An order of magnitude calculation is as follows. The kinetic energy is of order
mv^2 (Section 4.3.1), wheremis the mass of the egg andvthe (average) spinning
velocity. The energy dissipation rate would equalZaC^2 per unit volume [Eq. (5.3)].
For one egg this then becomesm?ZaC^2 =r. The time needed for the kinetic energy to
dissipate would be given by kinetic energy over energy dissipation rate. Taking into
account thatC&v=r, whereris the effective radius of the egg, we obtaint&rr^2 =Za.
Taking in S.I. unitsr¼ 103 ;r¼ 0 :015, andZa¼ 0 :1 (i.e., 100 times the value for
water), the result is 2 s, roughly as observed.
Question 2
Consider a semihard cheese that has the shape of a flat cylinder, height 10 cm. It is
put on a shelf and after one month it has gradually sagged to a height of 9 cm; the
shape now is roughly like a flat truncated cone. What can you conclude about the
rheological properties of the cheese?
Answer
Due to gravitation, the cheese is subject to a stress ofrgh, wherer¼mass density,g
the acceleration due to gravity, andhthe height of the cheese above the position
considered. Sagging means flow, and the cheese must thus have been at a stress above
the yield stress it may have. Since the shape of the sagged cheeses is fairly regular,
flow must have occurred even close to—say one cm below—the top surface of the
cheese. This would correspond to a stress of 10^361060 : 01 ¼100 Pa. The yield stress
must thus be below that value. (Actually, an unequivocal yield stress has never
established for semihard cheese.)
The flow of the cheese is largely elongational. The vertical strain after a month
would be about 0.1, and the time needed to achieve this is 1 month& 25? 105 s,
leading to a strain rateðCÞof about 4? 10 ^8 s^1. The average stressðsÞin the cheese
will have been about 10^361060 : 05 ¼500 Pa. Consequently, the apparent elonga-
tional viscosityðs=CÞwould have been of the order of 10^10 Pa?s.
5.2 DIFFUSION
Diffusion is caused by the thermal motion of molecules (and small particles),
which is briefly discussed in Section 4.3.1. The molecules (or particles) can
rotate and translate. This section will be restricted to translational diffusion
in liquids.