19.1  Rheological properties and terminology

Contributed by Jim Oliver
                                 
RHEOLOGY

What is RHEOLOGY ?
RHEOLOGY describes the deformation of a material under the influence of 
stresses. Materials in this context can be solids, liquids or gases. In this 
FAQ we will be concerned only with the rheological properties of liquids.[1]
Perry discusses the some aspects of the behaviour of gases, and Ullmann
discusses elastic solids.

When liquids are subjected to stress they will deform irreversibly and flow. 
The measurement of this flow is the measurement of VISCOSITY. IDEAL liquids 
are very few, whereas non-ideal examples abound. Ideal liquids are : water 
and pure paraffin oil. Non-ideal examples would be toothpaste or cornflour 
mixed with a little water. [2]

What is VISCOSITY ?
VISCOSITY is expressed in Pascal seconds (Pa.s) and to be correct the 
conditions used to measure the VISCOSITY must be given. This is due to the 
fact that non-ideal liquids have different values of VISCOSITY for different 
test conditions of SHEAR RATE, SHEAR STRESS and temperature. [3,4]

A graph describing a liquid subjected to a SHEAR STRESS (y axis) at a 
particular SHEAR RATE (x axis) is called a FLOW CURVE. The shape of this 
curve reveals the particular type of VISCOSITY for the liquid being studied. 
[3]

What is a NEWTONIAN LIQUID ?
NEWTONIAN LIQUIDS are those liquids which show a straight line drawn from the 
origin at 45 degrees, when graphed in this way. Examples of NEWTONIAN liquids 
are mineral oil, water and molasses.  (Isaac NEWTON first described the laws 
of viscosity) [1] All the other types are NON NEWTONIAN.

What does NON NEWTONIAN mean ?
a. PSEUDOPLASTIC liquids are very common. These display a curve starting at 
   the origin again and curving up and along but falling under the straight 
   line of the NEWTONIAN liquid. In other words increasing SHEAR RATE results 
   in a gradual decreasing SHEAR STRESS, or a thinning of viscosity with 
   increasing shear. Examples are toothpaste and whipped cream.
b. DILATANT liquids give a curve which curves under then upward and higher 
   than the straight line NEWTONIAN curve. (Like a square law curve) Such 
   liquids display increasing viscosity with increasing shear. Examples are 
   wet sand, and mixtures of starch powder with small amounts of water. A car 
   may be driven at speed over wet sand, but don't park on it, as the car may 
   sink out of sight due to the lower shear forces (compared to driving over) 
   the wet sand.

There are other terms used which include :

THIXOTROPY - this describes special types of PSEUDOPLASTIC liquids. In this 
case the liquid shows a YIELD or PLASTIC POINT before starting to thin out. 
What this means is the curve runs straight up the y axis for a short way then 
curves over following ( but higher and parallel to ) the PSEUDOPLASTIC curve. 
This YIELD POINT is time dependant. Some water based paints left overnight 
develop a FALSE BODY which only breaks down to become useable after rapid 
stirring. Also: the curve describing a THIXOTROPIC liquid will be different 
on the way up (increasing shear rate) to the way down (decreasing shear rate). 
The area inside these two lines is a measure of it's degree of THIXOTROPY. 
This property is extremely important in industrial products, e.g to prevent 
settling of dispersed solids on storage. [3]

A RHEOPECTIC liquid is a special case of a DILATANT liquid showing increasing 
viscosity with a constant shear rate over time. Again, time dependant but in 
this case _increasing_ viscosity.

Why do some liquids become solid ?
A few special liquids (dispersions usually) display  extraordinary DILATANT 
properties. A stiff paste slurry of maize or cornflour in water can appear to 
be quite liquid when swirled around in a cup. However on pouring some out 
onto a hard surface and applying extreme shear forces (hitting with a hammer) 
can cause a sudden increase in  VISCOSITY due to it's DILATANCY. The 
VISCOSITY can become so high as to make it appear solid. The "liquid" then 
becomes very stiff for an instant and can shatter just like a solid material.

It should be noted that the study of viscosity and flow behaviour is 
extremely complex. Some liquids can display more than one of the above 
properties dependant on temperature, time and heat history.

