Chaptr-5 Eltron Transport Proprtis for Argon and Argon-Hydrogn Plasmas Argon and argon-hydrogn plasmas hav important appliations in many thrmal plasma dvis (Patyron t al., 1992; Murphy, 2000; Crssault and Glizs, 2004; Colombo t al., 2008, 2009). Ths ar mainly usd in plasma spraying spially whn good hat transfr is rquird. Thr has bn a ontinud intrst in studying th rol of ltroni xitation in affting th thrmodynami and transport proprtis of loal thrmodynami quilibrium (LTE) thrmal plasmas (Singh and Singh, 2006; Singh t al., 2008, 2009a and 2009b; D Palma t al.,2006; Sourd t al.,2007a, 2007b; Bruno t al., 2007a, 2007b; Capitlli t al., 2003, 2004, 2008, 2009; Kustova and Puzyrva, 2009). Rsarhrs in th past ignord th importan of ltronially xitd stats (EES) on th thrmodynami proprtis suh as spifi hat at onstant prssur, du to som sort of ompnsation btwn ontributions from thir diffrnt trms. Th rol of EES on th thrmodynami and transport proprtis for hydrogn, nitrogn and oxygn thrmal plasmas has bn studid by many authors and thir rsults indiat that EES at high prssurs do afft ths proprtis. As th total nrgy ontnt in a gas or gas mixtur dpnd upon nrgy of various partils and hmial rations btwn thm whih is nown rsptivly as frozn and rativ nrgy. Th orrsponding spifi hats ar afftd by taing into aount th EES of th plasma spis. Th fft of EES on thrmodynami proprtis of argon plasma was studid many yars ago (Capitlli and Molinary, 1970) in whih th influn of hoi of nrgy lvls on th spifi hat was xamind at p=1 atm. Rntly th influn of EES on th spifi hat of hydrogn thrmal plasmas has bn widly studid (D Palma t al., 2006; Capitlli t al., 2008; Capitlli and Giordano, 2009). As disussd in Chaptr-2, in as of hydrogn plasmas, EES inras th frozn part and dras th rativ part in suh a way that th total spifi hat rmains unhangd at low prssur but not at high prssurs indiating th rol of ltroni xitation. In this haptr, an attmpt has bn mad to r-xamin th fft of EES on th spifi hat at onstant prssur for argon and argon-hydrogn plasmas in th 89
tmpratur rang 10000-40000 K at diffrnt prssurs. Th fft of EES on th transport proprtis has bn disussd in dtail for hydrogn (Bruno t al., 2007; Capitlli t al., 2004) and nitrogn plasmas (Kustova and Puzyrva, 2009; Sourd t al., 2007a, 2007b). Th thrmodynami and transport proprtis at atmosphri prssur for argon, nitrogn, oxygn and argon-hydrogn, nitrogn-hydrogn plasma mixturs hav bn studid at diffrnt tmpraturs (Colombo t al., 2008, 2009) without taing into aount EES. In th prvious haptr, ltrial ondutivity and ltron thrmal ondutivity for hydrogn plasma wr valuatd and th rol of EES omposition was dtrmind whih showd a signifiant dviation of ths proprtis with and without EES. In ordr to stimat th fft of EES omposition on argon and argon-hydrogn plasma mixtur, ltron transport proprtis for th plasmas hav bn valuatd at diffrnt prssurs and tmpraturs in this haptr. For both argon and argon-hydrogn plasmas, th spis ar onsidrd:, Ar, Ar +, Ar 2+,Ar 3+, H, H + For stimating th fft of EES on th thrmodynami and transport proprtis of argon and argon-hydrogn plasmas, two ass hav bn onsidrd: (i) GS plasma, in whih all th spis ar tan in th ground stat and (ii) ES plasma, in whih argon and its various spis as wll as hydrogn atoms ar tan in various possibl xitd stats dpnding upon prssur (Capitlli t al., 2004; Capitlli and Molinari, 1970 and Drllisha t al., 1963). Th partition funtion of argon atom and its ionizd spis at low and high prssurs ar displayd in Stion 5.1, whras for hydrogn atom, it has alrady bn dsribd in Chaptr-2. Stion 5.2 prsnts th mthod of alulation of quilibrium omposition and variation of onntrations for argon and 50% argon-50% hydrogn at p=1& 100 atm by inluding th fft of ltroni xitation for argon and argon-hydrogn plasma. Th gnral xprssions of frozn, rativ and th total spifi hat for th plasma mixtur ar prsntd in prsntd in Stion 5.3. Th variation of / / int pf, int p and p (GS ) and p (ES ) with tmpratur and prssur has bn displayd in Stion 5.4& 5.5. Th ltron transport proprtis, sour data for ollision intgrals and th influn 90
of EES omposition on ltrial ondutivity and ltron thrmal ondutivity is prsntd in Stion 5.6. Rsults and disussion along with th omparison with hydrogn plasma ar prsntd in Stion 5.7. Finally onluding rmars and futur sop of th wor has bn prsntd in Stion 5.8. 5.1 Partition funtion and utoff ritria For hydrogn w hav tan th wll-nown nrgy lvls and statistial wights as 1 1 n EH IH 2 and 2 g n 2n Th partition funtion and thir drivativs for th atoms and th ionizd spis of argon an b alulatd. For whih all lvls of Moor s tabl (Moor, 1949) as wll as thos from Aatsua (2009) ar usd. Th problm of divrgn of th partition funtion is ovrom by trunating it suh that, for hydrogn th radius of th Bohr s orbit dos not xd th intrpartil distan (alrady disussd in Chaptr-2) and for argon, th siz of th Bohr s orbit is mad qual to th Dby lngth (Capitlli and Molinary, 1970); Drllishat al (1963)) suh that th maximum quantum numbr usd in th alulation of partition funtion is givn as ni and 1/ 4 2 3 36.11 10 ff n, whr 2 ff nz i i i Z T Z is th fftiv harg of atom, Zi ar rsptivly th numbr dnsity and harg of ith hargd partil. Hr in th alulation of th Dby lngth, shilding fft of both ltrons and ionizd hargs has bn tan. Th lowring of ionization potntial has also bn tan into aount. Th variation of ltroni partition funtion of hydrogn has alrady bn disussd in Chaptr-2. For argon atoms and its ionizd spis, its variation with tmpratut has bn displayd in Figur 5.1 for p=1& 100 atm rsptivly. Ths figurs indiat that with inras in prssur, th partition funtion of atomi argon drass baus of lssr numbr of xitd stats. 91
1000 100 Ar Q 10 Ar ++ Ar + Ar +++ (a) 1 10000 20000 30000 40000 Tmpratur (K) 100 Q 10 Ar 2+ Ar 3+ Ar + Ar (b) 1 10000 20000 30000 40000 Tmpratur (K) Figur 5.1. Variation of ltroni partition funtion Q with tmpratur for diffrnt spis of argon at (a) p=1 atm and (b) p=100 atm. 92
5.2 Equilibrium Composition using Saha quation of ionization In this stion, th quilibrium omposition is alulatd by assuming all th plasma spis to b in th ground stat in th tmpratur rang 10000-40000 K and at p=1, 10 & 100 atm whih is rfrrd to as ground stat (GS) plasma. Th quilibrium omposition of th xitd stat (ES) plasma in whih th diffrnt spis ar distributd ovr th various possibl EES to b dtrmind by th utoff ritria. As is wll nown that at a givn tmpratur and prssur, th thrmodynami and transport proprtis of a givn plasma mixturs ar funtions of th dgr of ionization (and hn omposition) whih is usually obtaind by using Saha quation whr X j1, X j n 2mT 2 h 3 / 2 Q 2 Q j1, j Ij T (5.1) nj X j and I j ar th dgr of ionization and ionization potntial of jth n ionizd stat of th lmnt with n j as th numbr dnsity of atoms in th th ionizd stat. Q j and Q j 1, ar th partition funtions for th onsutiv stat of ionization j andj 1, whih furthr dpnd upon tmpratur and prssur. Th population of diffrnt stats of ionization for various lmnts omprising th plasma mixtur is alulatd by th abov quation. Th approah (Cardona (2009); Rous (1961, 1962)) involvs itration on ltron onntration for a givn rlativ abundan of various lmnts. In ordr to s th fft of EES on th omposition of argon and argon-hydrogn mixtur, quilibrium omposition of Ar plasma as wll as th Argon-Hydrogn plasma is valuatd at diffrnt tmpraturs and for wid rang of prssurs. Lowring of th ionization potntial has also bn tan into aount. 5.2.1 Composition for ground stat and xitd stat argon plasmas In ordr to assss th fft of EES, quilibrium omposition of argon plasma as wll as th argon-hydrogn plasma is valuatd at diffrnt prssurs ovr a wid rang of tmpratur (10000-40000 K) for both GS and ES plasmas. Figur 5.2 prsnt th quilibrium omposition of argon at p=1& 100 atm by taing ground and xitd stat partition funtion. 93
1 0.8 Ar X i 0.6 0.4 Ar + + Ar 2+ 0.2 0 (a) 10000 20000 30000 Tmpratur (K) 40000 Ar X i Ar + Ar ++ (b) Tmpratur (K) Figur 5.2. Conntration X i for diffrnt spis of argon plasma vs. tmpratur at (a) p=1 atm and (b) p=100 atm. Th solid and dashd urvs rfr to GS and ES plasmas. 5.2.2 Composition of ground stat and xitd stat 50% argon-50% hydrogn plasma Th fft of EES on th omposition of argon-hydrogn mixtur has bn valuatd at diffrnt prssurs ovr a wid rang of tmpratur (10000-40000 K) for both GS and ES plasmas. 94
Figur 5.3 prsnts th variation of onntration of diffrnt spis for th 50% argon- 50% hydrogn plasma mixtur with tmpratur at p=1& 100 atm by taing ground and xitd stat partition funtion. 0.7 0.6 0.5 H X i 0.4 0.3 Ar H + 0.2 0.1 Ar + Ar 2+ Ar 3+ (a) 0 10000 15000 20000 25000 30000 35000 40000 Tmpratur (K) H X i Ar H + Ar + Ar ++ (b) Tmpratur (K) Figur 5.3. Conntration X i of diffrnt spis of 50% argon-50% hydrogn plasma vs. tmpratur at (a) p=1 atm and (b) p=100 atm. Th solid and dashd urvs rfr to GS and ES plasmas. 95
From th figurs, it is lar that ltronially xitd stats of diffrnt spis of argon and argon-hydrogn mixtur afft th onntration at low and appriably at high prssurs. This is du to th fat that EES of th plasma spis ar mor populatd baus ionization pross of diffrnt spis slows down with inras of prssur. 5.3 Exprssions for frozn, rativ and total spifi hat at onstant prssur As th dgr of ionization and hn onntration hang both with tmpratur and prssur, th xprssion of nthalpy and th spifi hat of plasma mixtur must inlud th fft of ltroni xitation. Th xprssion for spifi hat at onstant prssur p for a plasma mixtur is givn by Cardona t al., (2009). with Whr int pr p pf pf pr 5 (1X ) NN 2 j0 X j and de dt j N X dx 5 T X X 2 (1 ) dt N int P (5.2) (5.3), (5.4) T N N (5.5) pf and pr ar th frozn and rativ ontribution to th total spifi n hat. X is th total dgr of ionization of th gas with n and nn dnsitis of ltrons and nuli rsptivly. V. n N as numbr N N is th total numbr of nuli in volum n is th rlativ abundan of th lmnt. N N is rplad by R / 0 nn with 0 as th man molular wight of th unionizd mixtur i.. X 0 in th quation A with 1X m A is th atomi wight of th lmnt and mh 96
