Chapter 6. The surface phenomenon of liquid

1
Chapter 6. The surface phenomenon of liquid

• Applications to life science

2
Summary to the last chapter

• Momentum and mass
• kinetic energy, rest energy and Total energy

3
1. Two postulates (Equivalent principle For
all physical processes, the reference frame with
uniform acceleration is equivalent to the local
region of gravitational field and the inertial
force is equivalent to the local region of
gravitation. General relativity principle
Physics law has the same form in all reference
frames, no matter inertial or non-inertial.) 2.
Space and time in general relativity 3.
Gravitational collapse and Black hole
4

• Sphere (??), spherical (???),boundary, border
• Curvature radius (????), anisotropic
• metal frame (???), tensional pellicle
• convex (???), concave (???)
• contact angle (???), lotus leaf ()
• Capillary (???), capillarity (?????)
• embolism (??), cohesion ???
• force of adherence ???, transfuse (??)
• vein (??), syringe (???)

5

• Macro-objects (????)
• microstructure (????)
• gravitational and repulsive (???????)
• isotropic (?????), anisotropic
• Boundary (???),border , edge
• pellicle ??, film
• Alveolus , alveoli /ælvi?l?i/ n ??

6
6.1 The micro-structure of matter
Macro-objects consist of a great number of
molecules or atoms which are all micro particles.
These particles also have physical quantities
such as sizes, mass, velocity and energy. The
molecules or atoms in macro objects are
permanently and irregularly in motion. Such a
motion which contains a large number of molecules
or atoms is called thermal motion.
7
It is well known that matter has three kinds of
states gas, liquid and solid. Liquid and solid
are called condensed matter as they are hardly
compressible. There exists interaction force
between molecules. The solid and liquid that can
be formed explains that the gravitational force
exists between molecules. On the other hand,
solid and liquid cannot be further compressed and
this means that the repulsive force exists among
molecules. What is the relation between them and
in what distance the gravitation dominates the
system and in what distance the repulsive force
controls the system?
8
The gravitational and repulsive force among
molecules is totally called Molecular Force.
According to experiments and the analysis of the
modern physics theory, the molecular force can be
expressed as
Gravitational elastic potential
9
where C1, C2, m and n are constants. As m and n
are quite big and m gt n , the molecular force is
short-distance force. r0 10-10 m. When r gt r0,
r is between 10-10 10-8 m. The above formula is
semi-experienced one. The four parameters in this
formula are determined by experiments. The
positive term express repulsion with m between
915, and the negative term denotes gravitation
with n between 47.
10
6.2 Thermal properties of matter
1. Equation of state for ideal gases
Where R 8.314 Jmol K-1, it is the universal
gas constant or mole gas constant. ? is the mass
of one mole molecules and M is the mass of gas in
container with unit of kg, V is the volume of the
container with units of m3, P is the pressure
with units of N m-2.
11
2. The model of the ideal gas (1). The size of
molecules can be ignored comparing with the
average distance between two molecules. (2). The
interaction forces between molecules and the wall
of container could be ignored except the
right-time of collision. (3). All collisions are
elastic (4). Ignoring the gravity suffered by
molecules
12
3. The pressure formula of ideal gases
Where
is the average translational kinetic energy
(?????), n is the number of molecules per unit
volume and m is the mass of one molecule.
13
4. The energy formula of ideal gases
As
14
is Avogadro constant.
is Boltzmann constant.
n is the number of molecules in unit volume.
15
5. The laws of ideal gases (1). Avogadro law
This law means that at the same temperature and
the same pressure, the number of molecules
contained in the same volume are the same. And
also the pressure is relative to the temperature.
16
(2). Doltan law
Suppose that there are many kinds of molecules in
one container and the number of molecules per
unit volume are n1, n2, respectively, The
average translational kinetic energy are the same
for all kinds of molecules and this means that
17
Where P1, P2, P3 are the pressures respectively
for that kind of molecules to be present alone in
the container. This is called Doltans law of
partial pressures.
Example 6-1 (page 110 in Chinese-text book)
Finished here on Friday!
18
Summary to the last chapter

