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f PRESSURE DROP - FLOW RELATIONSHIPS IN CIGARETTE FILTER RODS AND TOBACCO COLUMNS C. H. Keith Celanese Fibers Company, Box 32414 Charlotte, N.C. 28232 SUMMARY ict v3r.510r Using a liquidAisplacement flow system, pressure drop and flow measurements were performed on~f~ilter rods, tobacco columns and mul!ti- capillary pressure dtop standards. The purpose of these measurements was to determine the relative contributions of laminar or viscous flow, inertial or turbulent flow, and entry and exit effects to pressure drop. Pressure drops were obtained both by forcing and drawing air through the . article. No difference in pressure drop was obtained by either method provided that the flow was the same at a common point in the rod. This specification was necessary because of.the change in flow rate due to gas expansion inside the rod. Pressure drop contributions from gas expansion, thermal effects and rod collapse were negligible. From regression equations, the major pressure drop component in all three types of article was viscous flow„ ranging from 98$ to the total pressure drop in filter rods to 79$ in tobacco columns. Entry and exit effects were small in both filter rods and'tobacco columns but were appreciaba'e and the only other pressure drop contributor in multicapillaries. These measured entry and exit effects in multicapilllaries agreed well with those estimated by flow theory. lnertial flow was found to contribute 1.5 and 19% of the total pressure drop in filter and tobacco rods, respectively. These contributions are reasonable from flow theory for packed columns.

Pressure Drop - Flow Relationships in Cigarette Fiilterl Rods and Tobacco Columns C. H. Keith Cel!anese Fibers Company Box 32414, Charlotte, W.C., 28232 In the measurement or theoretical calculation of the pressure drop of cigarette filters and tobacco columns, the assumption is usually made that the flow inithe article is laminar or viscous. Using this assumption, pressure drop will be directly proportional to the volumetric flow rate and the length of the specimen. In other words, it obeys D'Arcy's Law of viscous flow. Fordyce et al (1) found this relationship to hold for filter rods. However, Meyer- Abich (2) Strydom and Qtto (3) and Palmade (4) found'that tobacco columns had a somewhat non-llinear pressure drop-flow relationship indicat'ing a degree of turbulent or inertial!flow: Conversely, Baker (5) indicates that D'Arcy's Law holds to a good approximation in the tobacco columns used in his work. To resolve this question, and to determine the relative pressure drop contributions of laminar flow, turbulent flow and the effects of channeling,air into and out of the rods, a series of measurements were undertaken on filter rods, tobacco columns and multicapillary pressure drop standards. A further object of this work was to determine whether gas expansion effects, thermal changes and holder effects were contributing to t~he observed pressure drops. Since it was necessary to have accurate and simultaneous measurements of pressure drop and'flow rate, a simple apparatus was devised to provide the necessary data. As shown~in Figure 1, this consists of an oil displacement burette, a manometer and a rubber sleeve encapsulating holder. The flow i's provided by pumping mineral oi'1 into or out of the burette by means of two Zenith gear pumps driven in tandem by a reversible variable speed motor. Since the oil can be pumped in either direction it is possible to obtain a pressure drop under pressure conditions, where air is being forced through the rod or under the normal vacuum condition, where air is being sucked tnto the rod from the surrounding atmosphere. The flow rate is determined by measuring the time 1Presented at the 33rd Tobacco Chemists Research Conference, Lexington, Ky., Oct. 30,, 1979 and the CORESTA Technology Group Meeting, Brist0l„ U.K. Sept. 4, 1979. faoaoasas7

