Polymerization Technology Laboratory Course

Transcription

1 Polymerization Technology Laboratory Course Viscometry/Rheometry Tasks 1. Comparison of the flow behavior of polystyrene- solution and dispersion systems 2. Determination of the flow behaviour of polyvinylalcohol in water Theory Although the concept of viscosity is commonly used to characterize a fluid, it can be inadequate to describe the mechanical behavior of non-newtonian fluids. The laters are best studied through several other rheological properties that relate the relations between the shear stress and share rate under different flow conditions. Examples of flow conditions are oscillatory shear or extensional flow, which are measured by using different devices or rheometers. The concept of viscosity, shear rate and shear stress is explained by the following cartoon. The substance, which is able to flow, is located between two parallel plates of the same area A. Now a force F [kg m/s 2 ] in x-direction is applied to the upper plate and it moves with the velocity v [m/s]. The lower plate is fixed. In this model the substance is considered to consist of separate and very thin layers parallel to the plates. These layers will move with different velocities, because the outer layer is as fast as the upper plate while lowest layer does not move. The layers in between have a velocity ranging from 0 to v. The velocity gradient (dv/dy) describes the change of velocity between the layers in y-direction. Newton s law of viscosity predicts that this velocity gradient is proportional to the force (in x-direction) per area (F/A) applied to the upper plate. The proportionality factor between the gradient and the force per area is called viscosity ([Pa s], [kg/m s] or [N s/m 2 ]): F dv [kg/m s] (1) A dy Viscometry/Rheometry (SS 2010) Seite 1/5

2 Now we define follows: dx / dy to be the strain that is applied to the substance. With dv dx / dt it dv / dy d / dt [1/s] (2) Viscometry/Rheometry (SS 2010) Seite 2/5

3 The change of the strain with time d / dt is called shear rate. It is identical to the velocity gradient in y-direction in the substance. The quotient F/A is called shear stress ( ). Therefore, equation (1) can be rewritten as: [kg/m s²] (3) In Newtonian liquids, shear rate and shear stress are proportional and therefore viscosity is constant over the whole range of the applied shear rate or stress. If is not constant but a function of the shear rate, we call the behavior of a substance to be pseudo plastic (viscosity decreases with increasing shear rate) or dilatant (viscosity increases with increasing shear rate). Also, some non-newtonian fluids show more complicated dependence of viscosity on shear rate (Figure 1). Polymeric systems usually show pseudo plastic behavior but a plateau of constant viscosity at very low shear rates is often observed. In this region the sample behaves like a Newtonian fluid and the viscosity at those very low shear rates is called zero viscosity: lim 0 [kg/m s] (4) 0 The flow behavior of pseudo plastic substances can be described with the Oswald De Waele equation: n K [1/s] (5) Measuring principle Figure 2. Measuring system. The measuring system (Figure 2) consists of a solid inner cylinder, which is rotating, and a hollow outer cylinder. The investigated samples are filled in the gap between them. The cylinder rotation speed can be set in 15 steps. Each step corresponds to a shear rate. Viscometry/Rheometry (SS 2010) Seite 3/5

4 Viscosity η and shear stress τ can be calculated by equations (6) and (7). The torque T is shown on the digital display in units of [mpas]. The viscosity factor depends on the dimension of the cylinder and is given in table (1). Speed step: Rotary speed [min -1 ] Shear rate [s -1 ] Viscosity factor f (DIN 125) Viscosity factor f (DIN 145) 1 5,15 6,65 171,6 29,4 2 7,37 9,52 119,9 20,5 3 10,54 13,62 83,8 14, ,09 19,5 58,5 10, ,6 27,92 40, , ,6 4, ,3 57,2 19,95 3, ,4 81,9 13,94 2, ,7 117,2 9,74 1, ,8 167,2 6,8 1, , ,75 0, ,32 0, ,32 0, ,62 0, ,132 0,1939 Table 1: Empiric parameters of the Contraves Rheomat measuring system [mpas] T f (6) [mpa] T f (7) Experimental 1. A solution of methyl cellulose (3 wt% in water) is filled into the measuring system (DIN 125). The flow characteristic is measured at different temperatures (25 / 35 / 45 / 55 C) by variation of the shear rate. 2. Fill different concentrations of methyl cellulose (0, 1, 2, 5 wt% in water) into the measuring system (DIN 145) and measure the flow characteristic at a temperature of 25 C by variation of the shear rate. Viscometry/Rheometry (SS 2010) Seite 4/5

5 Analysis 1. Plot the data of the first part of experiment in x/y graphs for each temperature: /, / (log/log plots) and / (linear plot). Determine the zero shear rate viscosities for each temperature and plot them in dependence on temperature. Calculate the activation energy E A of the Arrhenius-Andrade correlation (Equation 8). Use an appropriate linearization! E A 0 exp (8) R T 2. Plot the data of the second part of experiment in x/y graphs ( /, / (log/log plots) and / (linear plot)) and compare the specific concentrations. Discuss the curves and the flow behavior of different concentrations of methyl cellulose! Fit this data with the Oswald De Waele equation! Viscometry/Rheometry (SS 2010) Seite 5/5