• Momentum and mass
• kinetic energy, rest energy and Total energy

19
3. Two postulates (Equivalent principle For
all physical processes, the reference frame with
uniform acceleration is equivalent to the local
region of gravitational field and the inertial
force is equivalent to the local region of
gravitation. General relativity principle
Physics law has the same form in all reference
frames, no matter inertial or non-inertial.) 4.
Space and time in general relativity 5.
Gravitational collapse and Black hole
20
6 The microstructure of matter 7 The thermal
properties of matter Equation of state for
ideal gases
The model of the ideal gases (ignoring size,
interaction moment, elastic collisions, ignoring
gravity)
21
8. The pressure formula of ideal gases
9. The energy formula of ideal gases
22
10. The laws of ideal gases (1). Avogadro law
(av?gadr ?u/ )
(2). Doltans law of partial pressures
23
New today
(3) Boltzmanns energy distribution law
In the gravitational field, molecules not only
have kinetic energies, but also potential
energies. The number of molecules per unit volume
is followed by Boltzmanns energy distribution
law
Where n is the number of molecules per unit
volume and n0 is the number for Ep 0.
24
As the pressure is proportional to the number of
molecules per unit volume and Ep mgh. So we
have
Therefore
Where P0 is air pressure at the sea level, P is
the pressure at a height of h.
25
6.3 Surface tension (??) and surface energy

• The distance between molecules in a liquid is
  much shorter than in a gas, and the force between
  molecules increases obviously.
• A liquid molecule may move in every direction
  and this is isotropic (?????). However, on a
  boundary (??) of liquid, the properties of
  molecules are not isotropic and are quite
  different.

26

• In this section, we mainly discuss the process
  related to life science, surface tension and its
  effect.
• The surface of a liquid acts as a tensional
  (????) film which always tends to contract (??)
  to a minimum area. It proves that surface of
  liquid has tension (??). It is called surface
  tension (????).