r -2- tlthat it takes for the oil meniscus to travel between two graduation marks rep- resenting a volume of 1000 ml. it' was found that the manometer reading of pressure drop did not appreciably change during the filling or emptying of the burette, which indicates a constant flow rate through the pumps. Valves are 'provided to connect the appropriate end of the manometer to the flow apparatus and to leave the opposite end openito the atmosphere during the pressure or vacuum measurements. The rod holder consisted of a latex sleeve encapsulator of Celanese design. The article being measured was fully inserted into the encapsulator to eliminate air leakage through the wrapper. In addition, a wrapping of cellophane tape was generally applied to the filter rods and tobacco columns to further insure against wrapper leakage and to provide additional rigidity to obviate collapse of the rods at higher flow rates. Using this equipment, pressure drops were measured at 6 to 7 flow rates ranging from 2.5 to 22 mi/sec. Cellulose acetate filter rods of a normal 3.3y/44 tow and a coarse 25 R/50:tow were investigated as were tobacco columns consiisting of'an Americanrtype blend cut at 32 cuts per inch. All' items had a normal cir- cumference of, 24.8mm and the lengths ranged from 10 to 120mm for the filter rods and from 25 to 85mm, for the tobacco columns. In addition a series of 10 tube - glass multicapillary standards similar to those described by Keith and Corbin (6) of 120mm length and nomi',nal pressure drops between 100 and 643mm were tested. iln Table 1, data are presented for a 120mm 3.,3 dpf acetate tow filter under pressure and vacuum flow conditions. If we look at pressure drop as a function of the measured flow rate, we find that the pressure drops are different depending on whether a pressure or vacuum system is employed. For example at a common measured flow rate of 22.4'ml/sec., the pressure measurement gives 487mm and the vacuum 467rrtm pressure drop. The reason for this Is quite simple, we are not measuring the same flow rate In the two types of measurement. In the pressure case, the measured flow rate Is that entering the rod, while in the vacuum case It is that leaving the rod. Since the air passing through the rod is expanding, the exit flow rate Is always greater than the entrance flow rate because of this gas expansion. Using the ideal gas law, a simple'correcti,on can be applied as Indicated at the bottom of the table to convert entry flow rates Into exiit flow rates. When this correction is applied, we obtain flow rates as listed in the second' column of Table 1, and virtually identiical pressure drops are obtained at a common flow rate as shown at the bottom of the table. . 0000048468

-3- This point is quite important in any pressure drop measurement and is frequently overlooked. We occasionally have disagreements with other labora- tories in comparative pressure drop tests, and usually the cause of the dils- agreement iis that the two groups are not measuring fl'ow at the same place inm the filter rod or tobacco column. As reported by Gehring (Z), the flow leaving the rodi has beeni accepted as a standard condition by ISO/TC 126/SC I and the CORESTA Technology Group. Another poi:nt that is evident in Table 1 Is that the direction of!~flow Is unimportant in this ordinary acetate tow filter. Identical pressure drops of 364mm were obtained at an exit flow rate of 17.5 ml/sec in both the pressure and vacuum measurements in which the flow directions are reversed. This was found to be the case for all the filter rods of d'ifferi'ng lengths and deniers, the various lengths of tobacco column and for the series of multicapiillaries examined. This of course does not mean that structures such as ventilated' filters could not have a flow direction dependence, but only that these ordinary materials do not show this effect. ' A further point iniTabl'e l is the fact that an effect of rod collapse is not apparent in these data. -1'f this were present, the pressure drops under vacuum conditions would'tend to be higher than those obtained under pressure Londitions because of a reduction in rod diameter in the former case due to collapse under the positive pressure differential between, the exterior and interior of the rod. This does not appear to be the case for these rods. To further investigate this point, tobacco columns which would be more susceptible to collapse because of their lower firmness values were measured in several ways. In one experiment, the 85mm tobacco col!umn was simply placed In the rubber sleeve encapsulator without add'itional' tape wrapping. In a second,.the column was wrapped In tape and only one end was placed in the encapsulator and pressure drops were measured under both pressure and vacuum conditions. The same tobacco columns were used in all three experiments. The data obtained are shown in Table 2. As Is apparent in the second'part of this table, there Is relatively little difference between the three sets of measurements, indica- ting that rod collapse Is not a significant factor in this work. ln the measurements reported so far, we have examined pressure drop as a functdon of exit flow rate which is the recommended procedure for pressure drop measurements (7). However, to investigate the various components of pressure drop, It Is better to use an average flow rate, i.e. the flow at the 0000048469

-4- - center of the article as this quantity Is more easily related to the flows used in theoretical equations. It also has the advantage of requiring the least correction of the observed flows although all observed'flows now have to be corrected rather than just those obtained under pressure conditions. Average flow rates are obtained by multiplying the observed flow rate by one plus one half the ratio of the pressure drop to atmospheric pressure In the pressure measurements and by one minus one half this ratio in the vacuum measurements. Using these average flow rates, multiple regression equations were con- structed as listed In Table 3. The 3.3YJ44 filter rods were measured at lengths of 10, 20, 40, 60, 80, 100 and 120mm, while the 25 dpf rods were tested at 60„ 80, 100 and 1'20mm lengths. Tobacco columns lengths of 25, 45, 65 and 85mm were used,, and-five 120mm multicapillary standards ranging Tn nominal pressure drop between 100 and 643-were also measured. All the regressions closely fit the observed data,, with correlation coefficients of .999 or better (confidence level P =.999+). Deviations of individual measured values from ealculated values were generally much less than 2mrn or 1$' of the measured pressure drops. As i's apparent in the regression equations, some non-14neariity is present in all articles tested. Thiis is illustrated in Figure 2 where the experimentall points for a 120mm 3.3Y/44 tow rod, an 85mm tobacco column and the 208 mul!ti- eapillary are shown with the tinear part of the regression equations forming the respective lines. It ls evident that for the tow filter and the multi- capillary that a viscous flow assumption is quite a good approximation, while for tobacco columns the departures-from linearity are greater but a viscous flow approximation Is still useablie. To further assess the contributions to pressure drop, the regression equations were used to calculate the linear or viscous flow component, the quadratic or entry and exit component, and a lengthrdependent quadratic.term which is presumed to represent the turbulent or inertial flow contribution. These are listed in Table 4 for the various articles. Ilt should be noted that no subdiviision of the multicapillary quadratic term can be made, since only one length of these was available. However, as will be shown later and as found by Keith and Corbin (6) the quadratic term for these Is thought to be an entry and exit effect, and hence is iindependent of length. In Table 4 it is evident that the constant term is quite small for each 0000048470 1

-5- article article and represents less than 1$ of the overall pressure drop. This small term Is thought to arise from experimental errors In the measurements. The linear term, which represents the viscous or D'Arcy's Law component of the pressure drop is the major component in the overall pressure drop. It ranges from78.5$'ofthe total pressure drop for tobacco columns up to 97.9$ In + the case of the normal tow rod. The,quadratic term, which reflects the contribution to pressure drop from~ the energy expended In funneliing air into and out of the article Is generally small and relatively constant for the filter rods and tobacco columns, ranging from 1.5 to 1.9m. This is a reflection of the relatively low linear velocity In these items which would give low values. in the multicapililary standards, the flow ts channeled into and out of ten smalil capillaries where rather large linear velocities are present. From flow theory, it is expected that these entry and exit corrections should'be proportional to the product of the density of the fluid times the linear velocity squared, the proportionaltty-constant' being between .75 and 1.25 (8). , Table 5 lists these calculated entry and exit pressure drops and compares '.xhem:wiSfi the quadratic term,obtained from regression analysis. It also lists ,ahe hole diameters, average linear velocities, and Reynolds numbers for these 'multicapilleries. The agreement between the values estimated by regression analysis and those calculated from flow theory appears to be quite reasonable, the regression values generally falling in the range of theoretical values. Thus it appears as though the pressure drop in multicapillaries results from viscous drag and kinetic entry and exit„effects. Returning to Table 4,.the last component of pressure drop is a length- . dependent quadratic term which ranges from 5.9nrn for the lower dpf tow Item,tol 15.9mm for a tobacco column. , This term represents a turbulent or inertial flow contribution to the pressure drop. It is of interest to see whether these contributions are reasonable when compared to known information about flow in packed columns. ¢arman (9) found that turbulence exists in packed columns at Reynolds numbers of 2 or more. As shown In Figure 3, the Reynolds number in this case Is the ratio of the product of fluid density and linear velocity to the product of fluid viscosity and a specific surface area, I.e. the surface area of the particles divided by the volume of the bed. For a fibrous material such as filter rods and tobacco columns, this surface area is equal to the fiber perimeter times the volume fractioh occupied by fiiber divided by the fiber area. For solid fibers such as acetate this can be estimated from the 0000048471

-6= fiber surface area and the polymer density, while for porous maLerials such as tobacco, It has to be estimated from the strand dimensions. Table 6 lists the estimated perilmeter to area ratios,, the volume fraction occupied by fiber and the Reynolds numbers for the two tow Items and a tobacco column. It also lists the turbulent flow component of the pressure drop from Table 4. It is apparent that the materials with the higher Reynolds numbers have the larger turbulent flow components. Tobacco with a Reynolds number well above Carman's ('.9) turbulence criterion of 2 has a sizeable turbulent, flow com- ponent, while the tow Items with Reynolds numbers at or below this criterion show relatively little turbulence. Thus the findings for these articles appear to be consistent with those for packed beds of granular, solid materials. A final' point that should be considered is whether there are appreciable pressure drop contributions from thermal and kinetic effects arising from the expansion of air during•its passage through these articles. Using the integrated forms of D'Arcy's equation in which densi;ty iis considered to be a variable for isothermalland adiabatic flow, It is possibl!e to estimate the magnitude of these effects (1D). For the 64'3 multicapillary where these effects would have the greatest magnitude, it is calculated that under isothermal conditions, the gas expansion would contribute 1.5mm to the pressure drop. Under thermal expansion _ conditions up to 0.6mm of pressure drop would be obtained by cooling the gas stream by up to 7.4°C if a completely adiabatic expansion were achieved -- which Is unlikely. Since these contributions are only 0.2 and 0.1$ of the total pres- sure drop, they can be considered as being negligible in, this severest case.. In summary It has been found that the flow regime in cigarette fi'lters, multi~capillary pressure drop standerds, and tobacco columns Is largely laminar or viscous under ordinary conditions. For multicapillary standards a 3.5$ pressure drop contribution arises from chanelling air Into and out of the article. For cigarette filters there is a small: turbulent flow and entry and exit flow component of pressure drop. In tobacco columns, turbulent flow is more important, contributing up to 19$ of the pressure drop, while entry and exit effects remain small. Rod, collapse and thermal and kinetic effects from gas expansion within the rod were found to be negligible In these experiments. 4ooooasa7z

