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BRITISH - AMERICAN TOBACCO COMPANY LIMNED iii mmmm, T~ c ~llntad m~l ~ N Immlrty of Bmish-Ame6can Tobacco C.,omM~ limited .lind must not be co~d or shown to unm.qhmised persons.~ F,,~kT Co LTD - MINNESOTA TOBACCO LITIGATION

DZnuszqN ~ Z~Z,I).~C~. ~.~SU~)CCtS ON L~Ir.~ANDED TOB&C~:~ AND FZI.T~I~. RODS ~t~ No. RD.1830 • ... " 17.9.zgm / / ~HO~:..R.R. B&kec GROUP LEADER: R.~. B&lmc °. /* / ./ / ° ISSUED BT: C.X. AyTes /' / / PROG. ~. : 105.02 nx STlq3:]IUT ION: I~. L.C.F. Jl~ciman Dr. LA. Sau~ord R.M. Gibb, bq. R.S. Wade, ESq. R.¢. N£cholls, Esq. Rear E. R£ct,rshau8 l~r. F. hehofez: l~r. C.J.P. de S£qum£rx Vat, W. Van Puccen H. Tudor, hq. Dr. D.G. FalCon IA brary Copy No. 1, 2 " " 3, 4 n w 5 " " 6, 7, 8 " " 9, 10 " " 1 l " " 12 tt t, 13 " " 14 " " 15 " " 16 " " 17, 18 coeT ~.: "2. ¢.rl ¢d'l -...j I~,:~,T Co LTD - MINNESOTA TOBACCO LITIGATION

~ICALII14 Group Research & Developme, t Centre, BrlClsh-Amerlcan Tobacco Co..Ltd., SOUTKN-IPTON. - 17th ~ptember 1981. DIFFUSION AND INPEDAI4CE /.IEASUREHEI~TS OR EXPANDED TOBACCO A[~D FILTER RODS (Report No. RD.1830) 3UHH~/IY The amount of carbon monoxlde dellvered by a cigarette is eon~idcrably less than the amount generated in the combustion coal. Thls is because ,tlch of the carbon monoxide diffuses out: of the tobacco rod as the stroke t: drawn along the length of the cigarette durtng the puff. E~rl£er ~.:oL'k ~: concentrated on diffusion through the clgarette paper, nlthou,~h iltfuslon through the tobacco bed (and filter bed in unconvcn~lonal -~garettas) Is equally impore~ant. This report covers a deCall<.d study of :h~ diffusion of carbon monoxide through tobacco, expanded tobacco and ~]ter beds. It provides important informatlon on the effect of basic )rcpertlas of the tobacco and fllter partlcles on both the diffusion and ~m,T~dances of the beds. This information is essential for a full ~,,(~erstandir~ of carbon ~onoxtde delive~tes and for the on-goin~ development ,~ mathcmatical models of a burnlng cigarette. One potnt of toplcal lnterest Is the observed 15 to ]0~ hlgher :oncentr~tlon of carbon monoxide In aalnstream smoke from cigarettes :ontain£n8 expanded tobacco. The present study shows that this is not ~ a~T Co LTD - MINNESOTA TOBACCO LITIGATION

-2- diffusion effect. ~e major reason must be due to hisher quantities o£ ,arbon monoxide formed in the combustion coal of cigarettes eonta£nin8 ,~xpanded tobacco, and prelimlnary work has confirmed this. ~ ~.T Co LTD - MINNESOTA TOBACCO LITIGATION m Lrl

