegel,1 also obtained by means of computertomography, are depicted in Figure 7. These measurementswere carried out in a counter-current flow of water and air, butthe values displayed here are for gas loads below 1.5 Pa1/2,
where an interaction of gas and liquid flow may be neglected.The experimental results as well as the proposed model (theequation is given in the Appendix) for water as working liquidare in good agreement with the holdup determined in thisstudy.For a viscosity of 20 mPa s, the model by Suess and Spiegel1
agrees with the XCT measurements of this study; however, forintermediate viscosities, it overestimates the holdup. At thisviscosity (9.8 mPa s for the single sheet and 10 mPa s for thepacking respectively), both experimental setups show the samemoderate increase in holdup and the same dependence onliquid load. For wL < 15 m3/(m2 h), the increase of holdup withliquid load is smaller. For wL < 5 m3/(m2 h), the holdup for thesingle sheet at 9.8 mPa s matches the results for pure water.This is due to the strong dependency of holdup on the liquiddistribution at low loads.For viscosities of 16.1 mPa s ≤ ηL ≤ 36.5 mPa s, the
differences in density and surface tension between the twoexperimental setups increase. Nevertheless, the dependency onthe liquid load remains identical for both methods. In bothcases, the small change of holdup, resulting from the increase ofviscosities up to 10 mPa s, is accompanied by a more-pronounced increase of holdup for higher viscosities. In moredetail, for the single sheet, a viscosity of 36.5 mPa s is needed toobtain the same holdup as that at 20 mPa s for the packing.Hence, the impact of viscosity is higher in the case of thepacking. This difference can be assigned to the contact pointsbetween the packing sheets and the resulting liquidaccumulations, which are not present for a single sheet.Moreover, flooding of channels cannot occur on a single sheet.As shown previously by the drastic increase in the flow patternof flooded channels at high viscosity, it is reasonable that highviscosities cause discrepancies between the holdup determinedfor single sheets and that for packing.Furthermore, it can be assumed that the holdup on a single
sheet must be smaller for the same liquid load, since no C-Pliquid is present. In contrast, an active renewal of C-P liquid inthe packing would result in a reduction of liquid flow in thechannels. Consequently, for the packing, the holdup resultingfrom the flow in the channels is decreased at the same liquidload. This effect partially compensates the contribution of C-Pliquid missing for a single sheet.Overall, it can be concluded that, despite differences in the
setup, the influence of viscosity on holdup and liquid load issimilar for both experiments. The presented results also matchvalues reported for Mellapak 500.Y.1 Therefore, both methodscan be used complementary to exploit their advantages.
3.2.2. Influence of Viscosity and Liquid Load on theWetted Surface. Figure 8 compares the wetting behavior andthe influence of viscosity for the packing and for the singlesheet. Since the single sheet cannot be wetted in the bottomright corner (cf. Figure 6), only the left part of the sheet istaken for evaluation, as depicted in Figure 3. In this way,fractions of wetted surface of 0.7−0.8 can be determined athigh liquid loads. If the entire sheet, including the unwettedtriangle in the bottom right corner, was considered, a fraction ofwetted surface of 0.6 would be determined. Unlike for theliquid holdup, the two experimental methods show a distinctdifference, also for low viscosities. In all cases, the wettedsurface is smaller on the single sheet, compared to the resultsfor the packing as obtained from XCT. Although, for a viscosityof 1 mPa s, the wetted surface is ∼10%−15% higher for thepacking than for the single sheet, this difference increases as the
Figure 7. Liquid holdup as a function of liquid load on a single sheetand in packing determined by XCT for different viscosities.Experimental values from Suess and Spiegel1 with a counter-currentflow of air.
