Surface and Interface Chemistry

Rheology

Valentim M. B. Nunes

Engineering Unit of IPT

2014

Rheology: Study of deformation and flow of matter

The rheological studies allow to characterize colloid systems, namely colloidal dispersions and emulsions. The technological importance of rheology is manifest in areas such as rubbers, paints, textiles, pulp, etc.

The rheological behavior depends on :

Viscosity of the dispersant phase

Concentration of particles

Particle size and shape

Molecular interactions

Rheo = Deformation Logia = Science or Study

Importance of the rheological studies (examples)

Production of paint: the paint should be easy to spread and do not seeping through the walls.

Cosmetics and hygiene: how a cream spreads or the time it took to flow from a recipient.

Stability of emulsions or suspensions.

Viscosity: the viscosity of a liquid measures the resistance offered to flow. A liquid is Newtonian when the tangential force per unit area between two parallel planes of fluid is proportional to the velocity gradient.

D

Viscosity coefficient.

Methods of measurement

Capillary method (Ostwald, Ubbelohde)

tk

22

11

2

1

t

t

Rotational method (Couette viscometer)

Particularly useful for non-Newtonian fluids.

k

- angular velocity of the outer cylinder.

- angular deflection of the inner cylinder.

Viscosity of dilute solutions and colloidal dispersions

Concepts:

viscosityreduced - /c

viscosityrelative theofincrement - 1

viscosityrelative - /

dispersion theof viscosity-

phase dispersantor solvent pure of viscosity-

i

0i

0

0

Spherical particles, hydrodynamic calculation:

Einstein: k 10

- volume fraction

k =2.5

5.2

5.21

5.21

0

0

i

Solvation and asymmetry: the term must also include the solvent which kinetically acts as part of the particles. The asymmetry of particles also has a great effect on viscosity.

Intrinsic viscosity

Ci

C

0

lim

The Intrinsic viscosity has inverse concentration units.

Determination of relative molecular weight of polymers from measurements of viscosity.

Viscosity measurements cannot be used to distinguish between particles of different sizes but with the same format and degree of solvation. However, if the format (configuration) or solvation factor change with the size of the particle, then viscosity can be used to determine the size of the particles.

The intrinsic viscosity of a polymer solution is proportional to the molar mass. If the orientations of the macromolecular chain are random:

5.0rkM

Linear polymers in solution are more than oriented at random, and the relationship is (Mark and Houwink):

rkM - depends on the configuration.

The following viscosities were measured for solutions of cellulose acetate in acetone, with concentration of 0.5 g/100 cm3:

10-3 Mr 85 138 204 302

/10-4 Pa.s 5.45 6.51 7.73 9.40

The viscosity of acetone at this temperature is 3.2×10-4 Pa.s Derive an expression from these data that permits the routine determination of the relative molar mass of samples of cellulose acetate. What additional information from this expression?

Shaw, Introduction to Colloid and Surface Chemistry, 4th ed., Butterworth-Heinemann, Oxford, 1991

ri Mkc loglog/log

log Mr 4.93 5.14 5.31 5.48

log i/c -0.85 -0.69 -0.55 -0.41

y = 0,7998x - 4,7946

R2 = 1

-0,9

-0,6

-0,3

4,8 5 5,2 5,4 5,6

log Mr

log

vis

cosi

dad

e 138.05106.1 kgmM r

The average configuration of polymers is between random and extended.

The viscosity of a range of solutions of polystyrene in toluene were measured at 25 °C:

c/g.L-1 0 2 4 6 8 10 /10-4 kg.m-1.s-1 5.58 6.15 6.74 7.35 7.98 8.64

Calculate the intrinsic viscosity and estimate the molar mass of polymer knowing that in the Mark-Houwink equation, k = 3.8×10-5 L.g-1 and = 0.63

Atkins, Physical Chemistry, Oxford University Press, Oxford, 2006

c/g.L-1 2 4 6 8 10100(/0 -1)/c 5.11 5.20 5.28 5.38 5.49

y = 0,0011x2 + 0,0341x + 5,04

R2 = 0,9993

5

5,2

5,4

5,6

0 5 10 15

c (g/L)

visc

osi

dad

e in

trin

seca 1.0504.0 gL

13/1

.1090

molgk

M

Newtonian and non-Newtonian behavior

In some fluids, viscosity depends on the applied tension or the time of they application. For these fluids, viscosity is no more a constant for becoming a property dependent on the conditions under which the fluid is deformed or under tension. In this case, the viscosity of the fluid is called apparent viscosity

Fluids

Newtonian Non - Newtonian

Dilatant behavior: when the apparent viscosity increases with the application of a force (corn starch in water).

Pseudo plastic behavior: when the apparent viscosity decreases with the application of a force (creams, ointments, etc.)

tens

ion

visc

osity

Velocity gradient

1. Dilatant; 2. Newtonian; 3. Pseudo plastic

Non- Newtonian behavior (independent of time)

Viscoplasticity or Bingham Fluids

Fluids characterized by the existence of a value of tension that must be exceeded so that the material presents a viscous flow. It is necessary that the force exceeds this limit for seepage occurs (tomato sauce, etc.)

tens

ion

Velocity gradient

Thixotropy and Antithixotropy (time- dependent)

Certain materials present change of viscosity when the applied voltage is maintained for a certain time.

Thixotropy: when the viscosity decreases with time of application of force and retrieves the initial state after prolonged rest (paints, oils, yogurt, etc.)

Antithixotropy or Rheopexy: when the viscosity increases with time.

World’s Longest Running Laboratory Experiment – The Pitch Drop Experiment

Pitch – derivative of tar. At room temperature feels solid and can be shattered with a blow of a hammer. This experiment shows that in fact at room temperature pitch is a fluid!

http://www.physics.uq.edu.au/physics_museum/pitchdrop.shtml