27
1. Surface tension It is known that the
equivalent (???) distance between two molecules
is denoted by r0 which is about 10-10 m in
length. Generally speaking, when the distance
between two molecules, denoted by d, is less
than r0, the force between the two molecules is
repulsion (??) and when the distance between two
molecules
28
is larger than r0, the force between them should
be gravitation (??). However, when d gt 10-9m,
the gravitation between two molecules can be
taken as zero. Only if a molecule is in the
sphere of radius of 10-9 m, it can be gravitated
by the center of molecule. This sphere is called
molecular action sphere, we draw a thin layer on
the surface of a liquid. The thickness of the
layer is equal to the radius of the molecular
action sphere and the layer is called surface
layer.
29
The molecules in the surface layer and those in
the liquid experience different applied forces.
In liquid, the molecules are gravitated by their
neighbor molecules in all directions and the
total force for each molecule is zero, while the
molecules in the surface layer have different
gravitations in different directions.
The direction of total force acting on the
molecules in the surface layer is perpendicular
to the surface layer, pointing to the inside of
the liquid.
30
So generally, the total forces point to the inner
liquid. Due the total forces, the surface is in
tension. This is so-called surface tension. At
the same time, the gravitational force (??) is
balanced by the repulsive force (??) of nearby
molecules. So the molecules can stay on the
surface. If we want to move the lower molecules
to the surface, we have to do some work opposing
the gravitation from lower molecules. Therefore
the potential energy of molecules increase.
Obviously, the molecules on the surface layer
have higher potential energy than the molecules
in the inner liquid.
31
As any system always tends to (???) the smallest
potential energy, the molecules on the surface
tend to move into the liquid. Then the surface
area will reduce (??) to minimum. Contrarily, if
we want to increase the surface area, we have to
do work to move molecules to the surface while
the potential energy of the surface also
increases.
32
2. Surface energy (???)
The work done by increasing a unit area of liquid
surface is called surface energy.
Surface tension F can be described by the surface
tension coefficient (??????) ?. The relation
between them is
where L is the length of a line on the liquid
surface.
33
You can imagine (??) that there are two forces
(surface tensions) pulled (?) from both sides of
the line. ? ( Ftension/L) expresses the surface
tension per unit length. It is found that
different liquid has different ?, higher
temperature corresponds to (???) lower value of
?. Lets see the relationship between the
magnitude of surface tension and surface energy.
34
Look at the diagram. ABCD is a metal frame (???)
with a layer of liquid film (or pellicle ??). The
length of BC is L and it can move freely.
However,
the pellicle tends to contract, so there should
be a force F to pull BC. As there are two
surfaces of the pellicle, twofold (???) surface
tensions act on BC. Therefore, we have
35
Lets have a look at the relationship between ?
and surface energy. Assume that BC moves a short
distance because of Fpull. The surface area of
film increases
The work done by applied force is
This work should be the potential energy
increased on the film. So the potential energy
increased per unit area on the surface of the
film should be
36
So surface tension coefficient ? can be defined
as the increased potential energy per unit
increased area or the work done by increasing
each unit area.
37
6.4 The additional pressure under a curved surface
Surface of liquid is similar to a layer of
tensional pellicle (??????). If a surface is
horizontal, the surface tension is also
horizontal as it always along the tangential
direction (????) of the curved surface (??). If
a surface is convex (???), the surface tension
tends to pull the surface flat. Therefore the
surface tension will put an positive additional
pressure on the liquid under the surface.
38
Contrarily (??), if the surface is concave (???)
a negative additional pressure acts on the liquid
under the surface, that is, the pressure is lower
under the curved surface. This pressure change
can be worked out by calculating the pressure
difference between the inner and outer of the
liquid surface.
It can be calculated that
39
Tension T is the tension per unit length. That is
?. So the total force downwards is
Rsin?
?
R
T
Tsin?
Total force upwards for the same volume is
40
This is the formula for spherical (???) liquid
surface. Where R is the curvature radius (????)
of liquid surface. If the surface is convex
(???), ?p is positive and inner pressure is
greater than the outer pressure. However, if the
surface is concave (???), p is negative and the
outer pressure is greater than the inner
pressure. ?P is called the additional pressure
under the curved surface of liquid. Lets have a
look at the spherical (???) film which have the
inner and outer surface layers.
41
As the pressure is inversely proportional (??) to
the curvature radius, the pressure at point a, b
and c should have the following relations.
and
42
For a very thin film, the R1 should be equal to
R2 and they are all equal to R. so difference of
the pressure of inner and outer liquid surface
can be obtained as
Draw a graph, explain experiment. See next.
A simple experiment can explain the additional
pressure of spherical film. There are two bubbles
at two ends of a tube, one is bigger and the
other is smaller. There is a valve in the center
of the tube.
43
If we open the valve, the big bubble will be
getting bigger and bigger and the small one will
be getting smaller and smaller because the
additional pressure in the small bubble is
greater than the big one. This is very important
for us to know breath and the physical properties
of alveolus (??).
44
Example 6-1 Blow a bubble of diameter 10cm and
its surface tension coefficient is 40?10-3 N/m,
Calculate (1) Work done by blowing the bubble
(2) Pressure change of inner and outer of the
bubble.
45
Solution (1) According to the conservation
principle, work done during the process of
blowing the bubble should be equal to the surface
change of the bubble. On the other hand, no
matter how thin the bubble is, it has two
surfaces, therefore
46
(2) The pressure change of inner and outer of the
bubble can be calculated using the additional
pressure formula obtain previously as
The inner pressure of the bubble should be bigger
than the outer pressure. The difference is
related to the surface tension of the bubble. In
such a case, the difference of the two surface
areas is ignored.
47
6.4 Capillarity (?????) and air embolism (??)
1. Contact angle When liquid contacts with solid,
liquid can wet solid sometimes but not always. As
you know, water can wet many materials but not
lotus leaf (??). This phenomenon depends on
whether the force between liquid molecules (force
of cohesion ???) is less or greater than the
force between liquid and solid molecules (force
of adherence ???).
48

