Low yield stress measurements with a microfluidic rheometer†

Yield stress, τ_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 τ_y in the order of tens to thousands of pascals, the measurement of low τ_y, specifically below 1 Pa, remains underexplored. In this article, we present the measurement of low apparent τ_y using a Hele-Shaw microfluidic extensional flow device (MEFD). Using the MEFD, we observe a gradient in shear stress, τ, such that τ 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, τ exceeds τ_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 τ_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 τ_y as low as ∼10 mPa to ∼1 Pa, and comparing it with τ_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 τ_y, allowing for its real-time assessment. We further report τ_y of human blood samples between 30 to 80 mPa with their hematocrit ranging between 14 to 63%. Additionally, we determine τ_y for a mucus simulant (∼0.7 Pa), and lactic drink (∼7 mPa) to demonstrate the versatility of the MEFD technique.