Ran Tao would like to thank funding from the National Institute of Standards and Technology, U.S. Department of Commerce under grant 70NANB15H112. Funding for Aaron M. Forster was provided through congressional appropriations to the National Institute of Standards and Technology.

1. Rheometer setup
NOTE: The protocol in this section describes basic steps to run a rheology experiment (for either a separate motor-transducer rheometer or a combined motor-transducer rheometer), including preparation of the setup, installation of appropriate geometry, loading the test material, setting up the experiment procedure, specifying the geometry, and starting the test. Specific instructions and notes are provided for OSP operation. To minimize thermal gradients in the transducer, it ...

<ol>
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D. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=.">.</a> Viscoelastic Properties of Polymers. , (1980).</li><li>Yamamoto, M. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Rate-dependent+relaxation+spectra+and+their+determination.">Rate-dependent relaxation spectra and their determination.</a> Transactions of the Society of Rheology. 15 (2), 331-344 (1971).</li><li>Simmons, J. M. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=A+servo-controlled+rheometer+for+measurement+of+the+dynamic+modulus+of+viscoelastic+liquids.">A servo-controlled rheometer for measurement of the dynamic modulus of viscoelastic liquids.</a> Journal of Scientific Instruments. 43 (12), 887-892 (1966).</li><li>Tanner, R. I., Williams, G. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=On+the+orthogonal+superposition+of+simple+shearing+and+small-strain+oscillatory+motions.">On the orthogonal superposition of simple shearing and small-strain oscillatory motions.</a> Rheologica Acta. 10 (4), 528-538 (1971).</li><li>Schoukens, G., Mewis, J. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Nonlinear+rheological+behaviour+and+shear-dependent+structure+in+colloidal+dispersions.">Nonlinear rheological behaviour and shear-dependent structure in colloidal dispersions.</a> Journal of Rheology. 22 (4), 381-394 (1978).</li><li>Zeegers, J., et al. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=A+sensitive+dynamic+viscometer+for+measuring+the+complex+shear+modulus+in+a+steady+shear+flow+using+the+method+of+orthogonal+superposition.">A sensitive dynamic viscometer for measuring the complex shear modulus in a steady shear flow using the method of orthogonal superposition.</a> Rheologica Acta. 34 (6), 606-621 (1995).</li><li>Mewis, J., Schoukens, G. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Mechanical+spectroscopy+of+colloidal+dispersions.">Mechanical spectroscopy of colloidal dispersions.</a> Faraday Discussions of the Chemical Society. 65, 58-64 (1978).</li><li>Lin, N. Y. C., Ness, C., Cates, M. E., Sun, J., Cohen, I. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Tunable+shear+thickening+in+suspensions.">Tunable shear thickening in suspensions.</a> Proceedings of the National Academy of Sciences. 113 (39), 10774-10778 (2016).</li><li>Gracia-Fern&#225;ndez, C., et al. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Simultaneous+application+of+electro+and+orthogonal+superposition+rheology+on+a+starch/silicone+oil+suspension.">Simultaneous application of electro and orthogonal superposition rheology on a starch/silicone oil suspension.</a> Journal of Rheology. 60 (1), 121-127 (2015).</li><li>Sung, S. H., Kim, S., Hendricks, J., Clasen, C., Ahn, K. H. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Orthogonal+superposition+rheometry+of+colloidal+gels:+time-shear+rate+superposition.">Orthogonal superposition rheometry of colloidal gels: time-shear rate superposition.</a> Soft Matter. 14 (42), 8651-8659 (2018).</li><li>Colombo, G., et al. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Superposition+rheology+and+anisotropy+in+rheological+properties+of+sheared+colloidal+gels.">Superposition rheology and anisotropy in rheological properties of sheared colloidal gels.</a> Journal of Rheology. 61 (5), 1035-1048 (2017).</li><li>Jacob, A. R., Poulos, A. S., Kim, S., Vermant, J., Petekidis, G. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Convective+Cage+Release+in+Model+Colloidal+Glasses.">Convective Cage Release in Model Colloidal Glasses.</a> Physical Review Letters. 115 (21), 218301 (2015).</li><li>Jacob, A. R., Poulos, A. S., Semenov, A. N., Vermant, J., Petekidis, G. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Flow+dynamics+of+concentrated+starlike+micelles:+A+superposition+rheometry+investigation+into+relaxation+mechanisms.">Flow dynamics of concentrated starlike micelles: A superposition rheometry investigation into relaxation mechanisms.</a> Journal of Rheology. 63 (4), 641-653 (2019).</li><li>Moghimi, E., Vermant, J., Petekidis, G. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Orthogonal+superposition+rheometry+of+model+colloidal+glasses+with+short-ranged+attractions.">Orthogonal superposition rheometry of model colloidal glasses with short-ranged attractions.</a> Journal of Rheology. 63 (4), 533-546 (2019).</li><li>Tao, R., Forster, A. M. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=End+effect+correction+for+orthogonal+small+strain+oscillatory+shear+in+a+rotational+shear+rheometer.">End effect correction for orthogonal small strain oscillatory shear in a rotational shear rheometer.</a> Rheologica Acta. 59 (2), 95-108 (2020).</li><li>Schrag, J. L. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=Deviation+of+velocity+gradient+profiles+from+the+"gap+loading"+and+"surface+loading"+limits+in+dynamic+simple+shear+experiments.">Deviation of velocity gradient profiles from the "gap loading" and "surface loading" limits in dynamic simple shear experiments.</a> Transactions of the Society of Rheology. 21 (3), 399-413 (1977).</li><li>Ewoldt, R. H., Johnston, M. T., Caretta, L. M., Spagnolie, S. <a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?db=PubMed&cmd=Search&doptcmdl=Citation&defaultField=Title+Word&term=.">.</a> Complex Fluids in Biological Systems. Biological and Medical Physics, Biomedical Engineering. , 207-241 (2015).</li></ol>

