Etiket Arşivleri: Dilatant
Efficient Rheology Control Additives Rheology is defined as “the study of the change in form and the flow of matter embracing elasticity, viscosity and plasticity.” We concern ourselves with viscosity, further defined as “the internal friction of a fluid caused by molecular attraction, which makes it resist a tendency to flow.” Water is an invaluable solvent and vehicle but it is not without certain deficiencies. It is, above all, watery. The exercise of rheological control over water is a significant challenge for formulators. It is often too thin, it is generally runny and it is invariably unsupportive for insoluble particulates. Formulators are, therefore. forced to adjust water to suit their needs. Fortunately, this can be readily accomplished through the use of rheology modifiers. Specific control of water is enabled by the careful application of one or more of the rheology modifiers available for use in aqueous compositions. Familiarity with the rheological nuances of a particular modifier can at times make the difference between an exceptional formulation and a routine one. What follows is an overview of the hydrocolloids based additives most commonly used to control water. The intent is to make the formulator sufficiently familiar with the fundamental nature of each of these materials, so as to facilitate proper selection.
The terms used to characterize rheology are defined as follows:
Newtonian – The viscosity of such fluids will not change as the shear rate is varied. Water and thin motor oils show typical Newtonian behavior.
Non-Newtonian – The viscosity of such fluids will change as the shear rate is varied. There are several types of non-Newtonian flow behavior, characterized by the way a fluid’s viscosity changes in response to variations in shear rate. The most common types of nonNewtonian fluids you may encounter include:
• Pseudoplastic – This type of fluid will display a decreasing viscosity with an increasing shear rate. Probably the most common of the non-Newtonian fluids, pseudo-plastics include paints, emulsions and dispersions of many types. This type of flow behavior is
sometimes called “shear-thinning.” Moreover, they immediately recover their nonsheared viscosity once shear is removed.
• Dilatant – Increasing viscosity with an increase in shear rate characterizes the dilatant fluid. Although rarer than pseudoplasticity, dilatancy is frequently observed in fluids containing high levels of deflocculated solids such as clay slurries, candy compounds,
corn starch in water and sand/water mixtures. Dilatancy is also referred to as “shearthickening” flow behavior.
• Plastic – This type of fluid will behave as a solid under static conditions. A certain amount of force must be applied to the fluid before any flow is induced; this force is called the “yield value.” Tomato ketchup is a good example of this type of fluid; its yield value will often make it refuse to pour from the bottle until the bottle is shaken or struck, allowing the ketchup to gush freely. Once the yield value is exceeded and flow begins, plastic fluids may display Newtonian, pseudoplastic or dilatant flow characteristics.
Yield Value – Yield value indicates the minimum force (the yield stress) that must be applied to a liquid to start disrupting the structure imparted by the rheology modifier, so that flow can occur. In practical terms, solids, oils and gases are trapped and segregated by this structure unless gravity or buoyancy can exert a force greater than the yield stress. Some fluids display a change in viscosity with time under conditions of constant shear rate. There are two categories to consider:
Thixotropy – Thixotropic fluids show a time-dependent response to shear. When subjected to a constant shear rate, they will decrease in viscosity over time. Often this is seen as a large initial viscosity loss, followed by gradual further loss. Once shear is removed, thixotropic fluids recover their viscosity, but over a period of time, not instantaneously. These fluids are also considered to be pseudoplastic, but only in that they show decreasing viscosity in response to increasing shear rate. Thixotropy is frequently observed in materials such as greases, heavy printing inks and paints.
Rheopexy – This is essentially the opposite of thixotropic behavior, in that the fluid’s viscosity increases with time as it is sheared at a constant rate. Rheopectic fluids are rarely encountered. Both thixotropy and rheopexy may occur in combination with any of the previously discussed flow behaviors or only at certain shear rates. The time element is extremely variable; under conditions of constant shear, some fluids will reach their final viscosity value in a few seconds, while others may take up to several days.
In addition, the term “synergism” is used to indicate that a combination of two rheology control additives provides a stronger rheological effect (e.g., viscosity or yield value) than would be anticipated by adding the individual contribution of each additive.
the shear rate is directly proportional to the shear stress, and the plot begins at the origin.
Typical Newtonian foods:
-containing compounds of low molecular weight (e.g., sugars)
-do not contain large concentrations of either dissolved polymers (e.g., pectins, proteins, starches)
-containing insoluble solids.
Examples: water, sugar syrups, most honeys, most carbonated beverages, edible oils, filtered juices, and milk.
t(Shear stress)= -μ (dv/dr) ( shear rate)
μ constant ( independent of shear rate)
All other types of fluid foods are non-Newtonian,
– shear stress-shear rate plot is not linear
-and/or the plot does not begin at the origin
-or exhibits time-dependent rheological behavior
Flow behavior may depend only on shear rate and not on the duration of shear (time independent) or may depend also on the duration of shear (time dependent).
Foods that exhibit time-dependent shear-thinning behavior are said to exhibit thixotropic flow behavior.