What are Electrorheological Fluids? ( added by Bruce Hamilton ) 

Electrorheological (ER) fluids change their flow properties when an electric 
field is applied, and are usually dispersions of polarizable particles in an 
insulating base fluid [5]. Their apparent viscosity can change by orders of
magnitude in milliseconds when a fews watts of electrical power are applied.
The shear stress versus shear rate properties of ER fluids vary as a function
of the applied electric field, When an electric field is applied, the fluid
switches from a liquid to semisolid. The particles are usually irregularly-
shaped 0.5-100um and present at concentrations of 10-40% by mass. ER fluids
are dielectric particles in an insulating medium ( such as silicone oil ), 
along with additives ( such as surfactants, dispersants, and possibly a 
polar activator ). ER fluid effectively function as leaky capacitors. The 
electric field can be either AC, pulsed DC, or DC, with AC producing less 
electrophoresis of particles to electrodes.

There are two categories of ER particulate materials, extrinsically 
polarizable materials ( which require a polar activator ), and intrinsically 
polarizable  materials. Extrinsically polarizable materials can be polar 
nonionic compounds ( such as silica, alumina, or polysaccharides ), or polar 
ionic materials ( such as the lithium salt of polymethacrylic acid ), 
Intrinsically polarizable materials provide simpler systems - because a polar
activator is not required, and they have a lower thermal coefficient of
conductance. The most common examples are the ferroelectrics like barium
titanate (BaTiO3 ) and polyvinylidene difluoride, however their performance
has been poor, as has been that of metal powders  ( such as iron and 
aluminium - even when coated with an insulating layer ), and research is 
concentrating on conducting polymers ( such as polyanilines and pyrolysed 
hydrocarbons ) [5,6].

The ability to utilise computer-based electrical switching to control ER
fluid properties has resulted in vehicle suspension and industrial vibration 
control as major target applications for ER fluids. Demonstration systems
have been built, and they match performance predictions, however cost and
durability issues still have to be solved [7].  

19.2  Flammability properties and terminology 

There are several properties of flammable materials that are frequently
reported. It should be remembered that most discussions concerning
flammable liquids usually consider air as the oxidant, but oxygen and 
fluorine can also be used as oxidants for combustion, and they will result
in very different values. 

The flammability limits in air are usually reported as the upper and lower 
limits ( in volume percent at a certain temperature, usually 25C ), and 
represent the concentration region that the vapour ( liquid HCs can not burn ) 
must be within to support combustion. Hydrocarbons have a fairly narrow range, 
( n-hexane = 1.2 to 7.4 ), whereas hydrogen has a wide range ( 4.0 to 75  ).

The minimum ignition energy is the amount of energy ( usually electrical ) 
required to ignite the flammable mixture. Some mixtures only require a very 
small amount of energy (eg hydrogen = 0.017mJ, acetylene = 0.017mJ ), 
whereas others require more (eg methanol = 0.14mJ, n-hexane = 0.29mJ, 
diethyl ether = 0.20mJ, acetone = 1.15mJ, dichloromethane = 133mJ @ 88C ),
and some require significant amounts, (eg ammonia = >1000mJ ).  

The flash point is the most common measure of flammability today, especially
in transportation of chemicals, mainly because most regulations use the flash
point to define different classes of flammable liquids. The flash point of a
liquid is the temperature at which the liquid will emit sufficient vapours
to ignite when a flame is applied. The test consists of placing the liquid
in a cup and warming it at a prescribed rate, and every few degrees applying
a small flame to the air above the liquid until a "flash" is seen as the
vapours burn. Note that the flame is not applied continuously, but is
provided at prescribed intervals - thus allowing the vapour to accumulate.

There are a range of procedures outlined in the standard methods for 
measuring flash point ( ASTM, ISO, IP ) and they have differing cup 
dimensions, liquid quantity, headspace volume, rate of heating, stirring 
speed, etc., but the most significant distinction is whether the space above 
the liquid is enclosed or open. If the space is enclosed, the vapours will be 
contained, and so the flash point is several degrees lower than if it is 
open. Most regulations specify closed-cup methods, either Pensky-Martens 
Closed Cup or Abel Closed Cup. It is important to remember that these methods 
are only intended for pure chemicals, if there is water or any other volatile 
non-flammable compounds present, their vapours can extinguish or mask the 
flash. For used lubricants, this may be partially overcome by using the TAG 
open cup procedure - which is slightly more tolerant of non-flammable 
vapours. A material can be flammable, but may not have a flash point if other
non-flammable volatile compounds are present. For alkane hydrocarbons, flash 
point increases with molecular weight.

