152

FLUIDITY AND PLASTICITY

clear that collisional viscosity will increase not only with the
concentration but also with the size of the molecules. If the
particles were mere points, there would be no collisions and
therefore no collisional resistance to flow. On the other hand, if
the molecules completely filled the space they occupy, collisions
would be most rapid and the collisional resistance a maximum.
The discovery of Batschinski, that in unassociated liquids
the fluidity is directly proportional to the free volume, seems to
indicate that collisional viscosity is almost entirely responsible
for the viscosity of ordinary liquids and it must be highly impor-
tant in compressed gases. It is also clear why associated liquids
are exceptional. For the breaking down of association, as by
heating, would doubtless decrease the size of the molecules without
a corresponding decrease in the space which they occupy.
The Mixed Regime.—It has been indicated that in rarefied
gases viscous resistance is certainly diffusional and in very viscous
liquids it is collisional. In fluids at ordinary temperatures and
pressures the viscous resistance is evidently the sum of the
diffusional and the collisional resistances. The total viscous
resistance is in every case given by the equation
M __ M I____ fK>7\
?l — ^Id ~T~ We \& • )
where rjd is the diffusional viscosity and rjc is the collisional
viscosity.
According to Maxwell, as discussed in Chapter XIV, the
viscosity of a gas varies as the absolute temperature, so
rid = BT
where B is a constant. Later experimenters have found that this
formula does not accord with the experimental facts, and they
have therefore given to the temperature T an exponent n with
values varying from the theoretically deduced 0.5 to 1.0. The
discrepancy, however, may be due to the fact that collisional vis-
cosity has been overlooked. For diffusional viscosity we here
assume as a first approximation that n = 1.
We have seen that Batschinski's formula represents collisional
viscosity only, which we may now write in the form
= A
1) — co