-3- SCIENTIFIC ABSTRACT Measuremonts have been made of the Impedances to air flow duo to viscous and inertial forces, and the diffusion coefficient of carbon monox£de £n nitrogen, throush various expanded tobacco and filter rods. Both "impedances Ancrease as the bulk packing density of the sample ~ncreases, and as the proportion of either O-13 or DIET expanded tobacco '~.n the s~u~ple increases. At a standard air flow of 17.5 cm3 s-i, Inerclal ~orees contribute 16-23Z to the pressure difference alonE an unexpanded tobacco rod, 27-28Z for a G-13 or DIET expanded tobacco rod, and O.4-BZ ~or a f£1cer rod. The ~pedancc ~slues of Haunl expanded tobacco rods ~re much closer to the values of the unexpanded tobacco, reflectlnp the small effect that tim Hauni process ham on leaf expansion. l~umerically analysin~ the impedance values with equacicnc derive¢i ~=rom the Kozeny-Carmonr-ErEun treatment of porous soltds has enabled .:.~lu~s ,:,f the apparent avareBe density of the tobacco particles and the $urfacc area of the particles, to be obtalned. The values obta£ned, and how ch~_y vary as the proportion of expanded tobacco in the blend varies, are Ingles1 and broadly In lint with trend,.; from other flow sCudi~s. The tnta|l dlffus£on coefficient of carbon monoxlde/nltrogen through all the tobacco rods increases llnearly as the mean Sos flow race chrou:h ~he tobacco rod increases. This £s caused by a contribution of convective dlsperslon to the total diffusion, due to the bulk flow of the gas, as ,,bserved in other studies on porous beds of sand parClcles. The molccu]a:" diffusion and transverse convective dispersion components of the total ~£ffusion coefficSent have been calculated. The calculation was approximate because of affects of ~he porous paper wrapped round the rod. t~ ~T Co LTD - MINNESOTA TOBACCO LITIGATION "-,,4 eND """,-4

-4- The molecular diffusive component is related to the porosity (voLd feactlon) and tortuoslty of the porous maeerlal. The calculsted tortuosley factors are £n the range l.l to 1.3 for tobacco beds, and 1.6 to 1.9 for filter beds. These tortuosftles are entlrely reallst£c, and are effectively independent of the proportion of expanded tobacco In the blend, or the ~ik packing density of the tobacco. The var£ation Of the convective dLspersion component of total diffusion with total particle diameter and o=her tobacco bed parameters ts qualitatively (but not quantitatively) ~,~mLlar to that predicted by equations derived from studies on sand beds. ~ future work, convective dispersion must be included more directly Lnto the mathematical models of gaseous diffusion inside cigarettes. At a given flbv through the tobacco bed, there Ls no systematic effect of the proportion of expanded tobacco in the blend, or the porosity ~void fraction) of the tobacco bed, on the total d£ffusLon coefficient through the bed. The nLax~ effect of the total dlffuslon coefficient would glve s carbon monoxide concentration at the drewlnG end of s typical ctaarette containing expanded tobacco only 5X htaher than the equivalent c~garette containing unexpanded tobacco, when • carbon monoxide m~xture 1~ drawn through the cLgarette at a standard flow of 17.5 cz3 s-1. Thus t he observed 13 to 30Z higher concentration of carbon monoxide in mainstream smoke from cigarettes containing expanded tobacco cannot be a diffusion effect, gather, it must be • mechar~at4c e££ect of formation in the combustion coal. Preliminary work has confirmed this. ~ ~T Co LTD - MINNESOTA TOBACCO LITIGATION ¢..rl

KEY l~O~l)S Carbon monox£de Convecctve dispers:lLon Di£fus£on Disp@r|ion Zxpandsd tobacco Filters Inertial Imp@dance Impedance Kozeny-Carman Part£cle density Porosity Surface Area Vimcou8 impedance Vo£d frmcC£on !] a,T Co LTD - MINNESOTA TOBACCO LITIGATION rxo

-5- r NTRODUCTI 0 [~ In previous studies (1-[1) the effects of dilution and diffusion processes on carbon monoxide concentration as gases are drawn through a :Igsrette have been considered in some detail. It was showu tlmt light gases suc~ as carbon monoxide diffuse out of the cisarette £n three stages: radial diffusion throup, h tho tobacco bed, diffusion through the oaper, and di£fuslon away from the outer surface of the paper into the ~tmosphere. It Is the first two of these processes that have the major ~.ffect on carbon monoxide concentration. The diffusion coefficient of -arbon monoxlde in nitrogen through cigarette paper can nov be measured ,)n a rout£ne basts (12, 13), and the values through a range of commercial ~:£garette papers were reported in 1976 and 1980 (14, 15). It is known that the carbon monoxide concentration in mainstream ~moke from cigarettes conta£n~n5 expanded tobacco is 15 to 30Z higher :ban that frc~ the equivalent non-expanded tobacco cigarette (16-L8). ?his could be due to a higher concentration of carbon monoxide formed in c:he combustion coal, or to a lower carbon monoxlde dlffusion coefficient ¢.hroush the expanded tobacco bed. The obJectives of the present study were" Ca) To decet mlne the diffusion coefEicient of carbon monoxide in nitrogen through tobacco and filter rods. (b) To determine the effect of tobacco expansion on the diffusion coefficients • (c) To relate the diffusion coefficients and impedances of the rods to basic properties of the particles nmkln8 up the porous bed of t1~ rods. LJ~ B,:kT Co LTD - MINNESOTA TOBACCO LITIGATION

