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Brookfield Engineering

Rheology School

Neil Cunningham, Rheology School
www.rheologyschool.com

Open a new jar of mayonnaise and, without shaking or stirring, lay it on its side. If it hasn't been disturbed recently it shouldn't move noticeably over a period of a few minutes or so. It is safe to say that it has a very high viscosity indeed - but we can also say that under the gentle conditions here the mayonnaise is, in fact, exhibiting behaviour more akin to a soft-solid than a thick liquid.

Turn the jar upright again and carefully insert a large cooking spatula into it. If we push the spatula laterally with a gentle force the mayonnaise will deform but will then return to its original vertical position when the forced is removed - a dead giveaway of elastic (i.e solid-like) behaviour. We know that mayonnaise is not a true solid - it will flow, given long enough - but in some situations it suits us to assume that it is solid. So instead of measuring a liquid property, such as viscosity, we can then measure properties of solids and get a more representative characterization.

One property of a solid we can look at is yield stress. If the lateral force on the spatula exceeds a certain magnitude it won't relax back to its original position - we have caused the mayonnaise to yield resulting in a permanent (plastic or viscous) deformation - in other words, the mayonnaise has flowed. The yield stress is the applied stress we must exceed in order to make a structured fluid flow.

The presence of a significant yield stress will impart various qualities to a fluid that may or may not be desirable. A yield stress will often inhibit flow under the relatively low stresses induced by gravity; giving sag and slump resistance to products such as adhesives, plaster and stucco, thick-film inks, molten chocolate, paint and fire-retardant coatings. With some products the presence of a yield stress is not so desirable, leading to, for example, dosing problems in gravity-feed systems or an excess of residue on the sides of inverted bottles. Many products are modified to produce a yield value for the purposes of particle suspension and to keep them from flowing at very low shear stress.

Measuring Yield Stress

Approximate yield stress measurements can be gained by plotting the shear stress values for a range of shear rates, fitting a curve to the data, and extrapolating through the stress axis. The intersect on the stress axis gives us our yield stress (see fig). It is useful here to use a rheological math model, several of which are available on viscometer software packages - such as Brookfield's RheoCalc and Wingather - to quantify the intersect. In the example shown the Casson model would be employed.

A more exact method for obtaining yield stresses is to use a static vane-based test method. The vane is lowered into the undisturbed sample and then torqued slowly. The sample deforms elastically as the imposed stress increases until a yield stress is attained. At this point the sample starts to flow significantly and the measured stress falls from a peak (see below).

The table below shows typical yield stresses for a range of common products:

Ketchup 15 Pa
Salad Dressing 30 Pa
Lithographic Ink 40 Pa
Mayonnaise 100 Pa
Skin Cream 110 Pa
Hair Gel 135 Pa

The Brookfield YR-1 and DV-III Ultra both have the capability to make this type of measurement.

This yield measurement is more representative of the way a soft solid is used, since the test material starts from a static, structured condition which is normally what happens in the real world.