X j 1 Il X j j jx j, j1 j1 l0bt j 1 j 1 5 I I l, j1 j1 l0 2 BTl0BT l T X j 1 jx j S X jx j j jx j, j1 j1 j 1 5 I l S T Xj j jxj and j1 j1 l0 2 BT dx T dt P X (1X ) ST X (1X ) S X Whn th partition funtion dpnd upon tmpratur and prssur, instad of T and S T, / T and / S T rsptivly ar usd. Whr with Q / S / T j1 Qj, Q0 X jq j, Q0 T T T X j I P P l j 1 j 1 P l0 S T 1 j1 X dq j j j1 1 jx j dq TQ j, Q m l m, Ql P for any indx m andl. Qm dt P Ql dt P 0 P (5.6) (5.7) 5.4 Intrnal ontribution to th frozn and total spifi hat for argon and 50% argon-50% hydrogn plasmas Th sond trm of quation 5.3 dfind by quation 5.4 has bn inludd to gt th intrnal ontribution to th frozn spifi hat, whih dpnd on th produt of onntrations and singl and doubl drivativs of intrnal partition funtions of various lmnts of th plasma mixtur. This additional trm (Equation 5.4) aounts for th fft of ltronially xitd stats on th frozn spifi hat for a givn plasma mixtur. Similarly, quation (5.5) along with quations (5.6) & (5.7) inlud th ontribution of EES to th rativ spifi hat (Singh t al., 2010). Figur 5.4 shows th variation of ratios of intrnal ontribution to th frozn spifi hat ( int / pf ) and to th 97
total spifi hat ( / int p ) for argon plasma with tmpratur and prssur. Similar ratios for 50% argon-50% hydrogn plasma mixturs ar prsntd in Figur 5.5. int / pf 0.9 0.6 0.3 p=1atm p=10atm p=100atm (a) 0 10000 20000 30000 40000 Tmpratur (K) 0.6 p=10atm 0.4 int / p p=100atmm p=1atm 0.2 (b) 0 10000 20000 30000 40000 Tmpratur (K) Figur 5.4. Ratios of (a) intrnal int to th frozn spifi hat pf (b) intrnal int to th total spifi hat p vs. tmpratur for argon plasma at diffrnt prssurs. 98
0.8 p=10atm int / pf 0.6 0.4 p=100atmm m 0.2 p=1atm (a) 0 10000 20000 30000 40000 Tmpratur (K) int / p 0.3 0.2 p=10atm p=100atmm 0.1 p=1atm (b) 0 10000 20000 30000 40000 Tmpratur (K) Figur 5.5. Ratios of (a) intrnal to frozn spifi hats / int pf (b) intrnal to total spifi hats / int p vs. tmpratur for 50% argon- 50% hydrogn at diffrnt prssurs. 99
Ths figurs show that with inras of prssur, EES afft th intrnal ontribution to th frozn and th total spifi hat for both th plasmas. 5.5 Influn of EES on total spifi hat Th frozn and rativ ontribution to th total spifi hat in as of hydrogn plasmas is strongly afftd by inluding th ltroni xitation (Capitlli t al., 2007; D Palma t al., 2006) but ths bhav in opposit way suh that th total spifi hat by inluding and nglting th EES of plasma spis rmains unafftd at low prssurs but this sort of ompnsation fails at high prssurs. Th inlusion of ltronially xitd stats (EES) in rlvant partition funtion influns th intrnal ontribution to frozn and total spifi hat for argon and argon hydrogn plasmas and it has bn obsrvd that though th total spifi hat of argon plasma is lss than that of hydrogn plasma, yt its intrnal ontribution is mor. Compnsation btwn diffrnt ontributions to total spifi hat (by inluding and nglting EES) ourring in hydrogn plasmas at low prssurs has not bn obsrvd in argon and argon hydrogn plasmas. This ompnsation at low prssur is not obsrvd for argon and argonhydrogn mixturs and is strongly disturbd at high prssurs (Singh t al., 2010) (Figurs 5.6 & 5.7). Thrfor, ltroni xitation affts strongly ths proprtis spially at high prssurs. This fat an b undrstood mor larly from th plots of p p ( ES) (GS) vs. tmpratur for argon and 50% argon-50% hydrogn mixtur rsptivly in Figur 5.8. 