Ite rotating cylinder in Stokes flow is = four two , where is the dynamic viscosity from the fluid, will be the angular rotation rate, and r will be the cylindrical radius. We measured the torque on a rotating cylinder with radius r = six.35 0.two mm and length = 149 1 mm and, by assuming = , made use of the information to resolve for the viscosity with the fluid. We also assumed that the finite size of the tank did not affect the torque value within the middle, which was greater than 25r in the nearest boundary. Prior to each data collection run, we measured the temperature in the oil with a NIST-traceable calibrated thermistor (Cole-Parmer Digi-Sense-AO-3780404 Calibrated Digital Thermometer) and adjusted the previously determined viscosity using the manufacturer’s temperature coefficient of viscosity 1.00 10-6 kg/(m)/ C. See Section 2.three.two for a detailed description of the torque measurements.Fluids 2021, six,9 of2.3.1. Fabricating Helices We fabricated helices of varying wavelengths (two.26 /R 11.88) by wrapping straight stainless steel YQ456 custom synthesis welding wire about cylindrical aluminum mandrels with various helical V-grooves precisely machined applying a CNC lathe. The V-grooves transition to a flat face with a straight groove, to which the remaining straight section is usually clamped; see Figure 4.Figure four. Image of a model flagellum (helix), forming mandrel (bright aluminum), and annealing rod (oxidized stainless steel). The aluminum forming mandrel had helical V-shaped grooves that were used to create model flagella with distinct wavelengths. Just after forming, the flagella were annealed on a smooth precision annealing rod to enhance uniformity within the radius (R 0.1 mm). The helical parameters are listed in Table three.Mandrels have been held on a lathe, and the wire was hand-spun into the V-groove. The straight sections have been secured towards the flat faces, which left straight stems aligned with all the axes of the helices to be attached towards the motor through a rigid shaft adapter. Residual tension in the wires triggered the wavelengths and radii to differ just after they have been removed from the mandrels. The helices had been forced onto a precision stainless steel rod with radius R = six.350 0.013 mm for annealing. The helices on the rod had been then placed into a tube furnace (MTI GSL-1500X) and annealed at 900 degrees Celsius for two hours, which removed most of the variation in the radii from the helices and fixed the helical wavelengths. The helix parameters made use of in the experiments are listed Table 3:Table 3. Wavelengths and lengths of helices. /R 2.26 0.13 three.88 0.01 5.86 0.08 eight.65 0.01 10.91 0.01 11.88 0.01 L/R 22.3 0.five 24.3 0.5 30.0 0.five 23.3 0.5 24.two 0.five 23.1 0.The helical wavelength and axial length L are expressed in terms of the helical radius R; R = six.35 0.10 mm in all cases. The filament radius was a/R = 0.111 for all helices.Fluids 2021, six,ten of2.three.two. Axial Torque Measurements To measure the dependence of torque on boundary distance, we secured the tank onto a horizontal stage that permitted for motion within the x-direction, as shown in Figure five. The motion from the stage was controlled by a linear guide using a worm gear screw that advanced the stage 0.three mm per revolution. The screw was turned making use of a computer-controlled NEMA 23 stepper motor using a resolution of 400 steps/rev. This gave far better than one PTIQ Purity & Documentation hundred precision in controlling the boundary distance, which was needed: the step size close to the boundary was as compact as 0.five mm.Vertical stage Torque Futek reaction torque sensor (.7 mNm)Motor and encoder0.5 m0.3 mHorizontal stage -dir (.