Biomedical Engineering Reference
In-Depth Information
Figure 18.
Maximum bouncing height of Leidenfrost drops (
D
0
=
2
.
7 mm) impacting on a polished
aluminum surface heated at 400
◦
C: comparison between water and PEO solutions at various concen-
trations.
mass during rebound. For We
50, no significant differences can be observed be-
tween drops of pure water and viscoelastic drops. On the contrary, for We
>
50 the
maximum height reached by viscoelastic drops is significantly larger than that of
Newtonian drops, irrespective of the drop diameter. These results clearly show that
viscoelastic drops can recover a higher fraction of the initial impact kinetic energy
even if they store less in the form of surface energy.
Neglecting the momentum transferred to the drop by evaporation and the elastic-
ity of the vapor cushion [48] because their effects are similar for both the Newtonian
and the viscoelastic drops at the same impact Weber number, one can write a com-
parative energy balance for two drops (one Newtonian and one viscoelastic) at
maximum spreading after impacting on a hot surface with the same velocity, i.e.,
with the same initial kinetic energy [61]:
E
(
W
)
E
(
W
)
E
(
P
)
E
(
P
)
E
(
P
E
,
+
=
+
D
,
e
+
(6)
S
D
,
e
S
where
E
S
,
E
D
,
e
,and
E
E
denote respectively the surface energy, the energy dissi-
pated during expansion, and the elastic energy stored in the polymer solution, while
the superscripts indicate the water (W) and the polymer solution (P) drops. Since
Fig. 17 suggests that the surface energy of viscoelastic drops is smaller than that of
Newtonian drops, one can write:
E
(
W
)
E
(
P
)
=
+
δ
S
,
(7)
S
S
where
δ
S
is the difference between the surface energies of the two drops, which can
be estimated from the maximum spreading diameter data.
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