The Use of Pressure Drop Measurements for Estimating Ventilation and Paper Porosity* by C

Beitrage zur Tabakforschung International ·Volume 10 ·No. 1 ·December 1979

The Use of Pressure Drop Measurements for Estimating Ventilation and Paper Porosity* by C. H. Keith Celanese Fibers Company, Charlotte, North Carolina, U.S.A.

The recent increase in the number and volume of ven 20 °C. For measurements on ventilated filters, the perti tilated cigarette brands has created a need for a simple, nent readings are the normal open cigarette pressure drop, non-destructive means of measuring the degree of air L\p 0 , the cigarette pressure drop with the filter vents dilution. Two techniques currently in use require the use closed, L\ p0, and the filter pressure drop, L\ Pf· For measure of auxiliary equipment or specialized analyses. One of ments on tobacco columns, a fully encapsulated pressure these is the sleeve method of Norman (1) which encloses drop, L\ p6, is also required. the ventilation portion of the cigarette in a small chamber The basis for the calculation of diluting air flow from and measures the flow into this chamber while a puff or pressure drop is the observation (3, 4, 6, 7) that pressure alternatively a constant flow is withdrawn from the ciga drop is essentially equal to the product of an impedance rette. The degree of air dilution is thus estimated from coefficient, a flow rate and a length (Darcy's Law). While the ratio of the volumetric flow rates. A second method is this relationship is nearly exact only for filter tips, it is that described by Reynolds and Wheeler (2), which en usable to a good approximation in tobacco columns where closes the cigarette except for the burning coal in an at a more complicated flow regime exists. Using this assump mosphere of argon. The amount of argon in the main tion and one that pressure drops are additive, the diluting stream smoke provides a measure of the dilution. air flow for a single row of holes can be calculated by Since both of these techniques require enclosing the burn equation 1 of Figure 2. By extension of the multiple row ing or unlit cigarette in a chamber and separating the case in equation 2 to many rows of closely spaced holes ex diluting flow from the mainstream flow by means of seals, tending the length of the filter, equations for porous tipping they can sometimes be difficult to use in routine measure paper or porous cigarette paper can be derived. Equa- ments. A method which avoids these difficulties is to util ize the encapsulated and unencapsulated pressure drop of Figure 1. Dilution processes and pressure drop measure- the unlit or lit cigarette to estimate the amount of air menta. Dilution through pores and/or perforations dilution. Since pressure drop and volumetric air flow Ventilation are essentially directly proportional to each other in ciga rette filters (3, 4), the difference between the encapsul ated and unencapsulated pressure drop provides a measure of the degree of filter ventilation. This was recognized by Diffusion Reif (5), who derived the appropriate equations for a ventilated filter. While it is known that pressure drop in a tobacco rod is only approximately proportional to flow, SYMBOL MEASUREMENT the non-linear effects are small enough so that pressure drops can also be used to estimate ventilation in this ~Po portion of the cigarette. Figure 1 illustrates the dilution processes occurring in a cigarette, and the various pressure drop measurements that can be used to estimate these. Each of these pressure ~p. drops can be conveniently measured using an accurate pressure drop machine, and a rubber sleeve encapsulator. For the measurements reported herein, a critical flow 17.5 orifice pressure drop tester with an adjustable length rod cm•/s- ~iliiiiilii:l,::::::::::...::::....:::::...... :::...... -":...::::::....::::::..::::.:::::u encapsulator of Celanese design was used. The orifice was calibrated to a flow of 17.50 ± 0.15 mVs at 760 torr and 17.5 ~ • Presented, in part, at the Coruta Technology Study Group meeting held cm•/s-~ in Munich, Germany, in September 1977. Received: 29th September 1978- accepted: 6th July 1979. L~Pf~ Figure 2. Dilution equaUona. where:

