A sauce product is being formulated to match a reference...

A sauce product is being formulated to match a reference product (Product A) that has a consistency index of $12 \mathrm{~Pa} \mathrm{~s}^{\mathrm{n}}$ and a flow behavior index of 0.55 . Rheological measurements of the formulated product (Product B) on a wide gap rotational viscometer using a cylindrical spindle $1 \mathrm{~cm}$ in diameter and $5 \mathrm{~cm}$ long are as follows, with speed in rev/min and torque in \% of full scale, respectively: 2,$11 ; 4,18 ; 10,34 ; 20,56$. The viscometer constant is 7187 dyne cm. Calculate the apparent viscosity of Product A and Product B at $0.5 \mathrm{rev} / \mathrm{min}$. At this rotational speed, did the apparent viscosity of Product B match that of Product A?

Key Concepts

Power Law Model

The power law model is used to describe the flow behavior of non?Newtonian fluids. It relates the shear stress (?) and shear rate (??) through the equation ? = K(??)^n, where K is the consistency index and n is the flow behavior index. This model is essential for understanding how viscosity changes with shear rate, particularly for fluids that do not exhibit a constant viscosity, such as many food products and sauces.

Apparent Viscosity

Apparent viscosity is defined as the ratio of the shear stress to the shear rate at a particular point of measurement. For fluids described by the power law, the apparent viscosity can be calculated as ?_app = ?/?? = K(??)^(n-1). This concept is critical when comparing measured or targeted viscosity values at specific shear rates, as is often done when matching a formulated product to a reference product.

Rotational Viscometer Measurements

Rotational viscometers measure the torque required to rotate a spindle or cylinder in a fluid, which then can be related to the shear stress using a viscometer constant that accounts for the geometry of the system. Understanding the device's working principle is important when converting readings (like torque and rotational speed) into meaningful rheological properties, such as apparent viscosity.

Shear Rate Determination in Rotational Systems

In rotational viscometry, the conversion of rotational speed (in rev/min) to shear rate (in reciprocal seconds) is a crucial step in the analysis. This conversion typically involves the viscometer’s geometry and constants. Accurately determining the shear rate allows for the correct application of the power law model to calculate apparent viscosity, and ensures that comparisons between products are made at equivalent shear conditions.

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