106
MOLECULAR
DIMENSIONS
1.
A
parallel
displacement of
all liquid
particles
without
a
change
in
their relative
position;
2.
A
rotation
of
the liquid
without
a
change
in
the relative position
of
the liquid
particles;
3.
A
dilatational
motion
in three
mutually perpendicular
directions
[6]
(the
principal
axes
of
dilatation).
Let
us
now assume
that in the
region
G
there is
a
spherical rigid
body
whose
center
shall lie
at
the
point
x0, y0,
z0
and
whose
dimensions shall
be
very
small
compared
with those
of
the
region
G.
We
further
assume
that the
motion under
consideration is
so
slow
that the kinetic
energy
of the
sphere
as
well
as
that of the
liquid
can
be
neglected.
We
also
assume
that
the velocity
components
of
a
surface
element of the
sphere
coincide with the
corresponding
velocity
components
of
the
adjacent
liquid
particles,
i.e., that the
transition layer
(imagined to
be continuous)
also
displays
everywhere
a
[7]
coefficient of
viscosity that is
not
infinitesimally
small.
It is obvious that the
sphere
simply
takes
part in
the partial
motions
1
and
2,
without
modifying
the
motion of
the
neighboring
particles,
since the
liquid
moves
like
a
rigid
body
in
these partial
motions and
since
we
neglected
the effects
of
inertia.
However,
motion
3
does
get
modified
by
the
presence
of the
sphere,
and
our
next
task
will
be
to
investigate the effect
of
the
sphere
on
this
motion
of
the liquid. If
we
refer
motion
3
to
a
coordinate
system
whose
axes are
parallel
to
the
principal
axes
of
dilatation
and
put
-2~Ø
-yo
-zo
-*
=17
we
can
describe
the
above motion,
if
the sphere
is
not
present,
by
the
equa-
tions
Iuo=Ae
(1)
v0
=
Bri
,
w0
=
C(
;