100
(a) 12 9 p(j/g/k) p (J/g /K) Tmpratur (K) 6 3 (b) 0 10000 20000 30000 40000 Tmpratur (K) 10 8 p (J/g /K) 6 4 2 () 0 10000 20000 30000 40000 Tmpratur (K) 101
Figur 5.6. Total spifi hat p vs. tmpratur at (a) p=1 atm (b) p=10 atm () p=100 atm. Th solid and dashd urvs rprsnt th GS and ES argon plasmas. (a) 20 p (J/g /K) 15 10 5 (b) 0 10000 20000 30000 40000 Tmpratur (K) 15 12 p (J/g /K) 9 6 3 () 0 10000 20000 30000 40000 Tmpratur (K) 102
Figur 5.7. Total spifi hat p vs. tmpratur at (a) p=1 atm (b) p=10 atm and () p=100 atm. Th Solid and dashd urvs rprsnt th GS and ES 50% argon- 50% hydrogn plasmas rsptivly. b ( ES) p ( GS) p a (a) Tmpratur (K) b a ( ES) p ( GS) p a (b) Tmpratur (K) Figur 5.8. Ratios of th spifi hat with and without EES ( ES) p ( GS) p vs. tmpratur for (a) argon and (b) 50% argon-50% hydrogn plasmas. Th urvs a, b & rprsnt p=1, 10 & 100 atm rsptivly. 103
5.6 Eltron transport proprtis Th ollision intgrals rquird for valuating th ltron transport proprtis hav bn obtaind and th data sour has bn displayd in Stion 5.6.1. Using th xprssions for ltron transport proprtis usd in th Chaptr-4, a omputr program has bn dvlopd, suh that ltrial ondutivity and ltron thrmal ondutivity for both argon and 50% argon-50% hydrogn plasmas hav bn valuatd in th tmpratur rang 10000 K-40000 K and ovr wid rang of prssurs. Th influn of EES omposition on ths proprtis for th plasmas has bn obtaind by rplaing th xitd stat ross stions qual to that of ground ons in Stion 5.6.2. 5.6.1 Sour data for ollision intgrals Th Collision intgrals data for th intrations of th typ -H, -Ar and harg-harg intrations rquird for both th GS and ES argon and argon-hydrogn plasmas ar givn in Tabl 5.1. Tabl 5.1. Sour data for ollision intgrals Typ of intration Rfrns -H Gors and Capitlli (2001) -Ar Hayashi (2003) hargd spis Dvoto (1967a) In ordr to s th rol of ltroni xitation on th ltron transport proprtis of th argon and argon-hydrogn plasmas undr th onstraint of non availability of data of xitd stat ollision intgrals for argon atoms, ths as wll as thos of hydrogn atoms ross stions ar rplad by th ground stat ons. 5.6.2 Influn of EES omposition on th ltron transport proprtis of argon and 50% argon- 50% hydrogn plasmas Th xprssions usd to valuat th ltrial and ltron thrmal ondutivity ar alrady dsribd in Chaptr-4. Th ltron transport proprtis strongly dpnd upon th dgr of ionization of diffrnt spis, hn th quilibrium omposition of 104
