Low yield stress measurements with a microfluidic rheometer.

Abstract

Yield stress, <i>τ</i>_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 <i>τ</i>_y in the order of tens to thousands of pascals, the measurement of low <i>τ</i>_y, specifically below 1 Pa, remains underexplored. In this article, we present the measurement of low apparent <i>τ</i>_y using a Hele-Shaw microfluidic extensional flow device (MEFD). Using the MEFD, we observe a gradient in shear stress, <i>τ</i>, such that <i>τ</i> 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, <i>τ</i> exceeds <i>τ</i>_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 <i>τ</i>_y by measuring the size of the unyielded region, <i>S</i>. We validate this scaling relationship using Carbopol solutions with concentrations ranging between 0.015 to 0.3%, measuring <i>τ</i>_y as low as ∼10 mPa to ∼1 Pa, and comparing it with <i>τ</i>_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 <i>τ</i>_y, allowing for its real-time assessment. We further report <i>τ</i>_y of human blood samples between 30 to 80 mPa with their hematocrit ranging between 14 to 63%. Additionally, we determine <i>τ</i>_y for a mucus simulant (∼0.7 Pa), and lactic drink (∼7 mPa) to demonstrate the versatility of the MEFD technique.