The full description of the procedures used in this paper requires the identification of certain commercial products and their suppliers. The inclusion of such information should in no way be construed as indicating that such products or suppliers are endorsed by NIST or are recommended by NIST or that they are necessarily the best materials, instruments, software or suppliers for the purposes described.

In this protocol, we present a detailed experimental procedure for performing viscosity calibration measurements using Newtonian fluids for a commercial orthogonal superposition rheology technique with a double-wall concentric cylinder geometry. The calibration factors, i.e., the primary end-effect factor CL and the orthogonal end-effect factor CLo, are determined independently by conducting steady shear rate sweep and orthogonal frequency sweep tests. After obtai...

Understanding the rheological properties of complex fluids is essential to many industries for the development and manufacture of reliable and reproducible products1. These &#8220;complex fluids&#8221; include suspensions, polymeric liquids, and foams that widely exist in our everyday life, for example, in personal care products, foods, cosmetics, and household products. The rheological or flow properties (e.g., viscosity) are key quantities&#160;of interest in establishing performance metrics for end use and processability, but flow properties are interconnected with the microstructures that exist within complex fluids. One prominent characteristic of complex fluids that distinguishes them from simple liquids is that they possess diverse microstructures spanning multiple length scales2. Those microstructures can be easily affected by different flow conditions, which, in turn, result in changes in their macroscopic properties. Unlocking this structure-property loop via non-linear viscoelastic behavior of complex fluids in response to flow and deformation remains a challenging task for experimental rheologists.
Orthogonal superposition (OSP) rheology3 is a robust technique to address this measurement challenge. In this technique, a small amplitude oscillatory shear flow is superimposed orthogonally to a unidirectional primary steady-shear flow, which enables the simultaneous measurement of a viscoelastic relaxation spectrum under the imposed primary shear flow. To be more specific, the small oscillatory shear perturbation can be analyzed using theories in linear viscoelasticity4, while the non-linear flow condition is achieved by the primary steady-shear flow. As the two flow fields are orthogonal and thus not coupled, the perturbation spectra can be directly related to the variation of the microstructure under the primary non-linear flow5. This advanced measurement technique offers an opportunity to elucidate structure-property-processing relationships in complex fluids to optimize their formulation, processing, and application.
The implementation of modern OSP rheology was not the result of a sudden epiphany; rather, it is based on many decades of development of custom devices. The first custom made OSP apparatus is dated back to 1966 by Simmons6, and many efforts were made thereafter7,8,9,10. Those early custom-built devices suffer from many drawbacks such as alignment issues, the pumping flow effect (due to the axial movement of the bob to provide orthogonal oscillation), and limits to instrument sensitivity. In 1997, Vermant et al.3 modified the force rebalance transducer (FRT) on a commercial separate motor-transducer rheometer, which enabled OSP measurements for fluids with a wider viscosity range than previous devices. This modification enables the normal force rebalance transducer to function as a stress-controlled rheometer, imposing an axial oscillation in addition to a measurement of the axial force. Recently, the geometries required for OSP measurements, after the methodology by Vermant, have been released for a commercial separate motor-transducer rheometer.
