PHYSICAL CHEMISTRY IN BRIEF

CHAP. 10: TRANSPORT PROCESSES [CONTENTS] 336

10.3 Flow of momentum—viscosity

10.3.1 Newton’s law

Let us consider a fluid flowing laminarly through a tube in the direction of axisx. In the middle
of the tube, the velocity of the fluid in the direction of the flow is the highest while at the tube
walls it is zero. However, the molecules do not travel only in the direction of the flow but also
in the perpendicular direction, i.e. from the middle of the tube toward its walls and vice versa,
while transporting their momentum. For the flux of momentum it follows from (10.1)

Jz=

1

S

dpx

dτ

, (10.7)

wherepz=mvxis the momentum component in the direction of the flux,mis the molecule
mass, andvxis the velocity component in the direction of the flux. The driving force is the
change of the velocity component in the direction of the flux with the distancez from the
middle of the tube,ddvzx. The general equation (10.3) rearranges to

1

S

dpx

dτ

=−η

dvx

dz

. (10.8)

This equation is calledNewton’s law. The quantityηis theviscosity coefficient, or briefly
viscosity.

Note:Fluids obeying equation (10.8) are called theNewtonian fluids. There is a large

group of substances (macromolecular fluids, suspensions... ) for which relation (10.8) does

not apply, and these are called thenon-Newtonianfluids. Their study is the focus of

rheology.

The derivative on the left side of equation (10.8) is the forceFz

Fz=−S η

dvx

dz

. (10.9)

Fzis called theinternal friction force(acting on the molecule in the direction of the axisz).