1. Filter dilution - single row of holes AQ diluting flow (cm•fs) Q total exit flow (cm•fs) dilution = AQ = APe - Apo Q Ape -L1 Ap,jL, APo cigarette pressure drop unencapsulated (mm H20) 2. Filter dilution - multiple rows of holes APe cigarette pressure drop filter encapsulated (mm H 0) dilution = APe - Apo 2 APe -L1 Ap,jL, - (n - 1) AL Ap,/2L, Ap. cigarette pressure drop - total encap-

sulation (mm H20) 3. Filter dilution - porous tipping paper Ap, filter pressure drop - encapsulated (mm H 0) dilution = 2 L1 distance from mouth end to open vents (mm). For porous tipping this becomes the length of 4. Column dilution - porous cigarette paper, non-porous insertion Into the holder. tipping 2 (APe - APe) (Lo + Le) L, filter length (mm) dilution (APe - Ap,) Lo AL distance between)ows of vents (mm)

5. Column dilution - porous cigarette paper - vented length of tobacco column encased in Im ~ filter pervious wrapping or inside the holder (mm) 2 (Ap. - APe) (1 - D,) (Lo + Le) dilution = open column length (fnm) (Ap. - Ap,) L 0 number of rows of vents 6. Total Dilution filter dilution dilution = D, + Dt tobacco column dilution tions 3 and 4 are appropriate to porous tips and columns. 30 mm tipping paper, 21 mm filter length and 25 mm Equation 5 extends 4 to the case where vented filters are circumference. When smoked, the butt length was 33 mm. employed. Finally, equation 6 provides the total dilution Those equipped with the M 3.0 tipping paper had twenty for a cigarette. By addition of other pressure drops and oblong holes of 0.2 mmt area located 15 mm from the end lengths these can be applied to multiple filters and other of the filter, while those with the 1.5 paper had twenty constructions. The derivation of these equations is out holes of about 0.12 mm2 area located 12 mm from the lined in the Appendix (p. 15). mouth end. For some of Parker and Montgomery's samples, To test the validity of these equations for perforated tip cigarette and filter pressure drops from the control non ping paper, Parker and Montgomery (8) measured the perforated cigarettes were combined with the cigarette pertinent dilutions and pressure drops on a series of ciga pressure drops for the perforated samples to calculate the rettes equipped with various filters and two types of dilution values for the unlit cigarettes as shown in Table 1. Malaucene laser-perforated tipping papers, designated As is evident, the agreement between Parker and Mont M 3.0 and 1.5. Companion measurements on cigarettes gomery's (8) observed and our calculated dilutions is quite with non-porous tipping were also performed. The ciga good. The importance of the placement of the dilution rettes all had general dimensions of 85 mm overall length, vents is apparent here. Even though the M 1.5 paper had

Table 1. Calculated and measured dilutions (unlit cigarettes).

Calculated Observed Calculated Tipping Ap,• Tow Item APo * APe" dilution dilution* paper Observed (mm H2 0) (mm H20) (mm H2 0) (%) (%) (%)

M3.0 102 162 99 66 57 116 1.6R/50 M 1.5 104 162 99 55 55 100 M3.0 97 143 90 58 59 98 1.8Y/42 M 1.5 98 143 90 49 50 98 M3.0 93 142 90 63 62 102 2.5Y/48 M 1.5 91 142 90 56 59 95 M 3.0 63 96 49 54 51 106 5.0Y/40 M 1.5 66 96 49 44 45 98 av_erage 102

• : Data from Parker and Montgomery (8).

8 Table 2. Deliveries and removal efflclenclea. •

Conden- Calcu- Smoke sate Tipping Con den- Carbon Filter lated No. of Smoke** removal sate+ removal monoxide Conden- paper dilution puffs efficiency efficiency sate/CO (%) (mgfcig.) (%) (mgfcig.) (%) (mgfcig.)