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viscosity increases. One must consider that the fraction ofwetted surface determined by LIF does not refer to the truepacking surface, but rather to the 2D projection plane mappedby an image. The real surface is enhanced by the curvature dueto corrugation and embossment and the waviness of the liquidfilm. These effects must be considered, in addition to the C-Pliquid, which represents ∼25% of the entire liquid holdup and isabsent on the single sheet. Thus, the experimentally observeddifference between the two measurement methods is in goodagreement with the differences that must be expected.The results, obtained for the packing by XCT, show a
significant influence of liquid load, as well as viscosity. At a ηL =20 mPa s, the wetted surface fraction tends toward a value of1.0. For lower viscosities, significantly lower values are found.The difference of wetted surface due to the different viscositiesis slightly higher for low liquid loads. This corresponds to theobservations for single sheets, for which a broader range ofloads was investigated. Although, at wL = 40 m3/(m2 h), theinfluence of viscosity is small, liquid loads of <5 m3/(m2 h) andthe high surface tension of pure water cause very poor wettingat a viscosity of 1 mPa s. Despite the deviation of the two valuesat 9.8 mPa s for wL < 5 m3/(m2 h), a viscosity increase leads tosignificantly better wetting. These findings correspond to theflow regime in which droplets cause intermittent wetting. Inthis regime, the influence of viscosity is more pronounced, asillustrated in Figure 6.The results obtained in this study are also compared with the
corresponding gas−liquid interfacial area values calculated withthe models of Olujic et al.30 and Tsai et al.31 (equations aregiven in the Appendix). The latter is based on absorptionmeasurements with aqueous solutions, at viscosities of 0.8 mPas ≤ ηL ≤ 10 mPa s. For a viscosity of 1 mPa s, the data,calculated with the Tsai model, are in good agreement with theXCT measurements, but they overestimate the data for thesingle sheet. The strong increase of the interfacial area for thepacking at 20 mPa s and the minor increase for the single sheetare not predicted, since the model explicitly does not
incorporate an influence of viscosity. In the database, analyzedby Tsai et al., the highest viscosity under investigation was 10mPa s and, primarily, working liquids with lower viscosity andpackings with lower specific surface area were considered.Hence, the combination of high viscosity, a packing with highspecific surface area and thus narrow flow channels in thepacking and a high surface tension in this study might explainthe deviation.The model of Olujic et al.30 is based on the correlation of
Onda et al.,32 but incorporates geometric features of thepacking such as the perforation. Since approximately half of theholes were bridged by liquid, because of the high surfacetension of the working liquids, the reduction of installed surfacedue to the perforation was estimated to be 5%. The calculateddata significantly underestimate the experimental results of thisstudy for both packing and single sheet. The original equationby Onda et al. was developed for random packings, having quitelow specific surface areas, in comparison to the structuredpackings in this study. Mainly aqueous solutions with ratherhigh surface tensions were considered. The model validationcarried out by Olujic et al., on the other hand, refers to test datafrom distillation experiments under total reflux. In these,normally binary mixtures of organic solvents are employed.These can be supposed to have a rather low surface tension,compared to the working liquids in this study. Hence, theconditions of this study deviate noticeably, which may cause thelarge deviations. In the model, an increase of viscosity results ina decrease in the Reynolds number. Therefore, the modelpredicts reduced wetting at higher viscosities, while theopposite was found in the experiments. However, aside fromthis qualitative mismatch, the model by Olujic et al.30 reflectsthe increase in wetted surface with liquid load very well.
3.2.3. Film Thickness on Single Sheets. In the previoussections, it has been shown that the holdup on a single sheetcorrelates strongly with the film flow in the packing. Inaccordance to these findings, and since XCT is limited in itsspatial resolution, the mean value of the film thickness and itsdistribution are investigated by means of LIF for a single sheet.In the analysis of the flow patterns on the single sheet, the
correlation between film thickness and light intensity wasshown. This correlation is inverted to calculate film thicknessdistributions from the distributions of light intensity. Based onthe known mass of holdup, the coefficients in Lambert−Beerlaw are derived. Coefficients are calculated for all imagesrecorded for one viscosity value. This approach accounts forsmall deviations in the used liquid mixtures and the variety ofhold-up masses as well as light intensities, because of theinfluence of liquid load, which enables a robust solution.In order to validate this method, a mean thickness is
calculated from the distributions by averaging the values of allpixels considered as wetted. In Figure 9, these values arecompared with the mean film thicknesses according to eq 1.Although some deviations occur at low liquid loads, theconsideration of all images for each viscosity ensures reliableresults. Thus, the influence of an uneven liquid distribution tofront and back of the packing element for single images seemsnegligible. The deviations are typically smaller than 0.06 mm.Figure 9 shows that the mean film thickness on a single sheet
grows with increasing liquid load, while the increase due toviscosity is small, except for the highest viscosity. This is due tothe holdup increasing proportionally to the wetted surface.When comparing the results for viscosities of 16.1 mPa s and36.5 mPa s, it may be seen that the larger holdup at a viscosity
Figure 8. Wetted surface fractions on left part of the single sheet byLIF (see Figure 3) and ratio of the effective gas−liquid interfacial areato the specific surface area of packing measured by XCT, as a functionof liquid load at different viscosities. Physical properties fromexperiments on single sheets were applied to the models of Olujicet al.30 and Tsai et al.31
