Download An example of the importance of the Le-Chatelier

An example of the importance of
the Le-Chatelier-Braun Principle
in macroscopic physics:
The rheology
I. Santamaria-Holek
UMJ-Faculty of Sciencies,
National University of Mexico.
Juriquilla, Queretaro
UTP-Bydgoszcz, December 6, 2010
LeChatelier-Braun principle
Is the basis of the theory of transport processes.
Heat conduction (Fourier law), mass diffusion (Fick law),
thermoelectricity, piezoelectricity, rheology, etc.
Any process taking place in a macroscopic (thermodynamic)
system as a consequence of the action of an external force
is always directed to reduce the effects of such an action.
An example: Momentum transport and viscosity
-Imagine a fluid composed by particles. In equilibrium, one can imagine that
these particles move in directions parallel or perpendicular to some planes
arbitrarily defined in the fluid.
-These planes are very useful to define two important forces in fluid mechanics:
The pressure (perpendicular) and the shear stresses (parallel).
- When a shear force is applied on a liquid, it produces the relative motion
between different fluid planes.
The degree of movement is characterized by the fluidity.
The resistence to move is due to the viscosity.
F
When the force is applied on plane 1,
then it will move faster than plane 2:
Momentum transfer from 1 to 2.
1
2
The viscosity is the measure of this
momentum transfer between planes
The measure of viscosity is the central problem of Rheology
Quantifying the LeChatelier-Braun principle
Newton law for viscous flows: The force F opposing to the relative motion
of two fluid liquid planes is proportional to the area A and to the
velocity gradient dv /dx
∂
∆v
F ≡ ηA
v  x,t ≈ ηA ,
∂x
∆x
Aplicable to laminar flows
F
1
Viscosity coefficient
MKS
CGS
[kg / m s]
[g / cm s]
2
Rheology and rheometry
In order to measure the viscosity one uses
the so-called rheometers.
Flow rheometers, rotational or ball rheometers.
Flow rheometer:
-A pressure difference is established in the tube
-One measures the flow of liquid as a function of
time (the volume of liquid as a function of time)
Poiseuille equation
4
dV πR  P 2 − P1 
=
dt
8 ηl
 
πR  P 2 − P1  dV
η=
8l
dt
4
−1
What is rheology?
The word rheology comes from the Greek word for flow, rheo, and
–ology, meaning study of. The study of the mathematical
relationships that describe the behavior of non-Newtonian fluids are
called rheologists
Rheology is principally concerned with extending the "classical"
disciplines of elasticity and (Newtonian) fluid mechanics to
materials whose mechanical behavior cannot be described with the
classical theories.
Colloidal materials, sols, gels, synthetic rubbers and polymer solutions
Why is important rheology?
Rheology has applications in materials science engineering,
geophysics, physiology, human biology and pharmaceutics.
Materials science is utilized in the production of many industrially
important substances such as concrete, paint and chocolate have
complex flow characteristics.
Blod is a non-Newtonian viscoelastic fluid!
The Poiseiulle equation is not valid!!
What happens if we add particles or cells or polymers to a fluid?
THE VISCOSITY INCREASES!!
BUT HOW?!
Viscosity of the continuum phase
Viscosity of the dispersed phase
As always... Einstein...
Einstein calculated the first correction to the viscosity of a fluid
with particles suspended in it. A particle suspension
Hard sphere suspensions
Taylor
Emulsions
But Einstein and Taylor relations are not valid in general...
Generalizations of the fundamental formulas: The high
concentrated regime
During the last century, a large amount of work has been devoted to generalize
Einstein´s and Taylor’s results. Many theoretical, semi-empirical and empirical
formulas have been found and postulated to account for the viscous response of
these systems in the high concentrated regime
Saito
Phan, Pham 1997
Bedeaux et al.
Pal 2001
Krieger, Dougherty
Quemada
In general, all these expressions reproduce well
the behavior of the viscosity as a function
of in a single regime, low or highly concentrated,
but all of them fail in the other one
The better relations for viscosity of solid
and liquid particle suspensions... nowadays...
Relative viscosity for low (black) and high (red) shear rates
Symbols: Experiments;
Lines: Theory
C. G. de Kruif, et al, J. Chem. Phys. 83, 4717 1985
I. M. Krieger, Adv. Colloid Interface Sci. 3, 111 1972.
M. Krieger, Adv. Colloid Interface Sci. 3, 111 1972.
F. L. Saunders, J. Colloid Sci. 16, 13 1961.
M. Kops-Werkhoven et al , J. Chem. Phys. 77, 2242 1982.
Dashed line: C. W. J. Beenakker, Physica A 1984
Suspensions of solid particles
Master curve of the effective viscosity as a function of eff .
All the experimental data used for comparison colapse showing that
eff is the correct scaling variable
1.0
Equation (5)
[η(φ)/η0]
-2/5
0.8
0.6
0.4
0.2
0.0
0.0
0.2
0.4
φ eff
0.6
0.8
1.0
Emulsions of nearly spherical droplets
In the case of spherical droplets, the corresponding expression and results
from the
Improved recursive differential method are:
Comparison: Exp/Present model/Pal model
Pal-s model, 2001
So, for any rheological ocassion don't
forget to use the MAGICAL FORMULA
Carlos I. Mendoza, ISH, J. Chem. Phys. 130, (2009)
ISH,Carlos I. Mendoza , J. Coll. Int. Sci. 346 (2010)
Thank you for your attention