thrmal plasma. To now th influn of omposition on ths proprtis for th argon and argon-hydrogn mixtur with and without EES, th following ass hav bn onsidrd. (i) GS plasma, whr th partition funtion as wll as ollision rosstions of all spis of argon and hydrogn ar tan as qual to that of ground stat and (ii) ES plasma, whr th EES hav bn inludd in th partition funtions. Th problm of divrgn of th partition funtions is ovrom by trunating thm suh that for argon, th siz of th Bohr s orbit is mad qual to th Dby lngth (Capitlli and Molinary 1970; Drllisha t al., 1963) and for hydrogn th radius of th Bohr s orbit dos not xd th intrpartil distan (Capitlli t al., 2003). Du to la of availabl data on xitd ollision intgrals for argon atoms, ths as wll as thos of hydrogn atoms ar rplad by th ground stat ons. Th numbr of xitd stats ar usd in th partition funtion and thn th fft of omposition of argon and hydrogn is valuatd on th ltron transport proprtis. Tabl 5.2 prsnts th firstordr ltron thrmal ondutivity and sond-ordr ontribution to ltron thrmal (1) ondutivity f at diffrnt prssur and tmpraturs for 50% argon- 50% hydrogn whras Tabl 5.3 prsnts first ordr ltrial ondutivity (1) and third-ordr ontribution to ltrial ondutivity f for th sam mixtur and at th sam tmpraturs and prssurs. For omparison of argon and argon-hydrogn plasmas with and without EES, th ratios ( ES) and ( GS) ( ES) ar valuatd at diffrnt prssurs ( GS) in th tmpratur rang10000-40000 K and ar displayd in Figur 5.9 for argon and in Figur 5.10 for 50% argon-50% hydrogn plasmas rsptivly. 105
Tabl 5.2. First-ordr ltron thrmal ondutivity ( 1) (Wm -1 K -1 ) and sond-ordr ontribution to ltron thrmal ondutivity argon-hydrogn plasma mixtur at diffrnt prssurs. f for th xitd stat (ES) quimolar Tmpratur (K) (1) p=1 atm p=10 atm p=100 atm f (1) f (1) f 10000 0.197 1.1163 0.124 1.0001 0.052 1.0341 12000 0.476 1.2859 0.437 1.0282 0.252 1.0286 14000 0.827 1.4054 0.985 1.0831 0.784 1.0267 16000 1.172 1.4842 1.684 1.1421 1.885 1.0354 18000 1.482 1.5408 2.358 1.2020 3.697 1.0462 20000 1.789 1.5853 2.938 1.2614 5.899 1.0310 22000 2.108 1.6211 3.460 1.3172 7.835 1.0037 24000 2.429 1.6523 3.983 1.3649 9.240 1.0048 26000 2.749 1.6834 4.549 1.4009 10.32 1.0321 28000 3.085 1.7161 5.168 1.4260 11.329 1.0671 30000 3.451 1.7474 5.816 1.4467 12.453 1.0964 32000 3.841 1.7755 6.466 1.4699 13.786 1.1142 34000 4.237 1.8007 7.097 1.4976 15.300 1.1232 36000 4.626 1.8248 7.745 1.5243 16.818 1.1316 38000 5.009 1.8494 8.412 1.5475 18.235 1.1444 40000 5.402 1.8756 9.114 1.5648 19.513 1.1626 106
Tabl 5.3. First-ordr ltrial ondutivity ( 1) (Sm -1 ) and third-ordr ontribution to ltrial ondutivity mixtur at diffrnt prssurs. f for th xitd stat (ES) quimolar argon-hydrogn plasmas Tmpratur (K) p=1 atm p=10 atm p =100 atm (1) f (1) f (1) f 10000 1642.48 1.1600 948.932 1.0336 382.22 1.0107 12000 3457.33 1.2652 2972.34 1.0721 1625.07 1.0095 14000 5183.68 1.3270 5787.94 1.1044 4349.29 1.0033 16000 6469.06 1.3731 8613.82 1.1375 8756.35 1.0079 18000 7344.45 1.4098 10794.9 1.1757 14374.3 1.0379 20000 8028.37 1.4388 12276.5 1.2145 19900.9 1.0583 22000 8562.39 1.4615 13320.8 1.2502 24117.4 1.0481 24000 8838.6 1.4799 14151.7 1.2802 26829.7 1.0467 26000 8957.34 1.4981 14854 1.3031 28561.3 1.0629 28000 9157.16 1.5179 15400.9 1.3203 29836.4 1.0857 30000 9480.09 1.5370 15812.4 1.3363 30983.9 1.1060 32000 9829.99 1.5539 16190.5 1.3542 32124.9 1.1199 34000 10098.9 1.5683 16561.2 1.3741 33216.4 1.1288 36000 10240.7 1.5811 16970.3 1.3923 34079.8 1.1374 38000 10320.4 1.5939 17347.8 1.4075 34712.9 1.1480 40000 10433.7 1.6079 17674.5 1.4183 35154.4 1.1611 107
