Kinetic of drop spreading - OMICS Publishing Group
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Main Scientific Interests Victor M Starov Department of Chemical Engineering, Loughborough University, UK SCIENTIFIC INTERESTS KINETICS OF SPREADING MEMBRANE SEPARATION KINETICS OF REVERSIBLE COAGULATION RHEOLOGY OF CONCENTRATED SUSPENSIONS PUBLICATIONS
259 PRESENTATIONS AT SCIENTIFIC MEETINGS 200 h-index 29 Sitations 2816 PHD STUDENTS SUPERVISED More than 35
DSc SUPERVISED 3 OUTLINE SURFACE FORCES ACTION SPREADING OVER POROUS SUBSTRATES: SATURATED AND DRY, SURFACTANT SOLUTIONS SPREADING OVER SURFACES COVERED WITH FATTY ACID OR LIPID LAYERS SPREADING OVER HYDROPHOBIC SURFACES SUSFACTANTS ON THIN WATER LAYERS IMBIBITION INTO POROUS MEDIA A water droplet on three different substrates
contact angle Teflon Non-wetting, /2 Glass or mica Partial wetting, 02 WHAT IS THE REASON? Complete wetting Silicone wafer, water spreads out completely (t)t) dynamic contact angle
Disjoining pressure: 1 Complete wetting 2 Partial wetting S S cos 1 Disjoining pressure determines the liquid shape in the transition zone Contact angle Static advances and receding contact angles on smooth homogeneous substrates Deformation of soft solids in contact with transition zone Non-flat liquid layers Line tension
Influence of roughness Motion of drops/bubbles in thin capillaries Kinetics of spreading in the case of Experimental set-up 1-substrate, 2-hermetically closed, thermo stated chamber, 3-liquid drop, 4-syringe, 5, 14- front view and view from above CCD cameras, 6, 11-VCRs, 7, 13- light sources, 8, 12 collimating lenses, 9,14-tele-photo objectives, 15-flash gun, 16-PC. SPREADING OVER SATURATED POROUS LAYERS Spreading over saturated porous layers
Outer solution Matching of outer and inner solutions results in spherical cap L(t)t) L0 1 t Spreading law dL dt 3 3 L L
0.1 , 0 0 10 4V Effective lubrication coefficient can be both experimentally determined and calculated
3 SILICONE OILS ON NITROCELLULOSE MEMBRANES Fitted as: V 4 3 10 t L L0 1 10 L0 L L0 (t)1 t / )n
0.29 L, cm 3 0.28 0.27 0.26 1 - 12 point 0.25 n
0.24 0.23 0.13 0.01 3 - 12 point 0.22 n 0.11 0.01 0.21 0.20 0.19 0.0
0.5 1.0 1.5 2.0 2.5 0.1 Initial stage differs from the capillary regime! -1.20 -1.25 ln L -1.30 -1.35
EXPERIMENTAL VALUES OF EFFECTIVE LUBRICATION COEFFICIENT SPREADING OVER DRY POROUS LAYERS SIMULTENEOUS SPREADING AND IMBIBITION INTO THE POROUS SUBSTRATE COMPLETE WETTING Spreading over dry porous substrates radius of the drop base, radius of the wetted region inside the porous layer, (tt) dynamic contact angle L(t) l(t)
DRY POROUS SUBSTRATE Drop volume V (t)t ) V0 m l (t)t ) 2 SPREADING SHRINKAGE d v Ld v t velocity of spreading velocity of shrinkage SPREADING OF LIQUID
DROPS OVER DRY POROUS LAYERS: COMPLETE WETTING CASE 0. 0. 2/ 2 1 4V3 10 3 dL 1 mK t t0. 3 d 0.1
0 9 t K p pc / dl dt l l ln L p c p
4 V 0 ml Kppc is determined independently NO FITTING PARAMETERS 1/ 3 2 2
1 ln l L CAPILLARY IMBIBITION: DETERMINATION OF Kp pc d Experimental set-up 1-membrane, 2-lifting up/down device, 3-thermo stated chamber, 4Petri dish with liquid, 5-optical glass windows, 6-CCD camera, 7video tape-recorder, 8- PC Capillary imbibition of silicone oils: independent determination of Kp pc d 2 (t) 2K p
p c t / 0.9 0.4 - linear fit 0.3 0.5*d2 d, cm 0.6 0.2
0.3 0.1 0.0 0 30 60 t, s Nitrocellulose membrane 0.22 m 90 0.0 0 20
40 60 t, s 80 10 SPREADING OF SILICONE OILS OVER DRY NITROCELLULOSE MEMBRANES 8 L, l mm 7 6
SO20 V0 =3.1 mm3, r=0.2 SO20 V =9.0 mm3, r=0.2 0 5 SO20 V0 =15.6 mm3, r=0.2 SO20 V =3.8 mm3, r=3 l upper parts 0 SO20 V0 =5.5 mm3, r=3
SO100 V =8.6 mm3, r=3 4 0 SO100 V0 =14.5 mm3, r=3 SO500 V =3.6 mm3 , r=3 3 3 SO500 V00 =8.7 mm , r=3 SO500 V =14.5 mm3, r=3 2
0 L lower parts 1 0 0 500 1000 t, s 1500
Dimensionless values L L / Lm , l l / l * , t t / t*5 * l L, l, mm 4 Lm 3 2 1 0 t 0
60 120 t, s * 180 Universal behaviour: solid lines according to our theory predictions L L / Lm , l l / l * , t t / t* 1.0 1 .0 l
