Abstract:

This data contains information from simulations of swimming helical flagella in free space and confined in a tube. We have recorded the parameters used in the numerical simulations as well as the computed quantities: swimming speed, angular frequency, the flexural rigidity of the flagella, the non-dimensional sperm number, and the distance swam per revolution. We use this data to analyze how the swimming behavior of the flagella changes as we vary the driving torque and the flexibility of the flagella in free space and in confined tubes of varying radii. This dataset supports the publication: LaGrone, J., Cortez, R., & Fauci, L. (2019). Elastohydrodynamics of swimming helices: Effects of flexibility and confinement. Physical Review Fluids, 4(3). doi:10.1103/physrevfluids.4.033102

Suggested Citation:

John LaGrone, Ricardo Cortez, Lisa Fauci. 2019. Dataset for: Elastohydrodynamics of swimming helices: Effects of flexibility and confinement. Distributed by: GRIIDC, Harte Research Institute, Texas A&M University–Corpus Christi. doi:10.7266/n7-d849-2x63

Publications:

LaGrone, J., Cortez, R., & Fauci, L. (2019). Elastohydrodynamics of swimming helices: Effects of flexibility and confinement. Physical Review Fluids, 4(3). doi:10.1103/physrevfluids.4.033102

LaGrone, J., Cortez, R., Yan, W., & Fauci, L. (2019). Complex dynamics of long, flexible fibers in shear. Journal of Non-Newtonian Fluid Mechanics, 269, 73–81. doi:10.1016/j.jnnfm.2019.06.007

Purpose:

This data was collected from simulations to investigate the effects that elasticity and confinement have on helical swimmers.

Data Parameters and Units:

The dataset contains the following four data files: 1. The data_simulations.csv - This file contains the data and the parameters of simulations that were run with the flagellum swimming either in free space or centered in a tube. 2. The file data_angled_simulations.csv - This file contains the data and the parameters of simulations that were run with the flagellum swimming either in a tube with a prescribed initial angle relative to the axis of the tube. 3. The file data_summary.csv - This file contains a summary of the data contained in data_simulations and data_angled_simulations. In particular, it summarizes the ranges parameters used in the simulations and the resulting ranges. Additionally, it converts the data from the non-dimensional units used in the code to physical units using the time scale "T scale", the length scale "L scale", the force scale "F scale", and the velocity scale "Vel scale." These scalings were chosen to approximately match experimental observations and we have a label "DO NOT CHANGE THESE" to remind us that we should not edit this portion of the file. 4. The file data.xlsx - This file contains the data_simulations.csv, data_angled_simulations.csv, and data_summary.csv as separate sheets. We have included it as there are formulas which extract data from the data sheets to the summary sheet and also compute the scalings, which are not preserved in the CSV versions of the files. In these files the following headers are parameters of the simulations: dt = time step size; n_steps = maximum number of time steps to run the simulation for; out_freq = how many time steps to take between data outputs; flagella_polygon_degree = describe the cross-section of the flagellum discretization. 3 means the cross-section is triangular, 4 is square, 5 is pentagonal, 6 is hexagonal, etc.; inner_radius = radius of the flagellum structure; n_straight_cross_section = number of straight sections in the flagellum before the tapered helical structure begins; n_turns = the number of turns in the helical structure of the flagellum; arc_length = the target arc length to build the flagella; length = (unused parameter that remained in code); beta = parameter defining the helical tapering; gamma = parameter defining the helical tapering; max_radius = the maximum radius of the helix (on the centerline); h = the grid spacing (e.g. the distance between neighboring cross-sections); k = the hookean spring stiffness (with units of force); n_connected_levels = the number of neighboring cross-sections to connect with springs; rotation_angle = angle to rotate the flagellum after constructing it (in radians, in the yx-plane); rotlet_strength = amount of torque to drive the simulation; rotlet_seperation = the distance between the driving torque and the counter-torque placed in front of the flagellum; tube_r = tube radius if using a tube in the simulation (-1 indicates free space, so there is no tube); tube_l = length of the tube in the simulation (-1 indicates free space, so there is no tube); tube_min_z = the starting location of the tube in the z-coordinate (the axis of the tube is the z-axis); tube_h = the space between discrete points on the tube; reg_scale = the scaling factor used to convert h (or tube_h) to the regularization parameter \ varepsilon The remaining headers are computed quantities in the simulations:speed = the swimming speed of the flagellum; frequency = the frequency of rotation of the flagellum; energy = the spring energy in the flagellum; EI = the bending rigidity of the flagellum; xi perp = roughly, the perpendicular drag (this factor appears in the sperm number); sperm number = a non-dimensional number which characterizes the effects of viscosity and elasticity on the flagellum; distance per rotation = how far the simulation swims in a single rotation (on average).

Methods:

This data came from simulations of helical flagella in viscous fluids. The simulations were performed by constructing a flagellum in an initial "preferred" shape out of a network of Hookean springs. This shape was free to deform during the simulation. Hence, the achieved motion was not prescribed. The flagellum was turned by applying a torque at the front of the flagellum and a second torque of the opposite sign was added some distance in the front of the flagellum to maintain a zero net torque (this second counter-torque may be thought of as a crude cell body.) To couple the fluid and the flagellum, it was noted that the system was appropriately modeled using Stokes equations. The method of regularized Stokeslets was utilized, which gives an analytic expression for the velocity of the fluid based on the forces (which come from the springs) and torques (which we apply) for Stokes Equations. The system moves and evolves based on the computed velocities, then the spring forces are recomputed in the new orientation and were repeated.

Individual Files: