## IMATEK Twin-bore Capillary Rheometer R6000

## Calculation

The measurements are as follows
◇Sample’s volume flow : It is calculated by the dimention and speed of a piston.
◇Pressure drop through a die : It is measured at the entering pressure drop.

S Piston Speed(mm/min) Piston’s diameter(mm) Volume flow rate(m㎥/sec)＝ Long capillary length(mm) Short capillary length(mm) Capillary radius(mm) Pressure drop through a long die Pressure drop through a short die Pressure drop through a short die (or Pressure drop is calculated from the point the extrapolated line joining PL to PS intersects Y-axis)

### Apparent shear viscosity and shear rate

#### ▶ Calculation.01

◇No corrected shear stress(τ)＝ True shear stress is calculated by Bagley correction,.

#### ▶ Calculation.02

◇Shear rate(γ)＝ ### Apparent viscosity

#### Calculation.03

◇Apparent viscosity(η)＝Shear stress(τ)/Shear rate(γ)

### Bagley correction

PL(=Pressure drop through a long die) is P0(=Die entry pressure drop and Die exit pressure drop) and P capillary(=the pressure drop in the die) (see Figure09.10 diagram below).  True shear viscosity is calculated as the below.

#### calculation.04

◇True shear viscosity(τcorrect)＝ PO is the point that the extrapolated line joining PL to PS intersects Y-axis.（Figure11）

This is to say

#### calculation.05 ※R6000 can measure the value , turning off Bagley correction. ### Power law index : n

Power law index is the gradient of the shear viscosity graph.
The power law index of Newtonian fluid is 1.
It means viscosity decreases as the power law index approach zero
Power low index n is the value is calculated from the below definition

Shear stress(τ)=k ・Shear rate (γ)n

This is

#### calculation.06

Log(τ)＝Log(ｋ)＋n・Log(γ)

The value n is calculated from the gradient of a graph of log(shear stress) vs log(shear rate)In the case that sample has strong yield strength, the n’s value is 0 or － when shear rate is 0.As R6000 can’t calculate the value in this case, the value is showed 0.01 automatically.R6000 can’t draw a graph that includes inappropriate data.
As the software calculates n’s value by turns, the value of shear stress is always being corrected. To raise the accuracy of calculation, n’s value is calculated from the gradient of the quadratic equation, plotting measured values.

### Rabinowitsch correction.

Shear rate that is calculated from “formula” 2 is based on the premise that the polymer’s speed can be calculated from volume flow rate Q. The speed profile is assumed that it is Newtonian fluid, which it it power low index n =1.
However , polymer isn’t Newtonian fluid. Therefore shear rate can not be calculated from “formula 2”.
To get true shear rate, the shear rate is calculated from formula 2 needs to be corrected from Rabinowitsch correction.

#### calculation.07

◇True shear rate(γ)＝ This correction term (3n+1)/4n is valid when we measure viscosity in a capillary cylinder.
We use another correction term when we measure viscosity in a split die.
True viscosity should be calculated with turn shear rate of calculation7 and the shear Stress of calculation4.
You can turn off Rabinowitsch correction,if you like.

### Elongational viscosity.

There are various formulas lead to the approximate value of the elongational viscosity.
The below formula is accepted as the most practical one in the world
It is called Modified Cogswell formula, or Binding formula, which is named after advocators.

#### calculation.08

◇Elongational viscosity(λ)＝ #### calculation.09

◇Elongational stress(σE)＝ #### calculation.10

◇Elongational rate(έ)＝ 