non-porous 0 8.2 16.5 60.1 13.4 53.0 17.5 0.766 1.6R/50 M3.0 66 9.6 6.0 61.9 5.2 60.9 7.1 0.732 M 1.5 55 9.2 7.4 61.8 6.4 59.8 7.9 0.810 non-porous 0 7.8 17.5 56.7 14.2 49.6 18.2 0.780 1.8Y/42 M3.0 58 9.8 6.9 59.8 5.9 59.1 7.1 0.831 M 1.5 49 9.2 8.2 58.6 7.1 56.8 8.5 0.835 non-porous 0 7.8 18.0 57.1 14.6 49.6 17.6 0.830 2.5Y/48 M3.0 63 9.4 5.8 59.1 5.1 60.2 5.8 0.879 M 1.. 5 56 9.5 7.0 58.2 6.0 57.0 6.4 0.938 non-porous 0 7.1 21.3 43.4 17.4 34.7 18.3 0.951 5.0Y/40 M3.0 54 9.1 12.0 41.0 9.5 30.7 7.8 1.22 M 1.5 44 9.1 12.8 41.9 11.1 38.1 9.0 1.23

• : Data from Parker and Montgomery (8). •• : Particuiate matter retained on a Cambridge filter pad. + : Nicotine-free dry smoke.

approximately 60G/o the hole area of the M 3.0 paper, this a slower rate, i.e. there is a reduced volume passing did not reduce the dilution by as much as might be ex through this part of the filter in the same period of time. pected. The reason for this is that the holes on the M 1.5 Since diffusion, the major filtration mechanism, is more paper were located closer to the mouth end of the ciga effective at lower velocities, the efficiencies will increase, rette, thereby placing more pressure drop upstream of as was found by Overton (10) and Keith (11). The effect the vents. Thus the pressure drop across the vents is in is less marked for smoke removal efficiency as the slower creased, providing more flow through them than might flow rate also allows a great adsorption of vapor phase be expected on the basis of hole size alone. This effect is illustrated in a calculated plot of percent dilution versus Figure 3. Calculated effect of hole position on dilution. hole position as shown in Figure 3 for the 2.5Y/48 filter M 1.5 paper, 21 mm filter of 2.5Y/48 tow with M 1.5 paper. This figure also shows the calculated li Pc = 142 mm, li Pt = 90 mm

cigarette pressure drop as the vents are moved along the 70 120 filter. The values in Figure 3 were obtained by equating the diluting flow estimated from equation 1 of Figure 2

with the orifice flow through the dilution holes estimated 110 by Selke and Mathews' (9) equation with an exponent of one half. The resulting quadratic equation is solved for

!:! p 0 , and this value is reintroduced into equation 1 to 100 obtain the calculated dilutions. As can be seen, the dilution decreases and the pressure drop markedly increases as the c:: "0 ventilation site is moved away from the mouth end. .2 ; :; 90 g: To ascertain the effect of these diluting flows on smoke c:: composition, the deliveries of particulate matter, (nic- :0 ; . otine-free dry smoke) condensate and carbon monoxide c a. ~ 0 were determined for these cigarettes including the non Q) 80 "0 a.. 1> porous controls, and removal efficiencies for smoke and "0 condensate were also measured by Parker and Mont ~

gomery (8). The pertinent data are summarized in Table 2. 70 As noted by them, it is readily apparent that the venti lated filters reduce the delivery of smoke, condensate and carbon monoxide by 350/o to 65°/o depending on the 80 filter and component measured. Also, as can be predicted from filtration theory, introduction of diluting air into the filter generally slightly increases the removal efficien cies, particularly for dry condensate. This occurs because 0 0~------.75------~10~----~1~5------w~----~25 50 the smoke is drawn through the front part of the filter at Distance from mouth end (mm)

9 Table 3. Partlculate matter (observed and expected Table 5. Carbon monoxide (observed and expected deliveries). deliveries).

Observed* Expected Expected Tipping Observed Expected Exeected Filter delivery delivery Filter Tipping paper Observed paper delivery* delivery Observed (mg/cig.) (mg/cig.) (%) (mg/cig.) (mg/cig.) (%)