Since the advent of commercial OSP rheology, there is a growing interest in applying this technique for the investigation of various complex fluids. Examples include colloidal suspensions11,12, colloidal gels13,14 and glasses15,16,17. While the availability of the commercial instrument promotes OSP research, the complicated OSP geometry requires a deeper understanding of the measurement than other routine rheological techniques. The OSP flow cell is based on a double-wall concentric cylinder (or Couette) geometry. It features an open top and open bottom design to enable fluid to flow back and forth between the annular gaps and the reservoir. Despite the optimization made to the geometry design by the manufacturer, when undergoing OSP operation the fluid experiences an inhomogeneous flow field, geometric end effects, and residual pumping flow, all of which can introduce substantial experimental error. Our previous work18 reported important end-effect correction procedures using Newtonian fluids for this technique. To obtain correct viscosity results, appropriate end-effect factors in both primary and orthogonal directions should be applied. In this protocol, we aim to present a detailed calibration methodology for the OSP rheological technique and provide recommendations for best practices to reduce measurement errors. The procedures delineated in this paper on OSP geometry setup, sample loading, and OSP test settings should be easily adoptable and translated for non-Newtonian fluids measurements. We advise that users utilize the calibration procedures described here to determine the end-effect correction factors for their applications prior to OSP measurements on any fluid classification (Newtonian or Non-Newtonian). We note that the calibration procedures for end factors have not been reported previously. The protocol provided in the present paper also describes step-by-step guide and tips on how to perform accurate rheological measurements in general and the technical resource on the understanding of &#8220;raw&#8221; data versus &#8220;measured&#8221; data, which may be overlooked by rheometer users.

<table>
	<tbody>
		<tr>
			<td>Advanced Peltier System</td>
			<td>TA Instruments</td>
			<td>402500.901</td>
			<td>Enviromental control device</td>
		</tr>
		<tr>
			<td>ARES-G2 Rheometer</td>
			<td>TA Instruments</td>
			<td>401000.501</td>
			<td>Rheometer</td>
		</tr>
		<tr>
			<td>Brookfield Silicone Fluid, 12500cP</td>
			<td>AMTEK Brookfield</td>
			<td>12500 cps</td>
			<td>Viscosity standard liquid</td>
		</tr>
		<tr>
			<td>OSP Slotted Bob, 33 mm</td>
			<td>TA Instruments</td>
			<td>402796.902</td>
			<td>Bob, upper geometry</td>
		</tr>
		<tr>
			<td>OSP Slotted Double Gap Cup, 34 mm</td>
			<td>TA Instruments</td>
			<td>402782.901</td>
			<td>Double wall cup, lower geometry</td>
		</tr>
		<tr>
			<td>Pipette (1 &#8211; 10 mL)</td>
			<td>Eppendorf</td>
			<td>3120000089</td>
			<td>To load test materials</td>
		</tr>
		<tr>
			<td>Pipette (100 &#8211; 1,000 &#181;L)</td>
			<td>Eppendorf</td>
			<td>3123000063</td>
			<td>To load test materials</td>
		</tr>
		<tr>
			<td>Pipette Tips (0.5 &#8211; 10 mL)</td>
			<td>Eppendorf</td>
			<td>022492098</td>
			<td>To load test materials</td>
		</tr>
		<tr>
			<td>Pipette Tips (50 &#8211; 1,000 &#181;L)</td>
			<td>Eppendorf</td>
			<td>022491555</td>
			<td>To load test materials</td>
		</tr>
		<tr>
			<td>Spatula</td>
			<td>VWR</td>
			<td>82027-532</td>
			<td>To load test materials</td>
		</tr>
		<tr>
			<td>TRIOS</td>
			<td>TA Instruments</td>
			<td>v4.3.1.39215</td>
			<td>Rheometer software</td>
		</tr>
	</tbody>
</table>

