Flat Flow by Kamila Soukov 11 Slide 2 Task Fill a thin gap
between two large transparent horizontal parallel plates with a
liquid and make a little hole in the center of one of the plates.
Investigate the flow in such a cell, if a different liquid is
injected through the hole. 2 Slide 3 3 Slide 4 4 Slide 5 5 Slide 6
6 Slide 7 7 Slide 8 8 Slide 9 9 Slide 10 10 Slide 11 11 Slide 12 12
Slide 13 Interfacial Pressure 13 Slide 14 Understood Phenomena 14
Figure from Hornberger et al. (1998) k : permeability of medium h :
gap between plates Slide 15 Position, Velocity measure how fast the
interface moves at various places take the average 15 weight on
syringe removed Slide 16 Formation of Instabilities 16 Slide 17
Formation of Instabilities small instability pressure differences
instability grows fingers 17 Slide 18 Slow-Motion Video of Patterns
18 300 fps Slide 19 What Affects Instabilities? 19 destabilizing
high viscosity of liquid in the gap pressure differences big
pressure gradient stabilizing surface tension promotes disturbances
tries to dampen out disturbances Slide 20 Low Viscosity No Fingers
low viscosity symmetrical situation easier to spread out evenly no
fingers 20 Slide 21 Low Viscosity No Fingers 21 Ink (less viscous)
Glycerol (more viscous) Slide 22 PATTERN COMPLEXITY MEASUREMENTS
Slide 23 Equipment Liquid : more viscous: glycerol, motor oil less
viscous: water (colored), ink, ethanol Plates plexiglass (HeleShaw
cell): 25 x 25 cm gap: distance set by weights hole: size
customized to the syringe 23 Slide 24 Equipment 24 Slide 25
Equipment 25 Slide 26 What to Measure quantify the instabilities
count perturbances tells how interesting the pattern is to make
more objective: 26 Slide 27 VISCOSITY 27 Slide 28 Viscosity of
Medium water motor oil 5W water motor oil 10W Viscosity < 28
Slide 29 water glycerol water motor oil 15W Viscosity <
Viscosity of Medium 29 Slide 30 # of Fingers vs Viscosity of Medium
30 Slide 31 new ink (less viscous) glycerol Viscosity of Injected
Liquid old ink (more viscous) glycerol Viscosity > 31 Slide 32
DISTANCE OF THE PLATES 32 Slide 33 Gap Size (Water glycerol) 1mm0.8
mm 33 Slide 34 0.2mm 0.1mm 0.4mm 34 Slide 35 # of Fingers vs Gap
Size 35 Slide 36 PRESSURE IN SYRINGE 36 Slide 37 Pressure in
Syringe p = 15 kPa (300g) p = 22 kPa (450g)p = 49 kPa (1 kg)
changed by putting weights on syringe 37 Slide 38 # of Fingers vs
Pressure 38 Slide 39 INTERFACIAL TENSION 39 Slide 40 Interfacial
Tension Ethanol: glycerol Water: glycerol 40 Slide 41 Air water ( =
0.072 N/m) Air water with detergent ( = 0.025 N/m) Higher surface
tension more rounded Lower surface tension greater instability 41
Slide 42 FURTHER INVESTIGATION 42 Slide 43 An analogous experiment
Jose A. Miranda, Michael Widom: Radial Fingering in a Hele-Shaw
Cell: a weakly nonlinear analysis, Physica D 120(1998) 315-328 43
Slide 44 44 Slide 45 Gap Size h 45 Slide 46 Pressure p 46 Slide 47
Ethanol glycerol Water glycerol 47 Slide 48 Conclusion observed the
phenomenon showed when it does not work explained the mechanism of
emerging patterns 48 Slide 49 pressure surface tension Conclusion
viscosity gap between the plates Proved assumed influences on the
phenomenon:< 49 Slide 50 pressure surface tension viscosity gap
between the plates< 50 Thank you for your attention! Proved
assumed influences on the phenomenon: Slide 51 for your attention !
Thank you 11. Flat Flow Kamila Soukov Slide 52 APPENDIX Slide 53
Changing temperature of glycerol 80C the same patterns Slide 54
Data for experiments Slide 55 Motor oil glycerol ( = 1119,5. 10 -6
m 2 /s)