L 3 L S O 2 0 V0 = 3 .1 m m3 , r= 0 .2 3 S O 2 0 V0 = 9 .0 m m , r= 0 .2 3 S O 2 0 V0= 3 .8 S Om2 ,0 r= V03= 1 5 .6 m m 3 , r= 0 .2 m S O 2 0 V0 = 5 .5 m m , 3 r= 3 0.5
0 .5 3 S O 1 00 V0 = 8 .6 m m , r= 3 3 S O 1 00 V0 = 1 4 .5 m m 3 , r= 3 3 S O 5 00 V0 = 3 .6 m m , r= 3 S O 5 00 V0 = 8 .7 m m , r= 3 S O 5 00 V0 = 1 4 .5 m m , r= 3 T he o ry 0.0 0.0 0 .5
t 0 .0 1 .0 Universal behaviour: / m solid line according to our theory predictions 5 S O 2 0 V 0 =3.1 m m 3, r=0.2 S O 2 0 V 0 =9.0 m m 3, r=0.2 4 S O 2 0 V 0 =15.6 m m 3, r=0.2 S O 2 0 V 0 =3.8 m m 3, r=3 S O 2 0 V 0 =5.5 m m 3, r=3 / m
S 100 V 0 =8.6 m m 3, r=3 S O 1 0 0 V 0 =1 4 .5 m m 3, r =3 3 S O 5 00 V 0 =3.6 m m 3, r=3 S O 5 00 V 0 =8.7 m m 3, r=3 S O 5 0 0 V 0 =1 4 .5 m m 3, r =3 T heory 2 1 0 0.0 0.2 0.4
0.6 t e constant over the second stage! 0.8 1.0 SPREADING OF LIQUID DROPS OVER THICK POROUS LAYERS COMPLETE WETTING CASE SPREADING OF LIQUID DROPS OVER THICK POROUS LAYERS: COMPLETE WETTING CASE (t) effective contact angle
Different viscosities, the same glass filter 1.0 1.0 5 0.8 0.8 4 0.6 0.6 3
r1=0.22m r2=0.45m r3=3.0m SPREDING OVER FATTY ACID SURFACES OR LIPID LAYERS SOLID SUBSTRATE WITH ROTATIONALLY MOBILE CHAINS OF FATTY ACID NO LATERAL INTERACTION NO SPREADING SPREADING OVER HYDROPHOBIC SUBSTRATES SPREADING OF DROPS (2.50.2 l) OF
0.05% SDS SOLUTION OVER PTFE WAFER THEORY PREDICTION TRANSITION TIME, ON CONCENTRATION SPREADING OF SDS SOLUTIONS OVER PTMF SURFACTANTS ON THIN WATER LAYERS: MARANGONI FLOW SURFACTANT ON THIN WATER LAYER R(t)t) 100 R (mm)
10 0.01 0.1 t (s) 1 10 100 R (mm) 10 0.01 1/4
0.1 t (s) 1 10 Capillary imbibition of surfactant solutions NON-WETTING SYNTAMID-5 ON HYDROPHOBISED QUARTZ SURFACE IMBIBITION OF SURFACTANT SOLUTIONS INTO HYDROPHOBISED QUARTZ CAPILLARIES SPONTANEOUS
Imbibition length, l, on time, t , Syntamide-5 horizontal hydrophobized quartz capillary, r = 16 m. 1 1 0.05%; 2 0.1%; 3 0.4%; 4 0.5%; 5 1%. CAPILLARY IMBIBITION OF SURFACTANT SOLUTIONS PARTIAL WETTING Capillary imbibition of surfactant solutions: partial wetting d 2 (t) 2K pt p c
/ 0.9 0.4 0.3 d, cm 0.5*d2 0.6 0.2 0.3 0.1 0.0
0.0 0 30 60 t, s Nitrocellulose membrane SDS concentration 0.1% Average pore size 0.22 90 0 20 40
60 t, s 80 10 Capillary imbibition of SDS solutions: nitrocellulose membranes 0.04 Kppc 0.03 'MILLIPORE'
1.0 Capillary imbibition of surfactant solutions Theory rcr 2 a min cos max 2 2DcCMC I.r < rcr Surfactant concentration is zero on the moving meniscus at any SDS concentration: pure water on the meniscus! Surfactant concentration increases on the moving meniscus with SDS concentration,
which results in faster imbibition. II.r > rcr INFLUENCE OF CLUSTER FORMATION ON VISCOSITY OF CONCENTRATED SUSPENSIONS/EMULSIONS Cluster formation in yeast suspensions 50 m = 0.002 = 0.02 =
0.04 100 m No clusters Cluster formation Viscosities are different though particle volume fractions are equal eff m Viscosity on volume fraction of dispersed particles. Experimental data from review (t)Thomas), solid lines according to our equation 1.m=1, A=1 (t)particles do not form clusters) 2.m =0.73 (t)close to
hexagonal packing of particles inside clusters), A=0.61 3.m =0.65 (t)close to cubic centered packing of particles inside clusters), A=0.67 4.m =0.56 (t)close to simple cubic packing of particles inside clusters), A=0.72 EMULSIONS Developed flocculation m density of droplets inside flocs Theory of reversible coagulation f
0.3 1 0.25 0.2 0.15 2 0.1 3 0.05 4 0 0
2 4 6 * * volume fraction when clusters start to form Low flocculated emulsion 10 eff
m eff 0 1 0.0 0.1 0.2 0.3 0.4 Milk at different volume fractions of fat (t)Leviton, A, and Leighton, A., 1936).
Curve 1 our theory (t)cluster Curve 2 formation) no cluster DEADEND ULTRAFILTRATION Water soluble polymer, n-repeated units (t)n=5) Dissociation/association of each unit Cp/Cf >1 Cp/Cf >1
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