calibration procedures for orthogonal superposition rheology

Orthogonal superposition (OSP) rheology is an advanced rheological technique that involves superimposing a small-amplitude oscillatory shear deformation orthogonal to a primary shear flow. This technique allows the measurement of structural dynamics of complex fluids under non-linear flow conditions, which is important for the understanding and prediction of the performance of a wide range of complex fluids. The OSP rheological technique has a long history of development since the 1960s, mainly through the custom-built devices that highlighted the power of this technique. The OSP technique is now commercially available to the rheology community. Given the complicated design of the OSP geometry and the non-ideal flow field, users should understand the magnitude and sources of measurement error. This study presents calibration procedures using Newtonian fluids that includes recommendations for best practices to reduce measurement errors. Specifically, detailed information on the end-effect factor determination method, sample filling procedure, and identification of the appropriate measurement range (e.g., shear rate, frequency, etc.) are provided.

Representative results from the viscosity calibration measurements on a 12.2 Pa s silicone viscosity standard are represented in Figure 5 and Figure 6. Note that the primary end-effect factor and the orthogonal end-effect factor are both set to 1.00 for the calibration runs. Figure 5 shows the steady shear viscosity and the torque as a function of shear rate on a double y-axis plot. The silicone liquid is a Newtonian fluid; as expec...

Watch this Scientific Journal Video about Calibration Procedures for Orthogonal Superposition Rheology at JoVE.com

Calibration Procedures for Orthogonal Superposition Rheology

We present a detailed calibration protocol for a commercial orthogonal superposition rheology technique using Newtonian fluids including end-effect correction factor determination methods and recommendations for best practices to reduce experimental error.

Orthogonal superposition (OSP) rheology is an advanced rheological technique that involves superimposing a small-amplitude oscillatory shear deformation ...