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of 36.5 mPa s, in combination with a similar wetted surfacearea, yields a significantly higher film thickness.The experimental mean liquid film thicknesses significantly
exceed the calculated data according to Olujic et al.30 (theequation is given in the Appendix). Despite the quantitativeoffset, the model qualitatively describes the influence ofviscosity. In order to evaluate the deviation of calculated andexperimental values, one must consider that the film thickness,as implemented in the model by Olujic et al.,30 is the meanvalue for the entire packing surface. In other words, thesuperficial liquid flow is related to the specific geometric surfaceof the packing, instead of the wetted surface. Since a significantportion of the surface of the single sheets is not wetted,calculated and experimental values cannot correspondquantitatively. Hence, for a comparison of film thicknesses,the relationship of wetted surface, holdup, and film thickness, ascalculated in the model, must be taken into account. Since themodel predicts 20%−50% of the surface to be wetted (cf.Figure 8), the film thicknesses depicted in Figure 9 must bemultiplied by a factor ranging from 5 to 2, depending on liquidload and viscosity. The resulting values would still under-estimate the film thickness for a viscosity of 1 mPa s andsignificantly overestimate the film thickness for a viscosity of36.5 mPa s. Thus, it can be concluded that the model of Olujicet al.30 is not capable of matching film thickness as well aswetted surface for the conditions investigated here consistently.In the comparison of the mean film thicknesses with the
actual differences in light intensities depicted in Figure 6, it isobvious that the mean value does not adequately describe theinfluence of viscosity on morphology. Therefore, the median ofthe distributions is added, whose determination is shown inmore detail hereafter. It is apparent from Figure 9 that themedian of film thickness is significantly smaller, compared tothe mean values for η ≤ 16.1 mPa s at low loads. This originatesfrom the form of the film thickness distribution. At low loadsand viscosities, the intermittent wetting causes a highly
nonsymmetric distribution with a large part of the surfacebeing wetted with very thin films. This effect is reduced athigher viscosities. Hence, the discrepancy between mean andmedian value indicates a state of flow, where the mean is notsuitable to characterize the real conditions properly.To elucidate these observations, film thickness distributions
are shown in Figure 10 under variation of liquid load. Thedistributions are presented by the density function f 2,wet(δL),which describes which fraction of the wetted packing surface iswetted with a certain film thickness for each liquid load. Here,the integration over δL yields the following cumulativedistribution function:
∫δ δ δ=δ
F f( ) ( ) d2,wet L0 2,wet L L
L
(6)
with F2,wet = 0.5 for the median film thickness δL,50. Thisrepresents the film thickness for which 50% of the wettedsurface is wetted with a thinner liquid film. The observedmaximum values are below 3 mm, which is in agreement withthe geometry of the packing. The nonlinear relationship of lightintensity and film thickness results in a spatial resolution betterthan 0.04 mm for δL < 0.5 mm rising to a resolution of 0.14mm at a film thickness of 3 mm. Thus, the method permitsbetter evaluation of the thin liquid films, compared to XCT.At low viscosities, a pronounced peak for very thin films can
be observed for low liquid loads. The peak lies within a range of0.08 mm ≤ δL ≤ 0.25 mm, with a maximum at 0.12 mm. Thefilms corresponding to this peak originate from the surface thatis periodically wetted by droplets. In more detail, this is theliquid on the surface surrounding the dimples. This area isslowly reduced in a process of dewetting until a new droplettrickles over the surface. For a viscosity of 1 mPa s, the effect ofperiodic wetting occurs up to liquid loads of ∼25 m3/(m2h),which is depicted as region (1). An increase of viscosity shiftsthe transition (solid line) from this regime to more stable liquidfilms to lower liquid loads. In Figure 10d, the transition takesplace at liquid loads of ∼12 m3/(m2 h), which is in agreementwith the observations during the experiments. Moreover, theheight of the initial peak of very thin films recedes,corresponding to a decrease of the fraction of these films ofthe entire wetted area.Furthermore, in region (1), the viscosity influences the
correlation of liquid load and film thickness. The dashed line inregion (1) indicates the liquid load (wL) at which a certain filmthickness occurs with a fixed frequency, i.e., f 2,wet(δL, wL) = 0.5.It can be seen that this film thickness increases with increasingliquid load. This dependency is stronger for higher viscosities.Therefore, the transition to region (2) is reached at lower loads.Here, the film thickness, which occurs with the given frequency,does not increase any further. Nevertheless, in regime (2),higher viscosities lead to an increase in the maximum filmthickness. This is illustrated by the dashed line, shifting tothicker films.In addition, it can be observed that, for a viscosity of 1 mPa s,
the density function is strictly monotonic, decreasing with filmthickness for all liquid loads. For a viscosity of 4.5 mPa s, thedensity function decreases monotonically, with a plateau at 1.0mm. At higher viscosities, a second maximum evolves in theregime with stable films (region (2)). The maximum is shiftedfrom δL = 1.2 mm at a viscosity of 16.1 mPa s to δL = 1.6 mm ata viscosity of 36.5 mPa s. This maximum can be assigned to theliquid flow in the channels, formed by the corrugation. Thisflow pattern rather indicates rivulet flow than film flow. In a
Figure 9. Comparison of median and mean value of film thicknessdetermined from distributions with the mean value from the mass ofholdup and wetted surface, and calculated values from Olujic et al.30
Physical properties from experiments on single sheets were applied tothe model of Olujic et al.30
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complete packing element, each flow channel is enclosed by thefollowing packing sheet. Considering the maximum filmthicknesses of ∼1.8 mm at ηL = 16.1 mPa s and 2.2 mm atηL = 36.5 mPa s, observed in region (2), under theseconditions, the entire cross section of a flow channel mightbe filled with liquid. Thus, these results can explain thepronounced increase of flooded regions, observed for highvalues of load and viscosity in the XCT measurements.