• Liquid wets the solid.
• If the force of cohesion (???)between liquid
  molecules is smaller than the force of adherence
  between solid and liquid molecules, the boundary
  of liquid and solid tends to enlarge. A drop of
  liquid outspreads a layer of pellicle.
• liquid can not wet solid.
• Contrarily if the force of cohesion is greater
  than the force of adherence, the boundary tends
  to contract or reduce.

49
The boundary angle between solid and liquid is
called contact angle. This angle is defined that
the angle crosses the area which should contain
liquid. The size of the contact angle depends on
the force of cohesion and adherence. Usually we
have
We know that bigger adherence corresponds to
smaller contact angle. Liquid can wet solid. In
this case ? lt 90?. When ? 0, liquid can wet
solid completely.
50
Note that the contact angle of 90? is impossible
as in such case, cohesion has to be equal to
adherence and however, such a case can only
happen when the solid and liquid is the same
material. For the 90? lt ? lt180?, liquid cannot
wet solid. When ? 180?, liquid cannot wet solid
at all. (finished here from Boltzmanns energy
distribution law)
51
2. Capillarity The tube with very short diameter
is called a capillary tube. When a capillary tube
is put in a liquid, the liquid surface in it will
change. If liquid can wet the wall of the
capillary tube, the liquid surface in the tube
will go up and if the liquid cannot wet the wall,
the surface will go down. This phenomenon is
called capillarity. Lets have a look at the
case of liquid surface going up.
52
The liquid surface in the tube can be taken as
part of a spherical surface. Because the surface
in the tube is concave, the pressure in the tube
under liquid surface is lower than the pressure
out of liquid (atmospheric pressure).
53
From the figure, we know
Where r is the radius of the tube, R is the
curvature radius of the liquid surface, ? is the
contact angle. The pressure change of inner and
outer liquid is