There is an older measure, called the fire point, which is the temperature 
at which the liquid emits sufficient vapours to sustain combustion. The fire
point is usually several degrees above the flash point for hydrocarbons. 

The minimum autoignition temperature is the temperature at which a material 
will autoignite when it contacts a surface at that temperature. The procedure
consists of heating a glass flask and squirting small quantities of sample
into it at various temperatures until the vapours autoignite. The only 
source of ignition is the heat of the surface. For the smaller hydrocarbons 
the autoignition temperature is inversely related to molecular weight, but it
also increases with carbon chain branching. Autoignition temperature also
correlates with gasoline octane ratings ( refer to Gasoline FAQ available in
rec.autos.tech, which lists octane ratings and autoignition temperatures for
a range of hydrocarbons.) 
                     Flash Point    Autoignition   Flammable Limits 
                                    Temperature     Lower     Upper
                       ( C )           ( C )        ( vol % at 25C)
methane                -188             630          5.0      15.0
ethane                 -135             515          3.0      12.4
propane                -104             450          2.1       9.5
n-butane                -74             370          1.8       8.4
n-pentane               -49             260          1.4       7.8
n-hexane                -23             225          1.2       7.4
n-heptane                -3             225          1.1       6.7
n-octane                 14             220          0.95      6.5
n-nonane                 31             205          0.85       -
n-decane                 46             210          0.75      5.6
n-dodecane               74             204          0.60       -             
n-tetradecane            99             200          0.50       -
          
19.3  Supercritical properties and terminology? 

Supercritical fluids have some very unusual properties. When a compound is
subjected to conditions around the critical point ( which is defined as
the temperature at which the gas will not revert to a liquid regardless how
much pressure is applied ), the properties of the supercritical fluid become
very different to the liquid or the gas phases. In particular, the solubility
behaviour changes. The behaviour is neither that of the liquid or that of the 
gas. The transition between liquid and gas can be completely smooth.

The pressure-dependant densities and corresponding Hildebrand solubility 
parameters show no break on continuity as the supercritical boundary is 
crossed. Physical properties fall between those of a liquid and a gas. 
Diffusivities are approximately an order of magnitude higher than the 
corresponding liquid, while viscosities are an order of magnitude lower. 
These properties ( along with low surface tension ) allow SCFs to have 
liquid-like solvating power with the mass transport characteristics of 
a gas.

Potential Supercritical Fluids
Compound          Critical      Critical      Density
                 Temperature    Pressure
                   ( C )        ( bar )      (g cm^-3)
Ammonia            132.4         112.8        0.235
Carbon dioxide      30.99         73.75       0.468
CFC-12             111.8          41.25       0.558
Dimethyl ether     126.9          52.7        0.271
Ethane              32.4          49.1        0.212  
HCFC-22             96.15         49.90       0.524
HCFC-123           183.68         36.62       0.550
HFC-116             19.7          29.8        0.608
HFC-134a           101.03         40.57       0.508 
Methanol           240.1          83.1
Nitrous oxide       36.4          72.54       0.453
Propane             96.8          42.66       0.225
Water              374.4         227.1
Xenon               16.6          58.38       1.105   

Nitrous oxide is seldom used because early researchers reported explosions.
Note that using liquid CO2 at pressure ( as for the commercial extraction
of hops ) is still just liquid CO2 extraction, not supercritical CO2 
extraction. There are several good general introductions to supercritical
fluids [8,9,10]

19.4  Formation of gaseous bubbles in liquids

Discussions about the behaviour of dissolved gases in liquids, especially 
when discussing carbonated beverages, are usually more appropriate in 
sci.physics and/or sci.mech.fluids, and there is a good text available [11]. 

Section 23.9 of this FAQ lists the change in solubility with temperature 
for common atmospheric gases in water at near-ambient pressure. As the 
temperature increases, the solubility decreases, creating a supersaturated 
solution that can result in bubble formation. A similar effect occurs if the 
pressure is reduced. The formation of bubbles can be understood in 
thermodynamic terms using the Gibbs free energy of the bubble.