M3.0 6.0 6.3 105 M 3.0 7.1 7.0 99 1.6R/50 1.6R/50 M 1.5 7.4 8.0 108 M 1.5 7.9 8.8 111

M3.0 6.9 8.6 124 M3.0 7.1 9.6 135 1.8Y/42 1.8Y/42 M 1.5 8.2 10.4 123 M 1.5 8.5 11.0 129

M3.0 5.8 5.9 101 M3.0 5.8 7.9 136 2.5Y/48 2.5Y/48 M 1.5 7.0 7.3 104 M 1.5 6.4 9.4 147 M3.0 12.0 13.1 109 M3.0 7.8 10.8 138 5.0Y/40 5.0Y/40 M 1.5 12.8 15.7 122 M 1.5 9.0 13.1 145 average 112 average 130

* : Data from Parker and Montgomery (8). * : Data from Parker and Montgomery (8). water in the tobacco butt preceding the filter (12), thereby measured and calculated values is quite good, averaging reducing the adsorption component of the filter smoke 103 °/o. This provides an indication that most if not all of removal efficiency. the difference between the vented and unvented cigarettes Using these efficiencies and the dilution percentages, it is can be ascribed to the dilution process and its effects on possible to calculate the smoke, condensate and carbon filtration and burning rate. There does not seem to be monoxide deliveries that would be expected if only dilu any great differences in tobacco column adsorption of tion and filtration were operative. Since different num condensate components or a significant change in the mix bers of puffs were taken on the ventilated and non-ven of condensed smoke components generated by the slower tilated cigarettes, these expected deliveries have to be ad burning tobacco in the vented cigarettes. justed to a common number of puffs by multiplication by Table 5 shows comparable observed and calculated carbon puff count ratios. This comparison is shown for wet par monoxide deliveries, and here again the agreement is not ticulate matter in Table 3. For this smoke component, the good, averaging 130°/o. This indicates an increased loss of observed values are generally less than the calculated carbon monoxide by diffusion through the cigarette paper values, the average calculated to observed ratio being and vents, as was found by Morie (13), Baker and Crellin 112 oI o. This discrepancy is expected since this measure (14), Owen and Reynolds (15) and Muramatsu et al. (16). includes water and some water vapor. As has been in It may be noted for condensate that the calculated values dicated, water can be more effectively adsorbed by the are on the average slightly higher than the observed tobacco column and in the filter in the ventilated cigarette values. This can occur because the amount of dilution in because of their lower flow rates. This adsorption reduced creases once the cigarette is lighted. This increase comes the delivery below that which would be expected if only from the increased pressure drop of the burning cone. This dilution and straight filtration were effective. increased pressure drop in the tobacco column ahead of Table 4 shows a comparison of observed and expected de the ventilation holes causes more air to be drawn through liveries for nicotine-free dry particulate matter or con the vents, thereby increasing the overall dilution. This densate. Here it is evident that the agreement between the effect was measured by making pressure drop measure ments on a commercial ventilated cigarette during smok Table 4. Condensate (observed and expected deliveries). ing by connecting the cigarette to a constant flow pressure Observed* Expected Expected drop machine for two seconds once a minute, thereby Tipping delivery delivery Filter paper Observed using the pressure drop machine as a smoking machine, as (mg/clg.) (mg/cig.) (%) shown in Figure 4. This cigarette had an unlit pressure M3.0 5.2 4.6 89 drop of 114 mm of water, which increased to a fairly 1.6R/50 M 1.5 6.4 5.8 91 constant value of 123-125 mm for the first six puffs after lighting. In the last two puffs for this cigarette the press M 3.0 5.9 6.1 103 1.8Y/42 ur-e drop again increased up to 139 mm, probably because M 1.5 7.1 7.3 103 of an increase in the temperature of the smoke stream M 3.0 5.1 5.2 102 entering the filter. This pattern is similar to that found by 2.5Y/48 M 1.5 6.0 6.7 112 Baker (7). Using these pressure drops and those obtained on comparable cigarettes with the filter vents closed, the M3.0 9.5 10.9 115 5.0Y/40 M 1.5 11.1 11.8 106 dilutions shown in Figure 5 were calculated. This calcula tion assumes that the pressure drop increase in the latter average 103 puffs is occurring in the filter, which appears to be reason • : Data from Parker and Montgomery (8). able. It is evident that, as expected, the dilution increases

10 Figure 4. Smoking pressure drop apparatus (square wave Figure 5. Changes In dilution during smoking. puff}. 50

Vacuum - Ventilated 40 cigarette Cambridge reservoir filter pad c:: .5! 0 ~ "0

cG)

eG) a.