It is such a pressure that raises the liquid
surface in the capillary tube and it is pointing
upwards.
54
In a balance state, the pressure at point B
should be equal to the pressure at point C which
is atmospheric pressure P0. So
Where p0 is atmospheric pressure, h is the height
of the liquid surface in the tube, ? is the
density of liquid. The above equation can be
solved as
55
Therefore the height of liquid in a capillary
tube is proportional to the surface tension
coefficient, and is inversely proportional to the
inside radius. This means that smaller inside
diameter corresponds to higher liquid surface in
a capillary tube. For the opposite situation,
the liquid in a capillary tube is lower and
convex. The pressure in liquid is greater than the
56
atmospheric pressure. Now ? is greater than ?/2
and the formula we obtained can be still used.
The height h is negative in such a case and this
means that the surface in the capillary tube is
lowering down. Capillarity is a common
phenomenon in our daily life, such as absorption
and transportation of water in plant (??), blood
flowing in the capillary blood vessel (??)and so
on.
57
3. Air embolism (????) When liquid flows in a
capillary tube. liquid will
be blocked if there are bubbles in the tube. This
phenomenon is called air embolism. In figure (a),
there is a bubble in a tube containing liquid.
When the pressure at the left of the bubble is
equal to the pressure from right, the two concave
curvatures of the bubble are the same. So there
are the same magnitude additional pressure on two
curved surfaces but in opposite directions. The
liquid will not flow.
58
The pressure in the bubble is the same but
additional pressure caused by the surface tension
might not be the same if they have different
curvature radius. In such a case, the pressures
pushing to the right and left are given
respectively as
59
For the case shown in figure (b), if the pressure
on the left increases ?p, the radius of bubble on
the left will increase and the radius on the
right will decrease. if the bubble can move, the
necessary condition should be
60
In real case, there are some frictions between
the liquid and the wall of the tube. The
sufficient and necessary condition of the bubble
moving is generally
61
That is, the pressure change on two sides of the
tube is greater than a critical value ?. The
critical value ? depends on properties of liquid,
wall of tube and radius of the capillary tube. If
there are n bubbles in the tube, the pressure
difference between the two ends of the tube has
to be greater than n times ?.
62
When we transfuse (??) patients, we have to avoid
air embolism in the transfusing tube. Especially,
we have to avoid an air bubble in the syringe
(???) when injecting veins (??), otherwise the
air embolism might occur.
63
6.5 The surface active agent and the surface
absorption
Surface tension of solution (??) changes with
variation of solute (?? a substance is dissolved
in another substance.) Some solutes can decrease
surface tension of solution and some can increase
surface tension. The former is called
surface-active agent (??????) and the latter is
called non-surface-active agent. (solution
solute solvent )
64
The surface-active agent is called surfactant
(?????) or a wetting agent. For example, organic
acid (???) and soap are active agent of water
salt and gluside (??) are non-active agent of
water. When the surface-active agent dissolves
(??) in solvent (??, the liquid in which another
substance (solute) is dissolved to form a
solution), the attraction of solvent molecules is
greater than attraction between solvent molecule
and solute molecule.
65
In such a case, solvent molecules in the surface
layer tend to move into the liquid because the
greater attractions between solvent molecules.
The solvent molecules move into the liquid as
much as possible as in this way, the surface
energy will be lower and the system will be more
stationary. In the surface layer, the solute
molecules will increases in order to stabilize
the system.
66
Since the solute molecules concentrate in the
surface layer of solution, a little bit of active
substance can influence the properties of the
surface and decrease the surface tension. In some
situations, the surface layer of the solution
consists of solute molecules only and it can
extend larger and larger. This phenomenon is
called surface absorption. For example, the oil
film spreads over water.
67
Contrarily, when a non-active agent is dissolved
in a liquid, its molecules tend to leave the
surface layer and move into solution. The surface
tension in this case does not change very much
and most of the solute molecules are mainly
stayed in the solvent. Surface-active agent plays
a very important role in respiration.
68
All these alveoli form a cystiform (???) air
chamber. As the alveoli do not have the same size
and some of them are connected. Generally
speaking, as the surface tension in the lungs are
the same and the pressure in the small alveolus
is bigger than that in big alveolus. The air in
the small alveolus will go into the big ones. But
such a case is not happened as the theory
predicts because the surface-active agent exists
in lungs. In lung, bronchus was divided into a
great number of tiny bronchi. At each of the tiny
bronchus, there forms an alveolus.
69
Lets consider a process of a respiration. There
is a same amount of surface-active agent (SAA) in
lungs. When inhaling, the alveoli becomes larger
and less SAA on the alveoli and the surface
tension will be getting larger. Therefore, this
limits the enlargement of alveoli. On the other
hand, breathing out (exhaling), the alveoli
cannot become much smaller as more SAA will
accumulate on the surface of the alveoli and
reduce the surface tension of the alveoli. This
will help the next time inhaling very much and
will make the respiration process easier.
70
Summary to the last lecture

• 6.1 The microstructure of matter
• 6.2 The thermal properties of matter
• Equation of state for ideal gases

2. The model of the ideal gases (ignoring size,
interaction moment, elastic collisions, ignoring
gravity)
71
3. The pressure formula of ideal gases
4. The energy formula of ideal gases
72
5. The laws of ideal gases (1). Avogadro law
(av?gadr ?u/ )
(2). Doltans law of partial pressures
73
6.3 surface tension and surface energy 1.
Surface tension (surface layer)
2. Surface energy (???)
Surface tension F can be described by the surface
tension coefficient (??????) ? is defined as that
Where F is the surface tension, L is the
considered length on the surface of liquid.