Most of the foods that exhibit thixotropic behavior( reversible decrease in shear stress with time at constant shear rate)are heterogeneous systems containing a dispersed phase
( foods such as salad dressings and soft cheeses where the structural adjustments take place in the food due to shear until an equilibrium is reached. )
Time-dependent shear-thickening behavior is called antithixotropic( Formerly, it was called rheopectic) behavior. Reversible increase in shear stress with time at constant shear rate) ( ie gypsum suspension,bentonite suspension)
Shear-Thinning Behavior ( pseudoplastic)
t = K.(-dv/dr)n Power law eq.
t = K.(-dv/dr)n-1(-dv/dr)=μa(-dv/dr)
K=consistency index ( N.sn/m2)
n=flow behavior index, dimensionless
may be due to breakdown of structural units in a food due to the hydrodynamic forces generated during shear.
Most non-Newtonian foods exhibit shear-thinning behavior, including biological fluids, xanthan gum soln, starch suspensions many salad dressings and some concentrated fruit juices.
Shear-Thickening Behavior (Dilatant) n>1
This type of flow has been encountered in partially gelatinized starch dispersions.
shear-thickening should be due to increase in the size of the structural units as a result of shear.
Bingham plastic behavior
The flow of some materials may not commence until a threshold value of stress,
the yield stress (ty), is exceeded
t= -μ.(dv/dr) +ty where ty is yield stress
Shear-thinning with yield stress behavior is exhibited by foods such as tomato concentrates, tomato ketchup, mustard, and mayonnaise.
If the shear rate-shear stress data follow a straight line with a yield stress, the food is said to follow the Bingham plastic model.
Flow behavior of fluids under shear-stress
1-Flow: permenant deformation of fluid
Existance of flow mens: fluid does not recover its originl shape even we remove applied force
2- elastic behavior: all the applied force is stored as bond energy when force is removed it takes its original shape.
If some bonds are broken, so only some bonds are formed to store some of the applied force …. viscoelastic behavior
3-Yield stress(ty): elastic property changed at ty
(when you squeeze tooth paste,it comes out as a cylinder because t is max at wall so first wall side stars flowing)
4- n measures resistance to deformation
n=1 ( Newtonian)…deforms readily under force
As n 0 it becomes elastic( jells shows elastic behavior untill ty, after ty jell breaks down to deform fluid
Complex rheological models
( containing more than 2 parameters)
t= ty+K(-dv/dr)n (-dv/dr)=γ
μa= t/γ= ty / γ + K.γn-1
as γ increases μa decreases then μ becomes constant
When n =1 behaves like Bingham
When n 0 μa=(ty +K)/ γ so as γ increases μa decreaes
If μ constant for very low and very high γ values and obeys Power law for intermediate γ values,
Then cassan is a sutable model
(μ)1/2 =(μ∞ )1/2 +(ty/γ)1/2
Where μ∞ is viscosity at very high γ
Example: chocolate, cocoa soln
Viscoelastic fluids: exhibits elastic recovery from the deformation that occur during flow. They show both viscous and elastic properties.
Part of deformation is recovered upon removal of the stress.
Example : flour dough, polymer melts
LAMINAR FLOW OF TIME INDEPENEDENT NON-NEWTONIAN FLUIDS
Commonly capillary tube viscometers are used to determine properties of the fluids.
ΔP for a given flowrate q is measured in a straigt tube length L and diameter D at different q values.
For a power law fluid:
Plot of log (tw) vs log(8V/D) yields:
Slope n’ and intercept K’
For most fluids K’ and n’ are constant over wide range of D.ΔP/4.L or 8V/D For some fluids they will vary
In many cases rotational viscometers are used to determine fluid properties.
When the flow propertis are constant over a Range of shear stresses that ocurs for many fluids following equations hold;
Generalised viscosity :γ=K’8n’-1
Table 3.5-1 gives n’, K’ and γ values for some foods.
EQUATIONS FOR LAMINAR FLOW OF NON-NEWTONIAN FLUID IN TUBES
To calculate pressure drop or mech energy loss due to friction in straight pipe
1- ΔP= (K’4L/D)/(8V/D)n’ ..Ff= ΔP/ρ
2- NRe,Gen for power law fluid
ΔP=4fρ(L/D)(v2/2)…. Ff= ΔP/ρ
Friction loss in contractons, expansions, fittings for non-newtonian fluid, laminar flow
1- kinetic energy correction factor:
2-Losses in contraction and fittings:Calculate α as in 1 and use.
3-losses in sudden expansion
Non-Newtonian turbulent flow
1- kinetic energy correction factor α=1
2-contractions for fittings α=1
3-expansion treat as newtonian
For 0.36<n’<1 and upto NRe =3.5x104and smooth pipe use fig 3.5-3
For non-Newtonian, turbulent and rough tube use Moody with NRe,Gen as an approximation
Emprical testing instruments for foods
Since viscosity is related with molecular momentum transportation, t, measurement of viscosity should be performed under laminar conditions( resistance is mainly due to viscosity)
There are three major group of viscometers
1- Capillary tube viscometer ( poiseuille flow)
Falling sphere (ball)viscometers