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Nanomaterials 2020, 10, 2202 8 of 16 where A (microns), a, b and c are coefficients of the regression model. The units for particle size are in microns rather than nanometres to avoid large values of coefficient A and to keep all coefficients roughly of similar magnitudes. Furthermore, with coefficient A and particle size being in microns ensures dimensional agreement is preserved. The following models have been generated for the smooth and grooved discs: Smooth disc: Grooved disc: Particle size (microns) = 100.32Re−0.08Reω−0.13S−0.03 (11) R2 = 0.933, R2 (adj.) = 0.913 Particle size (microns) = 100.24Re−0.26Reω−0.08S−0.01 (12) R2 = 0.930, R2 (adj.) = 0.909 The models are applicable for the following ranges, with Re and Reω estimated at radial distances of 15 cm from the centre where the nanoparticles were collected and measured: 8.21 ≤ Re ≤ 52.4 3.04×105 ≤ Reω ≤ 1.94×106 116 ≤ S ≤ 1074 Figure 5 displays a comparison between the experimental data and data predicted from the models given in Equations (11) and (12). The negative sign of the coefficients in Equations (11) and (12) indicates a negative correlation between all the dimensionless parameters and particle size. Thus, it is predicted that an increase in Re would lead to a reduction in particle size. This would occur at high flow rates or low viscosities as described in Equation (5). Similarly, Reω is greater at higher disc rotational speeds, leading to a reduction in particle size. An increase in initial supersaturation ratio also results in smaller particles, although the magnitudes of the coefficients in Equations (11) and (12) indicate that particle size is least influenced by initial supersaturation, S, than Re or Reω for both disc textures studied. Figure 5. Comparison between predicted particle size and experimental particle size for smooth and grooved discs using the rotational Reynolds number (Reω). According to the range of rotational Reynolds numbers encountered in the SDR, the flow is primarily in the transitional or turbulent regime, although the conventional Reynolds number, Re, suggests the flow regime falls between laminar and wavy-flow regimes. It is apparent from Equations (11) and (12) that the rotational Reynolds number, Reω, hence disc rotational speed, isPDF Image | Hydro Starch Nanoparticles Precip Spinning Disc Reactor
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