Viscosity and its Relation to Bubble Removal

Most of the time we can be very causal when we talk about the viscosity of a fluid. We have a correlation between the measurements and process results and so long as that works we don’t need to pay it any further attention. However, when using lab data to predict process performance without the benefit of prior correlation to performance, one has to work with very specific information relating to that process.

Most fluids are non-Newtonian, meaning they have a range of viscosities according to the extent of deformation or shear rate they are experiencing. So to be correct, we need to talk about the viscosities of a fluid. These viscosities can vary greatly.

A few definitions are in order:

The severity of the flow conditions is measured by the velocity gradient of the flow field or the change in velocity over the distance of change. It is called the shear rate with units of 1/sec. {(ft/sec)/ft = 1/sec}
The force required to sustain this severity is the shear force. Its units are pounds/square inch or PSI. This is the PSI of shear not PSI of pressure. Consider the pressure drop required to push fluid through a pipe. The pressure drop times the cross sectional area is a force. The walls of the pipe or the wetted area resist this force. This force divided by the wetted area is the PSI of shear.
A plot of the shear force verses the shear rate is a rheogram. One can ascertain the rheology of fluid from this plot.
The apparent viscosity is the shear force divided by the shear rate. The shear force, G, equals the shear rate, g, times the apparent viscosity, m, at that shear rate. G = m g

When we talk about the viscosity of a fluid, that viscosity was measured at specific conditions. Other conditions may have a higher or lower viscosity. Consider a fluid that obeys a power law, G = m gn In this case n is less than 1.

High viscosity fluids usually thin out when subjected to more shear. A shear thinning fluid is called pseudoplastic. The slope or apparent viscosity of a pseudoplastic fluid increases as you approach zero shear. A shear thickening fluid increases viscosity with shear and is called dilatent. The following table shows the range of viscosities the above fluid has.

Power Law Fluid

Shear Rate	Shear	Visc
1/sec	Force	cps
	PSI
1	0.0292	200,000
5	0.0343	46,985
10	0.0368	25,179
50	0.0432	5,915
100	0.0463	3,170
500	0.0544	745
1,000	0.0583	399
5,000	0.0684	94
10,000	0.0733	50
50,000	0.0862	12

Another common type of fluid is a Bingham Plastic. These fluids exhibit a yield point. Little flow occurs until the yield point is exceeded and then additional resistance is slight.

Often a blowup of the low shear region shows an initial viscosity with a rapid transition to a second straight line. The slope of the second line is called the plastic viscosity.

Pipe flows typically have a shear rate of 200/sec or less. The pressure drop would climb steadily as flow is increased until this yield is exceeded and then it wouldn’t increase much above 100/sec.

Here is the viscosity data for this Bingham plastic.

Shear Rate	Shear	Visc
1/sec	Force	cps
	PSI
10	0.0292	20,000
50	0.146	20,000
100	0.292	20,000
500	0.3	4,110
1,000	0.31	2,123
5,000	0.35	479
10,000	0.38	260
50,000	0.73	100

High viscosity fluids have to thin out to be practical. Think about the equipment required to pump something five times thicker that what you use now. Even more important, think about the process forces at higher shear rates with a fluid forty to a hundred times more than what is developed now. We drop these fluids out of consideration now because they are impractical to run.

To determine if a bubble will move through a fluid fast enough we want to know its resistance force at an unknown shear rate, likely less than 200/sec. We have found from empirical work that extrapolating the capillary data back to zero shear gives an index the agrees with the observed deaeration performance. To be correct we should report this a yield force. We use the word viscosity only because it is more widely known.

The Brookfield Viscometer

Brookfield’s disk on a spindle viscometer is widely used because it is convenient to use. Measurements are quick and the cleanup is easy. This number is so widely used that it merits some discussion. Its viscosity is based on a shear field that is linear from the disk to the bottom of the beaker. This distance is set by the length of the spindle. Many operators do not bother the find the bottom of the beaker each time. The number is also affected by the diameter of the beaker. Few of us bother to control that either. More important than either of these is the rheology of the fluid. For power law and Bingham plastic fluids, the shear field is not linear. The calculation is therefore incorrect and one can get a high number that won’t show up with other measurements. As one can’t determine the shear rate acting on the disk, the number can’t be translated for process predictions.

The Capillary Viscometer

A capillary viscometer is nothing more than a pipe of a known diameter and length where you can measure the pressure drop at various flow rates. We use this method because it is extremely flexible and we use a pipe that is ranged for the low shear rates of bubbles moving through a fluid.

For more information on gravure coaters, coating components or systems, please contact Black Clawson Converting Machinery at 315-598-7121 or e-mail your questions to bc@bc-egan.com.