Gibbs free energy = -n * R * T ln(C/Cs) + gamma * A

  A      =  Surface area of the bubble.
  C      =  Concentration of gas in the liquid, 
  Cs     =  Concentration of gas in the liquid at saturation, 
  gamma  =  Interfacial tension between the gas and the liquid 
  n      =  Number of moles of gas in the bubble
         =  (P*V)/(R*T), where P = pressure, and V = volume of a sphere.
  R      =  Gas Constant 
  T      =  Temperature

After inserting the expressions for the surface area of a sphere (r = radius) 
and number of moles, and differentiating, then we obtain:-

  r(mininum) = 2 * gamma / ( P * ln(C/Cs))

This describes the size of a bubble that would continue to grow under the 
existing conditions, rather than redissolve. Of course, the expression 
assumes homogeneous precipitation of the bubble, and in real life most 
bubbles are created heterogeneously. Statistics and kinetics are also 
required to determine the rate of formation of bubbles, and predict the 
effect of changing parameters such as temperature. As the liquid is warmed, 
bubbles may be created faster, as the higher temperatures overcome the 
activation barrier - which is the difference between the Gibbs free energy 
when r is less than r(minimum), and the Gibbs free energy at r(minimum). 

The formation of a bubble also dramatically perturbs the system, even 
causing secondary bubbles to form. Secondary bubble formation may be 
implicated in the production of copious quantities of froth from shaken, 
quickly-opened, carbonated drink containers. The sites for gaseous bubble 
formation in supersaturated drinks are typically small particles, or minor 
flaws on the smooth surface of the container.  

19.5  Why is Mercury a liquid at room temperature?.

First, let's look at the melting points of some of the elements surrounding
mercury in the periodic table ( in degrees C ) :-
Period             IB             IIB            IIIA                  
4s3d4p           Cu  1083       Zn  419.5      Ga   29.8         
5s4d5p           Ag   960.8     Cd  320.9      In  157
6s(4f)5d6p       Au  1063       Hg  -38.4      Tl  304

The interesting comparison is between Hg and Au, as their properties differ
dramatically, although their electron structures are similar:-
                    14    10    1 
  Au(g)  :   Xe | 4f  , 5d  , 6s
79         54   
                    14    10    2
  Hg(g)  :   Xe | 4f  , 5d  , 6s 
80         54

Very few chemistry textbooks discuss relativistic effects on chemical
properties, despite the availability of a comprehensive review by P.Pyykko 
[12]. There several good introductory articles on the derivation and 
calculation of various relativistic effects in molecules and atoms, so I'm 
not going to include details [13,14,15].  Suffice to say, that whilst 
smaller elements can treated simply, larger elements need treatment based 
on the Dirac equation, which shows that the s electrons are approaching
the speed of light, consequently relativistic effects are important. 
If we take the relativistic mass of mercury (m);-
                                
                   Mo                  where      
 m   =   --------------------          c (speed of light) = ~137 atomic units
              _____________            v = Z = 80 
             /     ( v ) 2             Mo = rest mass
            /  1 - ( - )
          \/       ( c )

The masses of the 1s electrons are increased by approximately 20% over 
their rest masses, which means that the radius is decreased by 20% - since
mass appears in the denominator of Bohr radius calculations. All the other
s shells also contract, with the 6s contracting ~14%, because their electron 
speeds near the nucleus are comparable, and the contraction of the inner part 
of the wave function also pulls in the outer tails. The p orbitals also 
contract a similar amount, and these contractions also results in increases 
the screening for d and f orbitals, which may then expand - about 3% for the 
5d orbital of mercury. 

In mercury, the relativistically-contracted 6s2 orbital is full, thus the
the two electrons do not contribute much to the metal-metal bond, which is
not the situation for gold. The bonding in mercury is believed to be mainly 
van der Waals forces with a contribution from 6p orbital interaction. The 
relativistic contraction of the filled 6s2 orbital, when added to the 
contraction across the sixth row of the periodic table, results in relatively
weak Hg-Hg bonds that are responsible for mercury being a liquid at room
temperature. For those curious to know more, a recent article in J.Chem.Ed. 
provides much more detail and several good references [16]. Relativistic 
effects are also responsible for the colour of gold ( partially explained 
by the 5d -> 6s transition in gold requiring less energy than the 4d -> 5s 
transition in silver, resulting in a smaller d-s gap ) [12,14,16].