Rheological estimation of aggregate size for a colloidal suspension of carbon black particles
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Rheological estimation of aggregate size for a colloidal suspension of carbon black particles Dokyung Kim and Sangkyun Koo* Department of Chemical Engineering and Materials Science, Sangmyung University, Seoul 03016, Republic of Korea (Recieved January 22, 2020; final revision received July 27, 2020; accepted September 21, 2020) Colloidal aggregation is quantitatively characterized by a rheological analysis of the colloidal suspension at various particle concentrations. The rheological analysis is combined with fractal concept to estimate the compactness, size, and size variation with shear stress on colloidal aggregates. The rheological measurement is carried out for a colloidal suspension of 24 nm carbon black particles suspended in ethylene glycol. The particle concentration ranges from 6.0 to 8.5 percent in volume, which is non-dilute regime where colloidal gelation occurs. Elastic modulus behavior with the particle concentration provides fractal dimension of aggregates. With the fractal dimension, concentration-dependent shear stress behavior is used to estimate aggregate size and its variation with shear stress through a rheological modeling. The estimated fractal dimension of aggregate is 2.020 and the average aggregate size exponentially decreases with the shear rate in the range 1152.24 nm at 1 s1 to 150.00 nm at 1000 s1. These estimations are compared with those from optical measurement using static small-angle X-ray scattering (SAXS) technique. The SAXS analysis gives the fractal dimension of 2.495 and the average aggregate size is 320.56 nm. It is found that the optical measurement gives slightly higher fractal dimension and the aggregate size is numerically close to that predicted one around the shear rate 68.7 s1 where steep size reduction turns into being slow. Keywords: colloidal aggregate, fractal dimension, elastic modulus, yield stress, intrinsic viscosity, effectivemedium approximation
1. Introduction Rheological analysis has been widely carried out to investigate rheological behavior of materials at various circumstances. It is aimed at not only providing basic information for process design and optimization but also understanding relation between microstructure and microscopic behavior of the materials. A class of the materials in which microscale analysis is necessarily important is colloidal suspensions. Microstructure of colloidal suspensions has long been popular research subject due to its industrial as well as academic significance. One of the research approaches to the microstructure is rheological analysis which has much contributed to deepening comprehension of the suspension behavior. Numerous studies have been presented on the rheological behavior of the colloidal suspensions (Casson, 1959; Krieger and Dougherty, 1959; Mewis and Wagner, 2012; Nasser et al., 2016; Quemada, 1977; Smith and Bruce, 1979). Particle aggregation among the microstructure subject has been an important topic and it is reflected in rheological behavior of the colloidal suspension. F
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