" Spontaneous absorption of droplets into single pores of different radii ”

1. "Spontaneous absorption of droplets into single pores of different radii” G. Callegari 1 A. Neimark 2 K. Kornev 3 • TRI/Princeton, Princeton, NJ, 08540, USA • Chem. Eng. Dept., Rutgers University, Piscataway, NJ, USA • Sch. of Materials Sc., Clemson University, Clemson, SC, USA

2. Outline Aplications: Droplet absorption/ spreading in porous materials Introduction Spreading/wetting and absorption of droplets in porous materials 1- Absorption/Dewetting thin, small pores, smooth surface 2- Pure Fast absorption thick, large pores, rough surface Fast spontaneous absorption of droplets by capillaries Inertial vs viscous effects Introduction of Dynamic Contact Angle Viscoelastic effects

3. Droplet absorption/ spreading in porous materials: Applications Ink Jet Printing Spray Painting of porous materials Micro-chromatography Micro amounts of biological fluids for bio-components recognition Granulation process Agglomeration of fine powders using liquids as binders Industrial processes: Agriculture chemistry Pharmaceutical Mineral processing Food Detergency

4. Absorption/Spreading of droplets into porous media Marmur (1988) Marmur., J. Coll.Int. Sc.., 122, 209, 1988 Washburn Pinned contact line Absorbed dewetting, constant q Fv (Poiseuille) = FC Denesuk et al. (1993) Denesuk et al., J. Coll.Int. Sc.., 158, 114, 1993 Droplet absorption in thick porous material Washburn Borhan et al. (1993) Borhan et al., J. Coll.Int. Sc.., 158, 403, 1993 Starov et al. (2002) Starov et al., J. Coll.Int. Sc.., 252, 397, 2002 Droplet absorption in thin porous material Considered competition between spreading and dewetting while absorbed Dry Spreading + Aspired Dewetting First fast spreading without absorption, then dewetting absorption with constant q: maximum radius 8mx (dx/dt)/R= 2gcosq x a t 1/2 They all considered only viscous forces

5. Absorption/Spreading of droplets on thin porous materials A= 4 0 /(pq R03) B= 4H/(q R0) Polyvinyl alcohol Volume conservation (R/R0)3 =A-B(L/R0)2 A and B may depend on t (through q) q ~ 10° e H = 22 mm Dynamics dL/dt =kPc/[m ln(L/R)L] kPc =1.6 10-4 dyn = ger/(2ko) r = 0.74 mm Ro = 490 mm Pore size ~ 1-3 mm Hexadecane in PVA nanoweb 125 fps Well described by existing models (Starov et al 2002)

6. Pure and fast absorption (thick materials) Dry Spreading height (mm) Pure Absorption Rabs ~ 0.4 cm Rpore ~ 100 mm τabs~ 300 ms Re=r v Rpore/m ~ 1! Inertia is not negligible τDenesuk~ 1 ms time (ms) 0.8 mm Fast absorption in a capillary tube v=cte!! 10 mm Ink on a thick porous substrate (large pores, in the order of hundred of microns) Vol = 7 mm3 1000 fps Change of dynamics means transition from spreading to absorption

7. Fast Spontaneous Absorption of Droplets by Capillaries Reynolds numbersRe = ρUD/~ 10 – 150 ! The time interval between pictures is 10 ms. Linear Kinetics Kinetics of Droplet Absorption R = 375 m. 1000 fps

8. Fast Spontaneous Absorption of Droplets by Capillaries Quere, Europhys. Lett. 39, 533(1997) r[(z+cR)z”+z’2]+8mzz’/R2= 2gcosq/R-rgz Added apparent mass Experimental results can not yet fitted with the expression Quere Berezkin et al. .. Joos et al. Siebold et al. Hamraoui et al. Zhmud et al. Barraza et al. All of them working in different regimes, invoque the effect of the dynamic contact angle Bosanquet, Phil.Mag. 45, 525(1923) r[zz”+z’2]+8mzz’/R2= 2gcosq/R-rgz No inertia: Washburn eq. when z=0

