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(

;