4. CONCLUSIONS
In this study, the influence of viscosity and liquid load wasinvestigated in order to gain a more fundamental understandingof the liquid flow patterns in structured packings. Two differentexperimental methods were applied. Computer tomographyallowed a noninvasive analysis of the flow patterns in thepacking, while studying the flow on a single sheet enabled ananalysis by light-induced fluorescence, offering a good spatialand temporal resolution.Resulting from the morphological analysis of tomographic
images, three flow patterns could be distinguished: film flow,contact point liquid (C-P liquid), and flooded regions.22 Thesepatterns are influenced differently by liquid load and viscosity.Although the fraction of C-P liquid is independent of these
parameters and film flow decreases in favor of flooded regionsat high viscosity, it was shown that the absolute value of filmflow increases with viscosity. Since the identified flow patternsdiffer in their volume-to-surface ratio, changes in flowmorphology and the proportion of flow patterns will affectheat and mass transfer subsequently. Hence, these findings arerelevant for the modeling of separation efficiency. In commonrate-based models, integral values for the holdup are used, inconjunction with a mean film thickness and wetted surface area.Especially if mass transport in the liquid phase must beevaluated due to a higher film thickness and a decreaseddiffusion, the identification and quantification of different flowpatterns represents important information for model improve-ment.To overcome the limitations of tomography, with respect to
spatial and temporal resolution, the liquid flow on single sheetswas studied by light-induced fluorescence. As important fluiddynamic parameters, liquid holdup and wetted surface fractionwere presented for both methods. The packing material,investigated in the presented experiments, was slightly different,and for the analysis of a single sheet, the missing contact pointsto another sheet might be assumed to have a rather largeimpact on fluid dynamics. Nevertheless, the increase of holdup
Figure 10. Density functions of film thickness over liquid load for different viscosities: Solid lines indicate the transition from a regime with periodicwetting (region (1)) to a regime with stable films (region (2)). Dashed and dotted lines illustrate the impact of liquid load on the film thicknessoccurring with a fixed frequency.
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with higher liquid loads and viscosity is in good agreement forboth methods. Furthermore, the measured absolute values ofliquid holdup are in good agreement, up to a viscosity of 10mPa s. For higher viscosities, the holdup on single sheets showsa lower increase. For the wetted surface, the methods showeddeviations that arise from the particular experimental setup.Nevertheless, both methods show an increase of the wettedsurface with liquid load and viscosity, corresponding to apronounced decline of wetted surface at low loads and lowviscosity. Literature models were applied to predict theinfluence of increased viscosity. Good agreement was foundfor the determination of wetted surface by the equationproposed by Tsai et al.31 for pure water. Applying the equationfor liquid holdup that was reported by Suess and Spiegel1 gavegood results for pure water and at high viscosities; however, forintermediate values, the influence of viscosity was over-estimated. However, overall a rather poor quantitative agree-ment was found for the impact of viscosity on wetted surface, aswell as film thickness and holdup.Furthermore, the thickness distribution of liquid films on a
sheet was quantified. At liquid loads of wL < 15 m3/(m2 h), themedian δL,50 is more appropriate than the mean value todescribe the morphology and the changes arising fromvariations in liquid load and viscosity. Density functions ofthe film thickness show huge fractions of the surface to bewetted by very thin films. In this flow regime, at low liquidloads, droplets are wetting the surface periodically, leaving thinfilms behind. In this regime, viscosity and wetting propertieshave a large impact on film morphology. These results areconsistent with the observations made with XCT concerningthe flow patterns. In the range of liquid loads leading toperiodic wetting, the holdup identified as film flow and C-Pliquid increases strongly with the liquid load. Above 15 m3/(m2
h), the holdup originating from flooded regions increases,which corresponds to the observations on the single sheets. Onthese, the liquid film thickness increases with load after all flowchannels have been wetted.The combination of the two methods builds up a framework,
which shows the diversity of flow patterns and effects in astructured packing. Holdup varies in the axial direction,5 as wellas within one cross section of a column. Results concerningflow patterns and their dependency on viscosity and liquid loadmay support the improvement of theoretical models forseparation performance. In addition, the results can help tounderstand limitations of current models, e.g., at low liquidloads and high viscosity, and provide a better understanding ofthe interdependency of physical properties, geometry, andoperational parameters.
