Universal Dielectric Response of Atmospheric Ice using COMSOL

Transcription

1 Univesal Dielectic Response of Atmospheic Ice using COMSOL Umai N. Mughal and Muhammad S. Vik Atmospheic Icing Reseach Team, Navik Univesity College, Navik, Noway unm@hin.no

2 My Today s Talk Will Compise Atmospheic Ice Dipola Polaization Real Dielectic Response Results Numeical Setup UDR Fo Atmospheic Ice 2

3 Atmospheic Icing It occus when wate doplets feeze on object they contact. In-Cloud Icing Pecipitation Icing Fost Rime Glaze Wet Snow Feezing Rain Had Rime Soft Rime 3

4 Wate Molecule (H2O) Oxygen Atomic Numbe : 8 Electonegativity: 4.44 Hydogen Atomic Numbe : 1 Electonegativity : 2.2 Electonegative Citical Values Least Electonegative :.7 Highly Electonegative : 4 Non Pola Covalent Bond : Linea Pola Covalent Bond : -.7 Nonlinea Pola Covalent Bond : Ionic Bond : > 1.7 Oxygen and Hydogen.7 < ( )=1.22 < 1.7 4

5 Dipola Polaization Dielectic mechanisms Electonic polaization Ionic polaization Intefecial polaization Dipola polaization electonic ionic dipola int efecial Dipola Polaization Unequal electon shaing Fiction accompanying oientation 5

6 i. Dielectic Susceptibility χ ' '' ( ) ii. Models to detemine Dielectic Susceptibility Kame s Koing Model ' 2 d '' 2 2 '' 2 d ' 2 2 Debye Model ' s '' s whee is the elative pemittivity is the efeence fequency is the fequency fom to. s is elative pemittivity at D.C is elative pemittivity at high fequency is the elaxation time 6

7 Dielectic Responses of Ideal Fluid (Debye Fluids), Ref. [8] ( ) ( ) '' ' ' '' s 1 s p ve W kt whee v is the attempt to jump fequency W is the activation enegy k is the Botzmann Constant 7

8 Dielectic Response of Real Fluids Havikiak Negami Expession [1] i ( ) A1 p (1 n) m High Fequecny [1] ( ) n cot ( ) 2 '' ' Low Fequecny [1] The effect of dc conductivity on ε ε ac. (A) σ = (B) σ =σ 1 > (C) σ 2 > σ 1 (D) σ 3 > σ 2 ( ) m tan ( ) 2 '' ' 8

9 Univesal Dielectic Response '' ( ) ( ) Ref. [2] ( n 1 '' n 1 A Moe Geneal Relation fo Univesal Dielectic Response, Ref. [3] n ( ) A Whee, A and n ae assumed to be constant is the sweeping fequency. Resisto Capacito Netwoks fo a Doped Ziconia [3] 9

10 Analytical Model - Conductivity Relation fo Atmospheic Ice Paamete Value Refeence C 1.6x1 6 S/m [5] E.57 ev (@ C, 1kHz) E (@ C, 1kHz) s (@ 1 C) E s (@ T > 4 C ) ( ) x1-5 S/m (.56.4) ev (1.1.5)x1-8 S/m (.34.2) ev [6] [4] n ( ) A It is found that = f( s, ) A = g ( s, ) n = f(t) Low Fequecny Ce s s E s High Fequecny Ce E kt Expeimental esults of Fujino [1 ] fo Conductivity vaiation with fequency and tempeatue fo pue ice 1

11 Expeimental Model 11

12 Numeical Model 12

13 Tempeatue = 272 K, R 2 =.856 Results Tempeatue = 268 K, R 2 =.973 Tempeatue = 263 K, R 2 =.88 Tempeatue = 253 K, R 2 =.35 13

14 Conclusion and Discussion UDR foms the basis of the conductivity vaiation with a factional powe of excitation fequency but it does not elate tempeatue with the powe law. In this pape the Maxwell Boltzmann statistics is used fo themal excitation of poton jump fo atmospheic ice and is used in the conductivity elation Eq. 4 which adequately suppots the expeimental esults of Fujino [1]. Similaly the powe exponent n also vaies fom to 1 and is also used as tempeatue dependent. At some tempeatues the conductivity dependent on fequency and tempeatue shows moe deviation e.g. 253 K (Fig. 12) which may be due to the nonlinea exponential inteaction between the molecules but it s not clea. This study eflects that Univesal Dielectic Response as poposed by Jonsche need some additional explanations of the assumed constants which in conductivity elation Eq. (4) ae temed as, A and n. In this pape these all constants ae found to be explicitly dependent on the tempeatue. 14

15 Refeences 1. A. K. Jonsche, Dielectic Response of Pola Mateials, IEEE Tansactions on Electical Insulation, 25(4), A. K. Jonsche, The Univesal Dielectic Response, Review Aticle in Natue, 267, Bowen, C.R. and D.P. Almond, Modelling the 'univesal' dielectic esponse in heteogenous mateials using micostuctual electical netwoks. Mateials Science and Technology, (6): p Bulleme, B., H. Engelhadt, and N. Riehl, Potonic conduction of ice I.. High tempeatue egion. Physics of ice Steinemann, S., Dielektische Eigenschaften von Eiskistallen II. Teil Dielectische Untesuchungen an Eiskistallen mit eingelageten Femdatomen. Helv. phys. Acta, : p Camp, P.R., W. Kiszenick, and D.A. Anold, Electical conduction in ice. CRREL Res. Rep., : p R.M. Fous and J. G. Kikwood, J. Ame. Chem. Soc., 63, 385 (1941) 8. Kuoiwa, D., The dielectic popety of snow1954: Intenational Association of Scientific Hydology. 9. Mughal, U.N., M.S. Vik, and M.Y. Mustafa. Dielectic Based Sensing of Atmospheic Ice. in 38th Intenational Confeence on Application of Mathematics in Engineeing and Economics Sozopol, Bulgaia: In pess. 1. Fujino, K. Electical popeties of sea ice. in Confeence on Physics of Snow and Ice, II. (August, 14-19, 1966) Sappoo, Japan: Institute of Low Tempeatue Science, Hokkaido Univesity. 11. Stiles, W.H. and F.T. Ulaby, Dielectic Popeties of Snow. Jounal of Geophysical Reseach, (C2). 12. Evans, S., The dielectic popeties of ice and snow - A eview. Jounal of Glacialogy, : p Kao, K.C., Dielectic Phenemenon in Solids, 24, UK: Elsevie. 14. Panteny, R. Stevens, and C.R. Bowen, The fequency dependent pemittivity and AC conductivity of andom electical netwoks. Jounal of Feoelectics, 25(319): p

16 ACKNOWLEDGMENT The wok epoted in this pape was patially funded by the Reseach Council of Noway, poject no /16 and patially by the consotium of the ColdTech poject - Sustainable Cold Climate Technology. 16