9. Meniscus Dynamics: Dynamic Contact Angle Theoretical contributions: Hydrodynamic and Molecular models (from 1971…) Huh, Scriven, Dussand, Rame, Garoff, Hocking, Cox, Voinov, Shikmurzaev, etc Blake Wetting case: q a Ca1/3 Droplet spreading Tanner, Marmur et al and Cazabat et al. In capillaries Hoffman Petrov and Sedev Hoffman’s qd=(qs3+a3 Ca)1/3 (acc, 1% up to 140) There is still a big question mark in partial wetting cases Blake et al Callegari, Hulin, Calvo, Contact Angle, Wettability and Adhesion, Vol. 4, K. L. Mittal (Ed.), VSP, Leiden (2006) Air pushing glycerol Ca=mV/g m = viscosity Callegari, Hulin, Calvo, Contact Angle, Wettability and Adhesion, Vol. 4, K. L. Mittal (Ed.), VSP, Leiden (2006)

10. Fast Spontaneous Absorption of Droplets by Capillaries Bosanquet Viscous effects Bosanquet modif with prefactor b=0.67 Dyn Cont Angle with Hoffmann a=4.5 Two experiments in long horizontal capillaries water r[(z+cR)z”+z’2]+8mzz’/R2= 2gCos[(qs3+a3mz’/g)1/3]/R-rgz

11. Viscoelastic Fluids UB  R-1/2 ? 1000 fps DNA Racing Ss-lambda-DNAs. The time interval between pictures is 4 ms. Capillary radius in microns, from left to right: 250, 290, 375, 450, 580. Kornev, Callegari, Amosova, Neimark, Abs Pap ACS 228: U495 Kornev, Callegari, Neimark, XXI ICTAM, FM4L_10140, ISBN 83-89687-01-1.

12. Viscoelastic Fluids (Weissemberg effect) • UVEhas the maximum at RVE • For R < RVE, the velocity decreases due to the Weissenberg effect. • For R > RVE, the velocity decreases because of reduction of the driving capillary pressure. UVE cm/s Balance of momentum: A·[U2VE+ XX ]= A· P + 2   · R  A·  /R R, cm Real Fluids vs Ideal Fluids Viscous fluids Shearing stress: xy=  dV/dx ,  - viscosity xx= hydrostatic pressure Visco-elastic fluids (Maxwellian Model) xy=  dV/dx , xx=- 2 (dV/dx) xy = - (dV/dx)2  = relaxation time Kornev, Neimark JCIS, 262, 253(2003)

13. Viscoelastic Fluids (Weissemberg effect) water 0.02% PEO 0.05% PEO 0.1% ds DNA 0.1% PEO 0.1% ss DNA DNA PEO • Visc = 1 cp, g=65dyn/cm • = 0.0023s (0.02% PEO) • = 0.0055s (0.05% PEO) • = 0.008s (0.1% PEO) • Visc = 1 cp, g=65dyn/cm • = 0.001s • = 0.01s

14. Summary and Conclusions Droplet absorption experiments in glass capillary tubes of different diameters were performed. For the high velocity experiments conducted, Re is much larger than one and inertial effect prevails over viscous force. The velocity is found to be independent on time.  In fast absorption in thick and rough substrates two mechanisms with different timescales were shown. The constant slope in the decrease of the height of the droplet in function of time goes against Washburn like kinetics in the porous material. Inertial term is important. For simple liquids, it was shown that absorption velocity decreases with the capillary radius as predicted by Bosanquet. But the effect of the dynamic contact angle can not be neglected.   The spreading of droplets in thin smooth porous materials shows the “aspired dewetting” regime. The dynamic contact angle is constant in time. Experimental results agree with a simple model proposed. 

15. Summary and Conclusions For viscoelastic liquids, it was shown that the absorption velocity is a non-monotonous function of the capillary radius, with a well defined maximum. This important experimental result support the theoretical analysis previously done. For small concentration of polymer in water, a simple maxwellian model seems to cuantitative explain the effect. For larger concentrations even while the escential features are captured, the cuantitative agreement is not good. This is probable due to a cooperative effect in the interaction of the polymeric molecules.   