Water 10 manometer once the cigarette is lit. Because of the relatively constant pressure drop, it does not appreciably dlange during most unlit 1 3 4 s Puff number of the smoking process. In the last puff or two the dilution again increases for this cigarette, somewhat offsetting the higher deliveries of smoke components in these puffs. osmon, that dilution can be effectively measured by As a further test of the validity of measurement of dilution simple, non-destructive pressure drop measurements. by pressure drop, six commercial vented filter brands were In the measurements reported so far, and in the derivation examined. Table 6 lists measured and calculated filter of the equations, the only assumptions have been that the dilutions for these cigarettes, and in addition the total pressure drop along a tobacco column is linearly propor dilution for both the filter and tobacco column is cal tional to length and flow rate and that pressure drops of culated from pressure drop readings. In Table 6 it is again segments are additive. No assumption has been made as apparent that there is reasonable agreement between the to the nature of the flow through the. vents or porous measured and calculated dilutions although the calculated paper. As has been pointed out by Selke and eo-workers values are generally slightly higher than the measured (9, 17), this can be a combination of capillary flow where values. This discrepancy is thought to arise from the small flow rate is directly proportional to pressure drop, and internal pressure drop of the automatic dilution measuring orifice flow where flow rate is a function of the square apparatus used in this series of tests. This small pressure root of pressure drop. If we assume that only capillary drop would serve to slightly reduce the diluting flow flow occurs in porous tipping and cigarette paper, it is thereby giving lower dilution values. The brands measured possible to analytically derive pressure drop and dilution covered a wide range of filter dilutions and had a variety equations as was shown by Meyer-Abich (6). It is also of ventilation systems, whidl further supports the prop- theoretically possible to treat cases where orifice flow is the only flow regime present or where combinations of the Table 6. Measured and calculated dllutll)ns. two exist, but the solutions of the differential equations are very complex and difficult to handle except by Filter dilution Column Total numerical tedlniques. Type of dilution dilution In the case of capillary or viscous flow only, combination me as- cal- Brand filter dilution (calc.) (calc.) ured culated of the differential equations describing flow through the (%) (%) (%) (%) porous wrapper and pressure drop along the column results in a second order differential equation describing pressure Single row of A 13 18 5 23 drop as a function of length. Solution of this results in the vents first two equations given in Figure 6. The first equation is Single row of essentially that described by Fordyce, Hughes and Ivinson 8 vents (plastic 16 17 9 26 and others (3, 6, 17), and the second gives the fractional sleeve) dilution. The third equation is obtained from the first by using the first two terms of the series expansion of the Single row of c vents 30 31 9 40 hyperbolic tangent and substitution of terms containing the encapsulated pressure drop for the impedance co Four rows of D 68 70 5 75 efficient. The last equation provides the bracketed term in vents the third equation in terms of measurable pressure drops Five rows of and lengths. With these equations it is thus possible to E 46 51 59 vents 8 measure the paper porosity of a finished cigarette and the amount of dilution occurring in the tobacco column. If a F Porous tipping 49 53 8 61 porous plug wrap is also used, additional terms can be

11 Figure 8. Porous wrapper equations (non-porous plug wrap).

PRESSURE DROP: DILUTION: ot K· a .!la .!l p, + a . y c tanh (et Lo) + A . Le 2.0 1 - sech(ot · L0 ) • where: But by expanding the hyperbolic tangent in series, the unencapsulated cigarette and the filter it is found that: 2 pressure drops (mm H 0), 3a • (llPe - .!lp0 ) ·;(L0 + Le) 2 3. y a volumetric flow rate (cm 3 Is), and KyC · 1/ 1 ot = combined constant '= r--A- (cm- ) , 1/3 (llPe - llpo) · (Lo + Le)

K Impedance coefficient, tobacco column r (.!lp 8 - .!lp,) · L0 '

(mm H2 0 · s · cm-•) , where: y porosity coefficient. ( cm } , smm. H20 encapsulated pressure drop. C circumference (cm), by equation three. Considering the small differences be A column area (cm•), tween the encapsulated and unencapsulated pressure

L0 open column length (cm), drops, the agreement between the calculated and directly measured values seems adequate. For these two brands Le overwrapped column length less filter and for brands A-F, Table 8 compares tobacco column length (cm). dilutions calculated by the previous generalized pressure drop equations with those obtained from the equations added to the equations or they can be used as is with com of Figure 6. These calculations were performed using posite impedance and porosity coefficients. However it is pressure drops obtained with encapsulated filters, i.e. with generally simpler to consider the filter and the tobacco filter dilution excluded to heighten the comparison be column separately in such cases with due consideration of tween the two models. If filter dilution had been included, the interactions between the components. For the tobacco column dilutions similar to those given in Table 6 would

column dilution alone .!lp0 is used in place of dp0 in all have been obtained. In Table 8 it is readily apparent that the equations. To measure the filter dilution component, the dilutions predicted by the capillary flow model are

dp0 minus dpr replaced dpr in equation 1. In the third less than those given by the pressure drop equations which

and fourth equations, dp0 replaces dp6 in the numerator, do not specify the flow regime through the paper. The

and dpr replaces dp6 - dpr in the denominator. capillary flow dilutions are about 68-72'/o of the other To test the validity of these equations and the assumption values for brands A through G, and decrease to 60°/o for that capillary flow is predominant, the appropriate press brand H which is wrapped in a perforated paper. This ure drop measurements were made on two commercial trend is in line with the concept tha~ part of the flow cigarettes, one with a normal porosity paper wrapper, and through cigarette paper is like that through an orifice, one equipped with a perforated high porosity wrapper. which would give more flow and hence more dilution at Both had non-porous tipping paper, and two different any given pressure drop. Thus the capillary flow model is lengths of the normal porosity brand were measured. For not adequate to describe the dilution occurring in ciga both cigarettes the paper porosity was measured indepen rettes, and hence dilutions calculated from. measured dently by measuring the pressure drop across a 6.45 cm2 paper porosities via this route will be somewhat low. On area at a flow of 200 cm3/min. Table 7 compares the the other hand, dilutions calculated directly from pressure results of these measurements with the values calculated drops appear to be close to the actual values.

Table 7. Comparison of paper porosltles.

Cigarette Pressure drop (mm H2 0) Calculated Measured Calculated Brand length porosity porosity Observed (mm) encapsulated Iunencapsulated (mm .!lp) (mm .!lp) (%)

G normal 80 138 134 0.0047 0.0049 96 G normal 85 135 131 0.0052 0.0040 130 H perforated 84 119 112 0.0151 0.0157 97 H perforated 84 109 103 0.0200 0.0158 127 average 113

12 Table 8. Comparison of dilution models (tobacco column ing smoking by means of pressure drop measurements is dlluttons without filter dilution). outlined and results for a typical vented filter cigarette are shown and discussed. The use of pressure drop measure Percent dilution Open ments for estimating paper porosity and amount of di Brand column Capillary Pressure lution in the tobacco column on finished cigarettes is out length flow drop lined. The dilution obtained by this method was generally model model higher compared to the results found by a model based on A vented 53 4.3 6.0 a capillary flow regime, which suggests that flow through ordinary cigarette paper is a combination of capillary B vented 53 7.4 10.6 and orifice flow. The non-destructive nature and sim c vented 54 9.1 13.4 plicity of pressure drop measurements make this method D vented 52 10.7 15.7 of measuring dilution useful in quality control of cigarette E vented 55 10.6 15.5 production. F porous tipping 53 10.9 16.0 G non-vented 55 9.0 12.5 G non-vented 60 9.9 14.5 ZUSAMMENFASSUNG H non-vented 52 18.6 31.1 H non-vented 53 20.4 34.2 Es werden Gleichungen abgeleitet, mit denen die Ver diinnung in ventilierten Cigarettenfiltern und Tabak strangen aus ZugwiderstandsmeBwerten berechnet werden To summarize, it is found that: kann. Die errechneten Werte fur die Verdiinnung des 1. Dilution levels can be adequately determined by com Rauchstromes erwiesen sich als gut iibereinstimmend mit binations of encapsulated and unencapsulated pressure W erten, die durch direkte Messung an verschiedenen fiir drop measurements. Versuchszwecke und fiir den Markt gefertigten Cigaretten mit unterschiedlichem Cigarettenpapier sowie porosem 2. Since pressure drop measurements are simple and non und perforiertem Belagpapier (Mundstiicksbelag) erhalten destructive, they can be used to measure dilution levels in wurden. routine or semi-routine quality control. Der EinfluB der Anordnung der Perforationslocher auf die 3. The deliveries of major smoke components can be V erdiinnung und den Zugwiderstand d~r .Cigarette wird adequately predicted by considering dilution levels, bestimmt. Die Auswirkungen der Filterventilation auf die changes in filtration efficiency, and changes in burning Ausbeute an Partikelphase, Kondensat und Kohlenmon rate, and other factors such as diffusion. oxid werden diskutiert. Es wird ein V erfahren zur Mes 4. When vented filters are employed, the degree of dilu sung der Filterventilation wahrend des Rauchvorganges tion increases above that measured on the unlit cigarette, ii):>er die Zugwiderstandsmessung beschrieben, und die mit but is essentially constant throughout the smoking pro dieser Methode bei einer reprasentativcn ventilierten Fil cess until the last puff or two when it increases further. tercigarette erzielten Ergebnisse werden dargelegt und dis kutiert. Es wird gezeigt, wie die Messung des Zugwider 5. Vented filters can generally provide higher levels of standes zur Bestimmung der Papierporositat und des dilution ·than porous and/or perforated papers, but the Ventilationsgrades im Tabakstrang an fertigen Cigaretten level of dilution is quite dependent not only on the hole verwendet werden kann. Die mit diesem Verfahren er area but on the location of the vents. haltenen W erte fiir die V erdiinnung liegen fm allgemeinen 6. Although dilution is an effective means of reduction of iiber den Ergebnissen, die mit Hilfe eines auf Kapillar smoke component deliveries, it is most effective when stromung basierenden Modells erzielt werden; es ist daher combined with filters of reasonable pressure drop and re anzunehmen, daB die Stromung durch gewohnliches Ciga moval efficiency. rettenpapier aus einem linearen Anteil (capillary flow) und einem nichtlinearen Anteil (orifice flow) besteht. Da die Messung des Zug~iderstandes einfach ist und die Ciga SUMMARY rette unversehrt laBt, eignet sich diese Methode bei der Cigarettenherstellung im Rahmen der Qualitatskontrolle Equations for calculating dilutions in vented cigarette gut fur die Messung des Ventilationsgrades. filters and tobacco columns from pressure drop measure ments are derived. These calculated dilutions are found to agree closely with those directly measured for a variety of R~SUM~ commercial and experimental cigarettes wrapped with perforated and porous tipping and with different cigarette Des equations sont presentees qui permettent de calculer papers. des dilutions par des filtres ventiles et des boudins de The effect of hole placement on dilution and cigarette tabac a partir de mesures de la resistance au tirage. Ces pressure is estimated. The effects of filter dilution on par dilutions calculees correspondent de tres pres a celles ticulate matter, condensate and carbon monoxide delivery mesurees directement sur une variete de cigarettes com are discussed. A method for measuring filter dilution dur- merciales et experimentales enveloppees de papier de bout

13 perforti: et poreux et de diffti:rents papiers a cigarette. presented at 21st Tobacco Chemists' Resear

For appendix see facing page.

14 Appendix

DERIVATION OF DILUTION EQUATIONS

1. Assumptions: Pressure drop is proportional to flow rate and length, I. e. according to Darcy's Law for viscous flow. Pressure drops are additive.