From th tabls it is lar that at a givn prssur both, inras with inras in tmpratur. Abov 15000K, as prssur inrass ths valus inras (1) (1) 1.2 ( ES) ( GS) 1 10000 20000 a 30000 40000 0.8 b (a) 0.6 Tmpratur (K) 1.2 ( ES) ( GS) 1 10000 20000 a 30000 40000 0.8 b 0.6 (b) 0.4 Tmpratur (K) Figur 5.9. Ratios of (a) ltron thrmal ondutivity with and without EES (b) ltrial ondutivity with and without EES ( ES) ( GS) Th urvs a, b & rprsnt p=1, 10& 100 atm rsptivly. ( ES) ( GS) vs. tmpratur for argon. 108
( ES) ( GS) a b Tmpratur (K) (a) ( ES) ( GS) a b (b) Tmpratur (K) Figur 5.10. Ratios of (a) ltron thrmal ondutivity with and without EES ( ES) ( GS) ( ES) (b) ltrial ondutivity with and without EES vs. tmpratur for 50% argon ( GS) - 50% hydrogn plasma. Th urvs a, b & rprsnt p=1, 10& 100 atm rsptivly. 109
Figur 5.9 shows that as prssur inrass th dviation from th ground stat inrass with tmpratur and boms maximum around 20000 K. This may b xplaind by th fat that with inras in prssur, ionization shifts towards th highr tmpratur and thus onntration of xitd stats dominat. Figur 5.10 shows similar trnd for both th ltron transport proprtis for th plasma mixtur. As ltron transport proprtis strongly dpnd upon th dgr of ionization, thrfor largr rlativ rrors ar found for ths proprtis with and without EES and in ontrast to hydrogn plasma thr xist a dominan of ltron-atom rosstion at low tmpraturs and EES dominan at intrmdiat tmpraturs. 5.6 Rsults and Disussion (i) Intrnal ontribution to spifi hat at onstant prssur for argon and argonhydrogn mixtur (Figurs 5.4 & 5.5) is mor than that in hydrogn plasma. This is du to th larg numbr of EES of argon. (ii) Comparison of th ratios for hydrogn plasma ( int / pf =0.42 and int / p =0.15 at p=1atm),with th orrsponding valus for argon plasma (0.65 and 0.25) rsptivly shows that th inlusion of th xitd stats strongly influns th intrnal ontribution to th frozn as wll as th total spifi hat vn at low prssur. Th ratios bom all th mor important at high prssurs (ii) Th frozn and rativ ontribution of th total spifi hat in as of hydrogn plasmas rportd by Capitlli and oworrs ar strongly afftd by inluding ltroni xitation but thy bhav in opposit way suh that th total spifi hat by inluding and nglting th EES of plasma spis rmains unafftd at low prssurs but this sort of ompnsation fails at high prssurs. This ompnsation dos not our for argon and argon-hydrogn mixturs vn at low prssurs as is lar from Figur 5.6 for argon and Figur 5.7 for 50% argon -50% hydrogn at p=1, 10& 100 atm rsptivly (iv) From Figur 5.9, in ontrast to hydrogn plasma, ( ES) > 1 at all prssurs ( GS) around 10000 K for argon plasma, whih is du to th fat that around this tmpratur rang -Ar ross stions in as of argon as wll as th plasma mixtur dominat. 110
