Low yield stress measurements with a microfluidic rheometer

Yield stress, tau y, is a key rheological property of complex materials such as gels, dense suspensions, and dense emulsions. While there is a range of established techniques to measure tau y in the order of tens to thousands of pascals, the measurement of low tau y, specifically below 1 Pa, remains underexplored. In this article, we present the measurement of low apparent tau y using a Hele-Shaw microfluidic extensional flow device (MEFD). Using the MEFD, we observe a gradient in shear stress, tau, such that tau is lower near the center or stagnation point, and higher away from the stagnation point. For a yield stress fluid, we observe that, below a certain flow rate, tau exceeds tau y only in the outer region, leading to stagnation or unyielding of the fluid in the inner region. We use scaling analysis based on a Hele-Shaw linear extensional flow to deduce tau y by measuring the size of the unyielded region, S. We validate this scaling relationship using Carbopol solutions with concentrations ranging between 0.015 to 0.3%, measuring tau y as low as similar to 10 mPa to similar to 1 Pa, and comparing it with tau y measured using a standard rheometer. While the experimental lower limit of our technique is 5 mPa, modifying the geometry or improving the image analysis can reduce this limit to the order of 10-4 Pa. The MEFD facilitates rapid measurement of tau y, allowing for its real-time assessment. We further report tau y of human blood samples between 30 to 80 mPa with their hematocrit ranging between 14 to 63%. Additionally, we determine tau y for a mucus simulant (similar to 0.7 Pa), and lactic drink (similar to 7 mPa) to demonstrate the versatility of the MEFD technique. The microfluidic extensional flow device (MEFD) exhibits stagnation at the center for yield stress fluids, in contrast to Newtonian fluids. This enables cost-effective and rapid measurement of low yield stresses, attracting wide applications.