Orthogonal Superposition Radiology is an advanced technique that allows the measurement of radiological properties of complex fluids under non-linear flow conditions, which offer insights into the micro-structural changes that governs macroscopic properties. The information gained on the structured property processing relationships in complex fluids is important to many industries for the development and manufacturer of reliable products. OSP is now commercially available for the radiology community.Given the complicated geometry design, a protocol to quantify measurement error is critical to the successful use of this technique. The calibration protocol described in this video is the first standard operating procedure to properly determine the end effect factors, a proper accounting of the end effect factors reduces measurement error. Before installing the geometry, enable the orthogonal superposition feature in the rheometer software.After lifting the stage to maximum height, install a lower platinum resistance thermometer on the test station for temperature measurement and an environmental control device. Assemble the inner and outer cylinders, to complete the double wall cup configuration. Insert the cup into the environmental control device and align the geometry.Press the lower geometry cup downward to compress the spring-loaded platinum resistance thermometer, by using a torque screwdriver to tighten the thumbscrew. Disable the motor power and use a finger to spin the geometry to confirm that the cup rotates freely. Install the upper geometry bob onto the transducer shaft, and click the tear transducer button in the transducer control panel of the rheometer software to tear the normal force and torque.Then click the zero fixture button to zero the gap between the upper and lower geometries. To load the test material, lift the stage to provide enough workspace to load the test material into the cup, and carefully load the test material into the cup. Lower the upper geometry carefully into the fluid to reach the geometry gap set point of eight millimeters.When the bob end contacts the fluid, reduce the downward velocity of the bob. Lift the bob vertically to a position at which the wetted fluid contact line can be visually inspected. Carefully lift the bob to the previous loading position to allow enough workspace and load an additional amount of test material into the cup as needed.Lower the upper geometry into the fluid, and use the go-to geometry gap button to set the cup and final geometry gap. Repeat the adjustment until the wetted contact line on the bob is approximately two millimeters above the lower end of the upper bob opening. Then move the bob to the geometry gap set point and allow the test material to relax.To verify that the correct geometry has been selected, open the orthogonal double wall concentric cylinder geometry. If the orthogonal superposition radiology geometry is not listed, manually create a new geometry with the software, using the dimensions for the geometry as indicated in the table. Then specify the geometry constants, including the inertia and upper tool mass, and enter one for both the end effect factor, and orthogonal end effect factor.To perform a steady sheer rate sweep test, condition the sample at 25 degrees Celsius for 15 minutes. When the test material has reached thermal equilibrium, under the procedure tab in the rheometer software select flow and sweep. In the environmental control window, set the test temperature to 25 degrees Celsius.Set the sheer rate range from 0.01 to 100 inverse seconds, with data recording at 10 points per decade, logarithmically, and enable automatic steady state determination. Then start the experiment. To perform an orthogonal frequency sweep test, set the normal force transducer to conditioning and transducer mode.And condition the sample at 25 degrees Celsius for 15 minutes to ensure thermal equilibration. Select the orthogonal frequency sweep test with the test temperature set to 25 degrees Celsius. Specify the desired normal strain and enter zero inverse seconds for the sheer rate in the rotational direction.Then specify the angular frequency range from 0.1 to 40 rads per second at 10 points per decade, logarithmically, and start the experiment. To verify that the corrections are valid, using the calibrated end effect factors obtained from the calibration experiments, enter the calibrated values for the end effect factor and orthogonal end effect factor under the geometry constants. The stress constants will be automatically updated.Then set up an orthogonal frequency sweep test as demonstrated, using one inverse second for the shear rate and start the experiment. Here, representative results from the viscosity calibration measurements on a 12.2 pascal-second silicone viscosity standard are shown. The silicone liquid is a newtonian fluid with an expected constant viscosity independent of the applied shear rate.The measured torque increases linearly as the sheer rate increases and all of the data are above the low torque limit. The uncorrected viscosity value is higher than the actual viscosity. These orthogonal frequency sweep tests demonstrate different orthogonal strain amplitudes from 0.5 to 9.4%for the 12.2 pascal-second viscosity standard.Similarly, without correction, the measured orthogonal complex viscosity overestimates the actual viscosity of 12.2 pascal-second. Only the viscosity data with corresponding orthogonal force values above the lower limit of the axial oscillation force for the transducer, are used to calculate the average viscosity for correction. To calculate the end effect factors here, the primary in effect factor is equal to the uncorrected primary viscosity divided by the viscosity of the standard liquid.The orthogonal end effect factor is equal to the viscosity of the standard liquid divided by the uncorrected orthogonal viscosity. Here, an orthogonal superposition measurement was performed under steady shear for viscosity verification check. Only the data with values greater than the instrument force resolution were plotted.Since the correct and effect factors were applied, the measured viscosities in both directions matched the accepted oil viscosity value of 12.2 pascal-seconds. Now, you should have a good understanding of how to perform calibration for OSP using newtonian fluids. We recommend that users determine their end effect correction factors for their own instruments and geometries because the actual corrections are material and instrument dependent.Making accurate measurements are important for scientific research as well as product development. This protocol provides a technical resource for the instrument users and also guidance to manufacturers for optimizing the engineering design of future instruments.

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1.9K visualizações.  National Institute of Standards and Technology. Orthogonal Superposition Radiology is an advanced technique that allows the measurement of radiological properties of complex fluids under non-linear flow conditions, which offer insights into the micro-structural changes that governs macroscopic properties. The information gained on the structured property processing relationships in complex fluids is important to many industries for the development and manufacturer of reliable products. OSP is now commercially available for the radiology co...