Abstract:

The data to be shared consists of: i. an analytical function (a mathematical expression, no associated data) describing the extent of deformation of an interface due to the swimming motion of a micro-organism (swimmer) in its vicinity; ii. ‘time-averaged’ phase portraits [.dat/.xlsx files containing sets of values of U_z (swimmer’s linear swimming velocity normal to the interface) and \Omega_y (swimmer’s angular velocity or rotation rate)] that reflect the swimming dynamics for different relevant parameters; iii. instantaneous trajectories of the swimmer [.dat/.xlsx files containing sets of values of z (swimmer position in the direction normal to the interface), \theta_z (swimmer orientation) and t (time)] that show the exact motion of the swimmer near the interface.

Suggested Citation:

Vaseem A. Shaik, Arezoo A. Ardekani. 2017. Motion of microswimmers near a weakly deforming interface. Distributed by: GRIIDC, Harte Research Institute, Texas A&M University–Corpus Christi. doi:10.7266/N73R0QZ5

Publications:

Shaik, V. A., & Ardekani, A. M. (2017). Motion of a model swimmer near a weakly deforming interface. Journal of Fluid Mechanics, 824, 42–73. doi:10.1017/jfm.2017.285

Purpose:

The primary motivation behind generating this data was to study the motion of micro-organisms in the vicinity of air-fluid or even fluid-fluid interfaces. The emphasis was on analyzing the effects of viscosity ratio (of the two fluids making the interface) on the motion of swimming dynamics of the micro-organism.

Data Parameters and Units:

The name of the directories represents the data of the corresponding figure in the manuscript ("Motion of a model swimmer near a weakly deforming interface" by Vaseem A. Shaik and Arezoo M. Ardekani). Each folder contains a 'readme' file which explains the data provided. All the results are reported as dimensionless numbers that have been normalized as follows: the length is scaled by swimmer radius 'a', velocity by '3*U0/2' (which is the characteristic velocity of an 'isolated' micro-swimmer), time by '2*a/(3*U0)', and pressure and stress by 'mu*3*U0/(2*a)', where mu is the dynamic viscosity of the fluid in which the micro-swimmer is immersed. The following list explains the data held by various .dat files. len_m.dat: Distance of the center of the swimmer from the plane interface theta_m.dat: Orientation of the swimmer with respect to the normal of the plane interface U_zND.dat: Vertical velocity of a swimmer with steady squirming modes near a plane interface Omega_yND.dat: Angular velocity of a swimmer with steady squirming modes near a plane interface The deformation of the interface can be written as F = epsilon * f1(rho, phi), where epsilon is a parameter that is much less than 1. f1.dat: Leading order deformation of the interface due to the motion of a swimmer with steady squirming modes near it. f1 can be written as f1 = h0(rho) + h1(rho) * cos(phi) + h2(rho) * cos(2*phi). The files, 'h0.dat', 'h1.dat' and 'h2.dat' contain the data of the variables h0, h1 and h2 and these can be used to find the leading order interface deformation, f1. U_zm.dat: Average vertical velocity of a time-reversible swimmer near a deforming interface Omega_ym.dat: Average angular velocity of a time-reversible swimmer near a deforming interface Dz.dat: Change in the vertical position of a time-reversible swimmer near a deforming interface in one time period. Dtheta.dat: Change in the orientation of a time-reversible swimmer near a deforming interface in one time period. Translational and angular velocity of the swimmer are functions of the position and orientation of the swimmer with respect to the undeformed interface. So, for each entry (say i-th row and j-th column) of the position in the matrix len_m and corresponding entry of the orientation in the matrix theta_m, the translational and angular velocity of the swimmer are given (in the i-th row and j-th column) in the files U_zND and Omega_yND. Therefore the data provided is NOT a series of number but a 33X30 matrix. Variation of the velocities with the position of the swimmer, for a specific orientation can be obtained by plotting the specific row of the files U_zND or Omega_yND with the specific row of the file len_m.

Individual Files: