Ch 11 Paticulate upenion
Iue Stability (dipeion) edientation igation wall lip
Had phee Only igid epulion peent when paticle coe into contact Zeo hea vicoity ( 1+. φ) 5 1+.5φ + 6.φ d.5 ( φ) dφ exp( 5φ / ) exp( [ ] φ) [ ] li φ φ 0 φ [ ] φ 1 φ Kiege-Doughety equation
Had phee Vicoity can be educed when paticle of diffeent ize ae ixted Highe volue faction of paticle can be packed into a upenion Of pactical ipotance in the foulation of highly loaded upenion -> allow theal expanion coefficient be cloely atched to the device -> pevent cack and debonding
Had phee Shea thinning a T k D B 6π 0 T k a D a t B D 3 0 6π D B t T k a Pe γ γ 3 T k a B 3 σ σ σ c σ / 1 1 0 + tie fo a paticle to diffue a ditance equal to it adiu Univeal function of Pecle nube fo fixed volue faction
Had phee Mechani of hea thinning & hea thickening Shea thinning; 1.diappeaance of Bownian contibution -> vicoity eduction by a facto of.foation of line of paticle (ting) paallel to the flow diection -> evidenced by copute iulation & light catteing Shea thickening; 1.foation of clute containing paticle diven by hea into cloe poxiity.defoation of clute poduce lage lubication tee in the thin fil epaating cloely paced paticle 3.the echani depend on the natue of the epulive potential
Non-pheical paticle Dilute upenion Jeffey obit In the abence of Bownian otion and of intepaticle inteaction, p u u ω + p 1 + 1 ( u D uuu : D) In a heaing flow, γt tanθ p tan + tanθ0 p + 1/ p θ; the angle of the axi of yety eaued in the clockwie diection fo the flow diection θ i tie-peiodic; a non-bownian axiyetic paticle otate indefinitely in a hea flow with a peiod π 1 P p + γ p When paticle otation ae ditubed by Bownian otion, D D 0 0 3k 3k B B T (ln( p) 0.5) 3 π L T (ln( L / d) 0.8) 3 π L Rotay diffuivity fo a pheoid of apect atio p Rotay diffuivity fo od
Non-pheical paticle Dilute upenion of pheoid e v σ σ + σ + σ σ e p p 3 1 ν k + 1 B T uu σ υ { A uuuu D + B[ uu D + D uu ] CD} φ : + σ D
Non-pheical paticle Dilute upenion of high-apect-atio paticle o olecule 1 σ D + νς t uuuu : D + 3ν k B T uu δ 3 ς t π L ε T 3 B f ( ) 6ln(L / d) D 0 k
Non-pheical paticle Sei-dilute upenion of Bownian od + + δ uu D uuuu D σ 3 1 3 : T k B t ν νς 0 ˆ ) ( + u uuu : D u u u ψ ψ ψ D t ) ( 4 ) ( ˆ u d D D u u u u ψ π Oientation dependent otay diffuivity
Non-pheical paticle Sei-dilute non-bownian fibe upenion 1.vicoity inceae i not uch.noal te ~ 0.4 tie hea 5/ te N p φ p ln( p) 1 C 3/ 3.lage extenional tee 4 γ 4φp 3 + νς t 3 1 + 9ln( π / φ )
Electically chaged paticle Had phee; coated with an oganic laye that povide a teic baie to pevent flocculation The chage lead to long-ange epulion that can keep the paticle fa enough apat that they ae not dawn togethe by hot-ange van de Waal foce The uface chage inceae the effective paticle diaete vicoity at all volue faction 5 3 d 1.5φ.5 φ 0 40 eff + + + a d eff 1 ln κ { α / ln[ α / ln( α /)]}
Electically chaged paticle vicoity at effective volue faction lage than 0.1 φeff 1 φ (5/ ) φ
Electically chaged paticle vicoity: hea ate dependence a hea ate inceae, hydodynaic contibution inceae, the effective paticle diaete goe down, the paticle appoach each othe oe cloely
Electically chaged paticle Yield te and odulu The yield te appea when the paticle epulion ae tong enough to induce acocytallization. A the ionic tength deceae futhe, the epulion becoe tonge, and the yield te becoe lage. 3 ) / ( ) ( B y T k W K σ 3 1/ φ φ a ) ( 5 4 5 W N d W d d dw N G κ π φ π φ +
Electically chaged paticle Flow echani - foation of liding laye - beakdown of thee laye a hea ate inceae
Electically chaged paticle Shea thinning; due to lipping of the laye pat each othe Shea thickening equie not only that liding laye be boken down by hea, but that the fagent of thee laye ut otate and collide with each othe to fo tuctue whoe aveage dienion in the flowgadient diection ae lage. Such tuctue can ja the flow, leading to abupt hea thickening.
Electically chaged paticle Noal te diffeence N N1 σ appea only when - LCP copoed of od-like olecule - electoheological upenion which fo chain-like aggegate iilaity uppot the notion that in the hea thickening egion, the elevant flow unit ae no longe phee, but ae od-like o dik-like paticle aggegate
Paticle in vicoelatic liquid - to add pefoance, to ave cot, to potentially educe theal expanion tee effectively le elatic than polye alone effect of coupling agent enhanced hea thinning, becaue the hea ate expeienced by polye confined between two paticle can be uch lage than the oveall hea ate
Paticle in vicoelatic liquid Thixotopy; a the diffuion tie contant i too lage (ode of an hou) due to high vicoity, it take a long tie fo a gel-like paticle tuctue to elax o efo, hence, flow induce change in fluid tuctue that ae eaed only afte hou of quiecence