2. For a single row of vent holes

AQ + o---~~-ffi-1--~-®-2~~~~~~~:~=-a---_A_a______® ______~

+-L,--+ +-Lc-+~------L 0 ------+ +----L,----•+------Lt------+

where:

K,· L1 ·Q APo cigarette pressure drop - unencapsulated K, · (L, -L ) · (Q- AQ) 1 Ap1 pressure drop In region 1 Kt · L, · (Q - A Q) Ap. pressure drop in region 2 Therefore: APs pressure drop In region 3 A Po = K, · L, · Q - K, · (L, -L1) · A Q + K, filter Impedance + Kt· Lt · Q - Kt· lt · AQ Kt tobacco column impedance L1 L, lengths as indicated K, · L, · Q + Kt · Lt · Q Lt }= K, · L, · Q Q exit flow rate so: AQ diluting flow rate L1 AQ AQ Ap,·-·-- + Ap - Ap ·-- cigarette pressure drop - filter encapsulated L, Q C, c Q APe Ap, filter pressure drop - encapsulated Rearranging to give equation 1: AQ Q

3. For n rows of holes spaced AL mm apart with flow dQ in each row

Ap1 K,·L1 ·Q Ap. K, · A L · (Q - dQ) APs K, · AL · (Q - 2dQ) APn K, · AL · (Q - (n - 1) · dQ) APn+1 K, · (L, - L, - (n - 1) • AL) · (Q - n dQ) APn+• Kt · Lt · (Q - n · dQ)

but:

n·dQ AQ

Therefore: n-1

Ap0 = ~K, · AL • (Q - I dQ) + K, · L, · Q - K, · (n - 1) • AL · Q - K, · L, · AQ + 1-1

15 Substituting for K, and Kt as before and evaluating the sum of the series, we get: (n - 1) .1L .1Q L1 .1Q .1Q .1 Po .1 p, • • · .1 p, .1 Pc • llpo = 2 ~ a + ·~·a - a +

which yields equation 2: .1Q Q L (n - 1) .1 L llpc --1 • .1p, - . -- . .1p, L, 2 L,

4. As .1 L becomes smaller and n becomes larger, we approach a porous plug wrap situation. If this extends the length of the filter, (n - 1) • .1L equals L, -L1 where L1 Is now the length enclosed In a holder. Substituting in equation 2 gives: .1Q Q

or equation 3: .1Q Q

5. The same concept applies to a tobacco column with an unencapsulated length of L0 and an overwrapped or encapsulated

length of L 0 • The fully encapsulated pressure drop is .1p8 , while the open pressure drop is .1p0 • The exit flow rate Q is now the flow leaving the tobacco column and entering the filter.

Again summing pressure drops, we get: n K, • L, • Q + Kt • Le • Q + ~ Kt • .1 L · (Q - i dQ) K,·L,·Q K, • L, · Q + Kt • Le • Q + Kt • Lo · Q

Introducing the sum of the series and considering that when n is very large n · .1L ;;;; (n + 1) • .1L L0 and that n · dQ = .1Q: .1 Pc = K, • L, · Q + Kt • Le · Q + Kt • Lo · Q

Since the first three terms on the right side equal .1p8 , we get:

llp. - .1p, (Lo + Le) • Q so: Lo • (llPe - llp,) .1Q

2 (L 0 + Le) Q

Rearranging gives equation 4: .1Q 2 (.1p. - llpc) • (Lo + Le) -- = Q (.1Pe - .1p,) • Lo

If the cigarette is unfiltered .1 Po is substituted for .1 Pc and .1 p, = 0.

6. If filter dilution Is also present, the flow exiting the tobacco column will be less than the mouth end exit flow. If Q' equals the tobacco column exit flow and Q the mouth end exit flow, then Q' = (1 - D,) · Q where o, is the fractional filter dilution. Substituting Q' for Q in equation 4 and rearranging gives equation 5:

.1Q 2 (.1p8 - .1p0 ) • (1 - D,) • (L0 + Le)

Q (.1p8 - llp,) • Lo

7. Equation 6 is merely an expression of the additivlty of dilutions for various parts of the cigarette, provided-that the dilution of the tobacco column is calculated l!sing equation 5 rather than 4.