MULTI SCALE POROUS AND COLLOIDAL MATERIALS TEXTURE AND TRANSPORT PROPERTIES P. E. LEVITZ. Transport and invasion properties:
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1 MULTI SCALE POROUS AND COLLOIDAL MATERIALS TEXTURE AND TRANSPORT PROPERTIES P. E. LEVITZ Pat III: Tanspot and invasion popeties: 1 1
2
3 I/ Intoduction Unconfined diffusion; Diffusion popagato Compact eploation The Pein Epeiment o how to measue k B Intefacial media and confinement; shot and long ange eploation of the mati II/ Dynamical ange and epeimental tools - Scatteing and the stuctual dynamics - Elastic, static, dynamical. - Quasi Elastic Neuton Scatteing (QUENS III/ Tanspot and macoscopic compotment Road Map of G(q,t in confinement and some epeimental esuts The totuosity concept Diffusion vesus electic tanspot: the fomation facto and the esistivity inde IV/ Shot intoduction to convective tanspot: Pemeability of a poe netwok - 3
4 Diffusive tanspot at defined space scale. λ 1/ q - Foced Rayleigh - FRAPP - NMR Pulse gadient - QUENS G (, t : Self-Diffusion Popagato 0, t 0, t ~ G( q, t G(, tep( iq. d 3 ~ ~ G ( q, ω G( q, tep( iωt dt 4
5 Self-Diffusion Popagato G (, t 0, t G(, t t 0 D ( G(, t G (,0 δ (, t 0 1 G(, t ep( / (4 π d D t 4D t de 1 < ( t > Λ ( d e G (, t d d e Dt 5
6 COMPACT EXPLORATION AT TIME t: towad optimal eaction L( t t L V ep loation ( t L de ( t N visiting _ sites ( t t > new _ visited _ sites Efficiency N visiting _ sites 1 d e ( t V ep loation ( t ( t t / d e 1 d / > e 1 Efficiency of eploation diveges d e > 1 d / < e 1 Non compact eploation 6
7 UNCONFINED BROWNIAN DYNAMICS: The fist single paticle epeiment. D self kbt 6πηR (1907 7
8 8
9 I/ Intoduction Unconfined diffusion; Diffusion popagato Compact eploation The Pein Epeiment o how to measue k B Intefacial media and confinement; shot and long ange eploation of the mati II/ Dynamical ange and epeimental tools - Scatteing and the stuctual dynamics - Elastic, static, dynamical. - Quasi Elastic Neuton Scatteing (QUENS III/ Tanspot and macoscopic compotment Road Map of G(q,t in confinement and some epeimental esuts The totuosity concept Diffusion vesus electic tanspot: the fomation facto and the esistivity inde IV/ Shot intoduction to convective tanspot: Pemeability of a poe netwok - 9
10 II_1/ DYNAMIC AND/OR STATIC SCATTERING Monochomatic beam Noisy beam Monochomato k 0 k d S 0 ( ω Stuctuedynamics S ( q, ω I without mono ω ( q S( q, ω dω ω [ ] S( q, ωep( iωt dω t 0 Static Scatteing: I mono without S( q,0 I ( q ( q Ove all configuations at the same I static statistical time 10
11 11 0, ( (, ( τ ρ τ τ ρ D ep( ~, ( ~ τ ρ τ ρ Dq q q 0, ( ~, ( ~ τ ρ τ τ ρ q D q q ep(,0 ( ~, ( ~, ( τ ρ τ ρ τ Dq q q q S Space dependent self motion (dilute case ep(,0 ( ~, ( ~, ( ωτ ρ τ τ ρ ω i q q d q S ( 1, ( Dq Dq q S ω π ω
12 1
13 S ( q, ω 1 π ω Dq ( Dq 13
14 14
15 I/ Intoduction Unconfined diffusion; Diffusion popagato Compact eploation The Pein Epeiment o how to measue k B Intefacial media and confinement; shot and long ange eploation of the mati II/ Dynamical ange and epeimental tools - Scatteing and the stuctual dynamics - Elastic, static, dynamical. - Quasi Elastic Neuton Scatteing (QUENS III/ Tanspot and macoscopic compotment Road Map of G(q,t in confinement and some epeimental esuts The totuosity concept Diffusion vesus electic tanspot: the fomation facto and the esistivity inde IV/ Shot intoduction to convective tanspot: Pemeability of a poe netwok - 15
16 DIFFUSION IN CONFINEMENT I/ INTERMITTENT BROWNIAN MOTION AND BRIDGE STATISTICS n d A A B B II/ BROWNIAN DYNAMICS ON LONG RANGE (t0, 0 ( t, 16
17 Shot times eponential fom Long Times G( q, t Road Map of G(q,t in confinement. ( S. Rodts, P.L., 00,005 ~ 3 G( q, t G(, tep( iq. d 3 D Maco, Totuosity D /τ (t0, 0 Pseudo non confinement Pood egimes Algebaic fom (Intefaces - dimensional effects - diffaction effects t q D 17
18 Macoscopic compotment; the totuosity concept D p D /τ The totuosity depends on - Minimal path (geodesic between two distant points - Connection between these two points - Local facto: thoats vesus molecula size - Adsoption, nano-wettability 18
19 Relationship between electic conductivity and self diffusion The andom walk method D D p ( t ( ( t ( bulk F F R R p w 1 φ D p D bulk 6t τ Φ 0 ( t Sw 100% Rw: Electic esistivity of the patially bine Rp: Electic conductivity of fully satuated poe netwok Φ: The poosity 19
20 Achie s law R ind R R R ind : Resistivity inde. R t : Electic esistivity of the patially bine satuated poe netwok. R o : Electic conductivity of fully satuated poe netwok S w : Bine satuation atio in poe netwok n: Satuation eponent. n aound t 0 S n w 0
21 I/ Intoduction Unconfined diffusion; Diffusion popagato Compact eploation The Pein Epeiment o how to measue k B Intefacial media and confinement; shot and long ange eploation of the mati II/ Dynamical ange and epeimental tools - Scatteing and the stuctual dynamics - Elastic, static, dynamical. - Quasi Elastic Neuton Scatteing (QUENS III/ Tanspot and macoscopic compotment Road Map of G(q,t in confinement and some epeimental esuts The totuosity concept Diffusion vesus electic tanspot: the fomation facto and the esistivity inde IV/ Shot intoduction to convective tanspot: Pemeability of a poe netwok - 1
22 IV/ Shot intoduction to convective tanspot: Pemeability of a poe netwok Knudsen Diffusion D Knudsen, C poe Levitz CNRS-UPMC Molecula Diffusion t Pe t VR C poe, D 0 Local : Navie Convective Tanspot (<V> >0 diffusion convection p / D v ρ ( P η v t Maco:Dacy Kφ < q >< V > P η K: Peméabilité en Dacy 1 dacy10-1 m (Aquifée1d
23 3
24 Pemeability/ Totuosity Cylindical tube of adius K 8 Possible geneal elationship K 8τ 8ΦF Katz Thompson s equation K Rc 6 ΦF 4
25 Imbibition-Dainage (Fo a single cylindical poe R v ( d/ dt dp/ d 8η γ cos( θ dp/ d Pc / ( / R γ cos( θ P c ( R γ cos( θ R d dt 4η (Laplace-Young Law γ cos( θ R t η 5
26 END OF THE THIRD PART.
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