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" 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 . Outline.

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slide1

"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
slide2

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

slide3

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

slide4

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

slide5

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)

slide6

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

slide7

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

slide8

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

slide9

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)

slide10

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

slide11

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.

slide12

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)

slide13

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
slide14

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.

slide15

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.