-7- References: (1) Fordyce, W. B., I. W. Hughes and M. G. Ivinson, Tob. Sc1. 5 70-75, 1961. (2) Meyer-Abich, K., Beitrage z. Tabakforsch. 3, 307-329, 1966. (3) St'rydom, M. L. and J. P. Otto, Bull. CORESTA, 1972-2, 13-16, 1972. (4) Palmade, P., Annales d'u Tabac, 17, 37-48, 1979. (5) Baker, R. R. Beitrage z. Tabakforsch. 8, 124-131, 1975. (6) Keith, C_ H. and'J. A. Corbin; Beitrage z. Tabakforsch, 8, 60-64, 1975. (7) Gehring, M. Beitrage z. Tabakforsch. 9, 255-261, 1978, cf. CORESTA Bulletin 1!977-1,, p. 17-33. (8) Chemical' Engineers Handbook, J. H."Perry, Editor, p. 388, McGraw-Hill, • New York, 1950. (9) Carman, P. C., Trans. Inst. Chem. Engrs. (London) 15, 150, 1937. cf. Perry, p. 394. (10) Chemicali Engineers Handbook, Ji. H. Perry, Editor, p. 379, McGraw-Hill, New York, 11950. (11) Keith, C. H. and C. F. DeLaet, Tob. Sci. 10, 68-72, 1966. _j ' W

-8- . Table 1 Pressure Drop as a function of Flow Rate (120mm 3.3Y/44 Cellulose Acetate Tow) Pressure Measurement Vacuum Measurement ieasured 'low(entry) ml/sec) Corrected* Flow(exlt) (ml/sec) Pressure Drop (mm H20) Measured Flow(exit) (mi/sec) Pressure Drop (mm H20) 2.7 2.7 51.7 2.8 58.8 5.1 5.1 107.5 5.2 108.4 7.6 7.7 160.7 7.7 160.3 10.0 10.2 213.5 10.1 210.5 13.9 14'.3 296.7 14.0 291.3 17.8 18.4 3B2.7 17.9 370.7 22.4 23.4 487.3 22.4' 467.3 Pressure Drop at 17.5 mi/sec Pressure Drop at 17.5 ml/sec Measured:flow = Pressure Drop at 378.3 mm H20 ' 17.5 ml/sec Measured flow ~ 364.2mm H20 Corrected flow - 364.1mm H20 *Corrected Flow - Measured Flow x Patm'+ P.D. Patm Patm = 750mm Hg - 10160mrn H20 %I k

l r -9- Table 2 Investigation of Rod Collapsing Effects (85 mm Tobacco Columns) Untaped Column in rubber Taped Column Taped Column sleeve encapsullator (vacuum meas.) (pressure meas.) (vacuum meas.) Experimental Data: Flow (ml/sec) Pressure Drop (mm H20) Flow (mt/sec) 2.7 10.2 2.9 6.,0 24.4 5.1 7.6 10.0 42'.2 10.2 13.9 61.8 14.1 • 17.4 81.4 17.8 22.2 108.4 22.4 Calculated from regression equations: 5.0 19.8 5.0 10.0 42.3 10.0 15.0 67.7 15.0 17.5 81.4 17.5 20.0 95.8 20.0 Pressure Drop (mm H20) Flow (ml/sec) Pressure Drop (mm H20) 11.4 2.8 1l1.1' 20.7 5.0 20.3 31.8 7.5 31.5 43.3 10.1 43.5 62.6 14.1 62.6 82.4 17.8 82.9 107.8 22.6 109.3 20.4 5.0 20.4 42.9 10.0 42.9 67.5 15.0 67.6 80.6 17.5 80.8 94.3 20.0 94.6 ~ ~