■ APPENDIX
The following literature equations were used to determine andcompare values for liquid holdup and the fraction of wettedsurface with the experimental results of this study.Liquid holdup can be described by the following equation,
from Suess and Spiegel:1
ηη
=⎛⎝⎜⎜
⎞⎠⎟⎟h ca w xL P
0.83L
L
L,0
0.25
with
=<
>⎪⎪⎧⎨⎩
cw
w
0.0169 (for 40 m /m h)
0.0075 (for 40 m /m h)
L3 2
L3 2
and
=<
>⎪⎪⎧⎨⎩
xw
w
0.37 (for 40 m /m h)
0.59 (for 40 m /m h)
L3 2
L3 2
The fraction of wetted surface area, as determined using theequation from Tsai et al.,31 is defined as
ρσ
= × ⎜ ⎟⎡
⎣⎢⎢⎛⎝
⎞⎠
⎛⎝⎜⎜
⎞⎠⎟⎟
⎤
⎦⎥⎥a a g
QL
1.34GL PL 1/3
p
4/3 0.116
However, the fraction of wetted surface area, as determinedusing the equation from Olujic,30 is given as
σ= − Ω − − ·
−
⎜ ⎟⎪
⎪
⎪
⎪
⎧⎨⎩
⎡⎣⎢
⎛⎝
⎞⎠
⎤⎦⎥⎫⎬⎭
a a
Re Fr We
(1 ) 1 1.450.075
GL P
0.75
L0.1
L0.05
L0.2
The liquid film thickness can be determined using thefollowing equation from Olujic:30
δη
ρ α=
⎛⎝⎜⎜
⎞⎠⎟⎟
u
ga
3
sin( )LL LS
L P p
1/3
Definitions of the terminology used in these equations aregvien in the Nomenclature section.
■ AUTHOR INFORMATIONCorresponding Author*Tel.: +49 531 391 2780. E-mail: [email protected] ContributionsThe manuscript was written through contributions of allauthors. All authors have given approval to the final version ofthe manuscript.NotesThe authors declare no competing financial interest.
■ ACKNOWLEDGMENTSThis work was supported by Deutsche Forschungsgemeinschaft(DFG), under Grant Nos. SCHO 842/12-1 and KE 837/19-1.The authors wish to thank Sulzer Chemtech, Ltd., for theprovision of the packing material.
■ NOMENCLATUREaGL = specific gas−liquid interfacial area [m2/m3]aP = specific surface area of the packing [m2/m3]Ap = projected area of packing sheet [m2]cfluor = concentration of fluorescein [mol/m3]f 2,wet = probability density function of film thickness [m−1]F2,wet = cumulative distribution function of film thicknessFrL = Froude number for liquidg = gravitational constant [m/s2]H = frequency distributionI = intensity of fluorescence [W/m2]I0 = intensity of black light [W/m2]
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LP = wetted perimeter in cross-sectional slice of packing [m]mhL = mass of liquid holdup [kg]n = number of experiments for one value of viscosityQ = volumetric flow rate [m3/s]rwet = ratio of wetted surface; rwet = Awet/AgeomReL = Reynolds number for liquiduLS = superficial liquid velocity [m/s]wL = liquid load [m3/(m2 h)]WeL = Weber number for liquid
Greek LettersαL = angle of corrugation to horizontal [deg]δL = film thickness [m]δL,50 = median film thickness [m]ε = extinction coefficient [m2/mol]ηL = dynamic liquid viscosity [mPa s]ηL,0 = dynamic liquid viscosity of water at 20 °C [mPa s]ρL = density of liquid holdup [kg/m3]σ = surface tension [N/m]Ω = fraction of surface occupied by holes
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