Microfluidics and Rheology of Carbon Black Dilute Suspensions: Modeling, Measurement, and Applications C. Aramphongphun * , O. Hemminger ** , J. M. Castro * and L. J. Lee ** * Department of Industrial, Welding and Systems Engineering, The Ohio State University 1971 Neil Ave Columbus, OH, USA 43210, castro.38@osu.edu ** Department of Chemical and Biomolecular Engineering, The Ohio State University 140 West 19th Ave, Columbus, OH, USA 43210, lee.31@osu.edu ABSTRACT Microfluidics and rheology are critical in designing microfluidic systems. A study of the slip flow and rheological properties of suspension fluids becomes more challenging at microscale levels. In this work, a customized microslit rheometer has been developed and used to test carbon black suspensions using micrometer-sized channel gaps (25 µm and 100 µm). A reduced viscosity of the suspension fluid due to wall slip was found in the 25-µm- gap channel. Rheological models for the microslit rheometer were derived using no-slip and slip boundary conditions to calculate the viscosity of the suspension fluid at the microscale level. By analyzing the viscosity data using the developed rheological models, we can determine the values of the slip parameter, known as slip length (β). Keywords: microfluidics, rheology, slip flow, and carbon black suspension 1 INTRODUCTION Microfluidics deals with transport phenomena of fluid flows in fluid-based systems at microscopic length scales, typically 1 to 100 µm. In recent decades, microfluidics has become a popular and promising research topic due to the development of microelectromechanical systems (MEMS) technology and biochemical lab-on-a-chip devices. Microfluidic devices provide benefits over macroscopic devices such as lower material consumption, faster response/reaction time, better portability, and the possibly new functionality. The understanding of the flow behavior in microchannels is essential in designing, analyzing, and modeling microfluidic systems. As the length scale of the fluid domain reaches the microscale level (1-100 µm) and below, several unusual phenomena that are not observed at the larger scales appear. One of the significant changes due to the very small length scale occurs at the fluid-solid boundary. Fluids, particularly polymer systems and suspensions, may slip or appear to slip at the fluid-solid interface [1] leading to the invalidity of the no-slip boundary condition, which is commonly assumed in conventional flow modeling. The wall slip occurring in the microflow changes the flow field of the fluid resulting in the apparent reduced viscosity of the fluids. These microscopic phenomena can be explained by the characteristics of the microflow including: (i) high surface-to-volume ratio, (ii) high rate-of-deformation (e.g. high shear rate and high extensional rate), (iii) high heat and mass transfer rate, and (iv) low Reynolds number (Re). 2 EXPERIMENTAL SETUP A slit rheometer is suitable for the rheological measurement of microfluidics because it can measure the viscosity at high shear rates, it is geometrically and fundamentally similar to the relevant flow, and it is relatively easy to fabricate a micrometer-sized channel gap. An experimental setup of a customized microslit rheometer is shown in Figure 1 and consists of: (i) a microslit die, (ii) a high-precision syringe pump with an on-pump pressure transducer, (iii) a data acquisition system, and (iv) heating tape for high temperature measurement. The microslit die with a micrometer-sized channel gap was built by machining a shim stock of stainless steel following the channel design and clamping it between two die halves (25 mm thick each) made of tool steel. The thickness of the channel gaps is then defined by the thickness of the shim stocks (25 µm and 100 µm thick). The microslit die was connected to the syringe pump via stainless steel tubing (6.35 mm ID). The high precision syringe pump was used to drive the fluid through the microchannel of the microslit die at a given volumetric flow rate. The fluid flowed from the pump into the tubing, and then into the microchannel of the microslit die and exited at the end of the die, where the fluid was collected in a container underneath the die. The total pressure drop (∆p tot ) in the flow system was measured by the on-pump pressure transducer and monitored by a data acquisition system (LabView version 7.1) to find out the pressure drop at steady state. The total pressure drop was corrected by the end pressure drop (∆p end ) to obtain the pressure drop across the channel (∆p). For higher temperature testing, heating tape with an adjustable power controller was used and wrapped around the tubing and the die to increase the operating temperature (50°C). The setting temperatures were controlled at the inlet, where the material flows into the die, by a surface thermometer. NSTI-Nanotech 2006, www.nsti.org, ISBN 0-9767985-7-3 Vol. 2, 2006 633