Ostwald-de Waele equation
What is Ostwald de Waele equation?
A simplified power law relationship used to describe non-Newtonian fluids as ?=a?n. Depending on the value of the power index, n, the fluid can be classified as being pseudoplastic (n < 1), Newtonian (n = 1), or dilatant (n > 1). It is named after German chemist Friedrich Wilhelm Ostwald (… …
What is Ostwald de Waele model?
From Wikipedia, the free encyclopedia. A power-law fluid, or the Ostwaldde Waele relationship, is a type of generalized Newtonian fluid (time independent Non-Newtonian fluid) for which the shear stress, ?, is given by.
What is the power law model?
The Power Law model (sometimes known as the Ostwald model) is an easy-to-use model that is ideal for shear-thinning, relatively mobile fluids such as weak gels and low-viscosity dispersions.
What is n for power law model?
n is the power law constant (unitless) K is the flow consistency index, (mPa-s) The power law model, also known as the Ostwald de Waele relationship, is used to fit non-Newtonian data across shear rates where there is no evidence of a Newtonian plateau region.
What is Bingham plastic model?
The Bingham plastic model is the most common rheological model used in the drilling industry. This model is a two parameter model that includes yield stress and plastic viscosity of the fluid. As it is shown in Figure 2-15, the fluid initially resists flowing until the shear stress exceeds a certain value.
What are pseudoplastic fluids?
In contrast to a Bingham fluid, a pseudoplastic fluid is a fluid that increases viscosity as force is applied. A typical example is a suspension of cornstarch in water with a concentration of one to one. This cornstarch behaves like water when no force is applied; however, it is solidified as force is applied.
How do you calculate shear rate?
Shear Rate = (Distance / Time) / Distance = Time-1 Using seconds as the unit of time, Time-1 becomes seconds-1. expressed in units of reciprocal seconds (sec-1). Shear sensitive liquids can behave very differently when sheared.
What is the consistency coefficient?
The consistency coefficient K measures the average viscosity of the non-Newtonian fluid, and n is the flow behavior index that measures the deviation of the fluid from Newtonian flow. It is the shear-thickening fluid when n > 1, and the shear-thinning fluid when n < 1.
What is viscosity units?
The unit of viscosity is newton-second per square metre, which is usually expressed as pascal-second in SI units.
What is the power law formula?
A power law distribution has the form Y = k X?, where: X and Y are variables of interest, ? is the law’s exponent, k is a constant.
What is power law coefficient?
Polymers can be described by the power-law coefficient, which is a simple relationship derived from the shear-rate/viscosity curves at different temperatures. It describes the viscosity in most of the processing range of the extruder.
How do you make a power law model?
What are Bingham bodies?
A Bingham plastic is a viscoplastic material that behaves as a rigid body at low stresses but flows as a viscous fluid at high stress. It is named after Eugene C. Bingham who proposed its mathematical form. It is used as a common mathematical model of mud flow in drilling engineering, and in the handling of slurries.
What is Herschel Bulkley model?
The HerschelBulkley fluid is a generalized model of a non-Newtonian fluid, in which the strain experienced by the fluid is related to the stress in a complicated, non-linear way. Three parameters characterize this relationship: the consistency k, the flow index n, and the yield shear stress. .
How do I calculate Herschel Bulkley model?
The model relates the shear stress y to the strain rate x by the formula:(1) y = y 0 + Kx n , where y0 is the yield stress of the material, K is the consistency factor, and n is the flow behaviour index. Essentially, the behaviour of the material is governed by these three HerschelBulkley parameters.
What is Casson model?
Casson fluid model is a non-Newtonian fluid with yield stress which is widely used for modeling blood flow in narrow arteries. Many researchers have used the Casson fluid model for mathematical modeling of blood flow in narrow arteries at low shear rates.
How is plastic viscosity calculated?
The plastic viscosity (PV) of the drilling fluid is calculated by subtracting the 300-rpm shear stress (R300) from the 600-rpm shear stress (R600). The yield point of the drilling fluid (YP) is calculated by subtracting the PV from the R300 reading. Multiplying the rpm by 1.7 changes the units to re- ciprocal seconds.
What is the difference between Bingham plastic and pseudoplastic?
Summary Plastic vs Pseudoplastic Flow
The key difference between plastic and pseudoplastic flow is that plastic flow describes the flowing behavior of a material after application of stress, whereas pseudoplastic flow exhibits the behavior of both Newtonian flow and plastic flow.
How does pseudoplastic and dilatant fluid differ?
An example of dilatant fluid is sand in water. On the other hand, when viscosity decreases when stress increases, the fluid is called pseudoplastic fluid.
Is consistency the same as viscosity?
About the only common characteristic is that all viscosity values change with temperature. Consistency is an attribute that relates to firmness or thickness. The term is used for many materials that flow with the application of only gravitational force.
What is consistency index in fluid?
“k” is known as the “consistency index”, and is indicative of the pumpability of the fluid. “n” is the power index, denoting the degree of how “non-Newtonian” the fluid is. Both parameters can be determined from the Fann VG meter. “k” is defined as the viscosity of a fluid at a shear rate of 1 sec-1.
What is consistency of fluid?
Consistency is a measure of how a liquid material reacts to gravity.
What is the formula for calculating viscosity?
Viscosity = (2 x (ball density liquid density) x g x a^2) (9 x v), where g = acceleration due to gravity = 9.8 m/s^2, a = radius of ball bearing, and v = velocity of ball bearing through liquid. Plug your measurements into the equation to calculate the viscosity of the liquid.
How is Reynolds number calculated?
The Reynolds number (Re) of a flowing fluid is calculated by multiplying the fluid velocity by the internal pipe diameter (to obtain the inertia force of the fluid) and then dividing the result by the kinematic viscosity (viscous force per unit length).
What is the dimensional formula for viscosity?
Or, ? = [M1 L1 T–2] [M0 L2 T0]–1 [M0 L1 T–1]–1 [M0 L1 T0] = [M1 L–1 T–1]. Therefore, viscosity is dimensionally represented as [M1 L–1 T–1].