(vi) At tmpratur gratr than 16000 K, ( ES) <1 and th ratio boms mor ( GS) pronound at high prssur (urv ) for both th plasmas, whih is du to th dominan of EES at intrmdiat tmpraturs and at high prssurs. Similar trnd follows for th ltrial ondutivity as shown in Figur 5.10. (vii) Th ltron transport proprtis ar afftd strongly spially at high prssurs by th inlusion of EES of plasma spis. Ths proprtis bhav diffrntly from thos in hydrogn plasma du to th non similarity of tmpratur dpndn of ollision ross stions of -Ar and -H intrations. (viii) Th strang bhavior of f as obsrvd for th ground stat hydrogn plasma in our rnt wor (Singh t al., 2008) is also obsrvd for th GS argon and argonhydrogn plasma at p=100atm. With th inlusion of EES rosstion for hydrogn th abnormal bhavior for hydrogn was liminatd but ould not b xplaind hr du to la of availability of xitd stats ollision rosstion data for argon. 5.8 Conluding rmars and sop for futur wor In th prsnt wor it has bn shown that th transport proprtis of hydrogn, argon and argon-hydrogn thrmal plasmas ar afftd by inluding ltronially xitd stats (EES) spially at high prssurs. A simplifid rlationship to stimat highr-ordr ontributions to visosity has bn rommndd for hydrogn thrmal plasma. It is onludd that though th unli intrations ar important in valuating first and sondordr visosity yt thir rol in stimating highr-ordr ontributions is insignifiant at high prssurs. This simplifid rlationship stimats satisfatorily th sond-ordr ontributions to visosity (or sond-ordr visosity) of hydrogn thrmal plasmas using th highr-ordr ontributions of pur omponnts, involving lssr numbr of ollision intgrals and thus avoids th umbrsom omputational produr. Highr-ordr ontributions to ltrial ondutivity, ltron thrmal ondutivity and thrmal diffusion ratios strongly dpnd upon EES, whih signifis that with th givn ross-stions usd in valuating th ontributions, onntration dpndn of EES dominats through -H (n) intration. It is only this intration whih mas th rsults for th ltron transport proprtis diffr from thos in th ground stat. It is onludd 111
that EES must b tan into aount whil valuating th highr-ordr ontributions at high prssurs. Th ompnsation btwn frozn and rativ spifi hats obsrvd in hydrogn plasma at low prssur is not nountrd in argon and argon-hydrogn plasma du to th larg numbr of EES of argon. With th inlusion of EES, th total spifi hat for hydrogn plasma is afftd at high prssurs, but for argon and th plasma mixtur, it is afftd at both low and high prssurs. Similarly th ltron transport proprtis ar afftd at low prssurs and signifiantly at high prssurs. Ths proprtis bhav diffrntly than thos in hydrogn plasma du to th non similarity of tmpratur dpndn of ollision ross stions of -Ar and -H intrations. Th study of quilibrium omposition, thrmodynami proprtis and transport proprtis with and without EES for diffrnt thrmal plasmas ar th futur prospts of th prsnt rsarh wor. Th rlationship of stimating highr-ordr ontributions to visosity for hydrogn thrmal plasma ould b attmptd for stimating th ontributions for othr plasmas. Th fft of EES omposition on thrmodynami and highr-ordr ltron transport proprtis of diffrnt thrmal plasmas nd to b xamind. Th influn of non quilibrium paramtr on thrmodynami and transport proprtis inluding EES for diffrnt thrmal plasmas ould also b word out at diffrnt tmpraturs and prssurs. Th ltron transport proprtis of argon plasma at diffrnt tmpraturs and prssurs may b xplaind ompltly if th xitd stat ross stion data for argon ar mad availabl. Th attmpts ar also nssary for improvmnt of xitd stat transport ross stions as wll as bttr thory for th numbr of xitd stats to b tan into aount. 112