-6- The results from (a) and (b) should help to clarify the cause Qf the ~igh carbon monoxide concentrations from expanded tobacco cigarettes, as ~ell as providing a useful survey of diffusion coefficient values through different types of packed beds which will complement those through cigarette ~apers. The empirically determined diffusion coefficLents and impedances are essential parameters in the mathematical models of diffusion (3-6). In previous studies (19-22) pressure/flow impedance measurements on :obacco rods hove been related to the density and surface area of the t~bacco strands Jn the rod. In objective (c) the relationships will be e~tcnded to the d£ffunion coefficients. I. DETER~]INATION OF DIFFUSION PARAt~TERS AND ZHPEDANCES OF TOBACCO AND FIL'IER KUDS In Appendix I it is shown that when there is gross flow of a gas ~Ix~ure through a porous medium, individual components in the gas mix by both diffusion and convective dispersion. The total dlffuslon coef£iclent iue to both diffusion and convective dispersion) of carbon monoxide/ nitrogen through the tobacco or filter rod in a radial direction is ~_termlned as described in Appendix If, at a series of steady flows out oE th= rod in the range 3.5 to 34 cm3 s-t. The relationship between pressure difference (P, cm water) across a p~rous medium and gas flow through the modlum (Q, em3 s-t) is non-linear, and this non-llnearity is explicable in terms of the occurrence of both viscous and inertial forces In the flow*. Thus, tJ~ impedances of the *Hie oecurrt.nce of sllp flow of the gas would also give a non-llnear relationship b~tween P and Q. ~lls occurs when the mean free path of the ~ns molecules is a significant fraction of the pore diameters, the gas ~elocity is not zero at the pore walls and the gas molecules "sllp" ~t th(; wmlts, llot:-ver, for tobacco al~d filter rods, the men,~ pore linmeter~/~- mean free path (see Appendix I, Section 2), so that Sllp ~lo~: %'IIi ,at occur. t.+AT Co LTD - MINNE.+qDTA TOBACCO LITIGATION

--I-- rod due to viscous forces (¢, cm water s c~-2)* and inertial forces (c', cm water s2 cm-3) are calculated from a regression** of the pressure difference (~', cm water) across the encapsulated rod a~alnst the flow rate of air through the rod (Q, c-~3 s-l) : ^ ...(1) ~here L is the length of the rod (cm) s~d A is the total area of cross section (cm2). For each rod of a given ~Ight, the quoted values of t and ¢' are based on five replicates, each repllcate consisting of fifteen flay and pcessure measurements in the range t to 42 cm3 s-I. Z. EqUATIOtIS RFI.%TING IF~EOA~CES A~D TOTAL DZFFUSZON COEFFICIENT TO BASIC PARA],~T'ERS OF PO:~OUS HEDIUH 2.1 Viscous and lnortlal Impedances For a non-consolldated porous medium such as a tobacco or filter rod CL.e. a granular bed of particles), elm viscous impedance c is given by the Kozeny-Carman equaClon (23, 24): ¢ = k n 02 02 (I-E)2 S 981 E3 wilere k ,nd ...(2) is an empirical constant (dimensionless), equaZ to (tortuosity factor)2. shape factor, q is gas viscosity (poise, i.e. K cm-I s-l), e is surface area of particles per g (cm2 g-l), OS is the apparent average density of the solid particles (g cm-3), including any internal holes not accessible to the flowing gas, E is the porosity of the medium (dimonsionless), i.e. the vold volume/total volume. *1 cm ~raCor = 98 I~ =-2 *'111e minimlsatton of a sum of squares of a non-linear function prograJ. was used for Lhe regres~ion, whtr.h tncorpornto.d Davtdeon'~ cubic line search to utnlm~ r.i~e /unction along the direct/on found by the Gauss-Newton method. B ~T Co LTD - MINNESOTA TOBACCO LITIGATION