Numerical data on the shear stress distribution generated by a rotating rod within a stationary ring over a 35-mm cell culture dish

The data contained within this article relate to a rotating rod within a stationary ring that was used to generate shear stress on cells and tissues via a medium. The geometry of the rotating rod within a stationary ring was designed to work with a 35-mm diameter culture dish. The data of the shear stress distribution are presented in terms of area-weighted average shear stress and the uniformity index, which were calculated for medium volumes of 4 and 5 ml at various rotational speeds ranging from 0 to 1000 rpm.


a b s t r a c t
The data contained within this article relate to a rotating rod within a stationary ring that was used to generate shear stress on cells and tissues via a medium. The geometry of the rotating rod within a stationary ring was designed to work with a 35-mm diameter culture dish. The data of the shear stress distribution are presented in terms of area-weighted average shear stress and the uniformity index, which were calculated for medium volumes of 4 and 5 ml at various rotational speeds ranging from 0 to 1000 rpm.
& Value of the data The data provide CAD drawing of the rotating rod within a stationary ring that can be used to generate shear stress on cells in a 35-mm diameter culture dish with a uniformity index up to 0.82.
The uniformity index data can be used by researchers as a benchmark in designing the geometry of a rotating rod or disk for shear stress loading on cells.
The data present the set up condition of the rotational speed to achieve a desired average shear stress at a specific medium volume.
Researchers may use the mathematical models obtained from the relationship between the average shear stress and the rotational speed to determine their own desired set up conditions.

Data
The data presented in this article are based on the numerical simulation of the shear stress distribution generated via a medium by a newly designed rotating rod within a stationary ring that was used to load shear stress on cells and tissue cultured in vitro [1]. The rotating rod within a stationary ring is designed to be used with a 35-mm diameter culture dish. Fig. 1(a)-(c) presents the CAD drawing of the rotating rod within a stationary ring of which the rotating rod is chamfered to be coneshaped with 15°tilt angle and the stationary ring has inner and outer diameters of 25 and 34 mm, respectively. The rest dimensions in the Fig. 1    the bottom of the culture dish generated by the rotating rod within the stationary ring at various rotational speeds are presented in Table 1. These data are also plotted with rotational speeds for the medium volumes of 4 and 5 ml in Figs. 4 and 5, respectively.

Experimental design, materials, and methods
The geometry of the computational domain of the fluid (Fig. 1d) was discretized into computational cells using the finite volume method in the ANSYS WORKBENCH R16.2. The CFD simulation was performed using ANSYS FLUENT R16.2 software to analyze the shear stress distribution at the bottom of the culture dish. The medium temperature was set at 310.15 K. The medium was treated as a Newtonian fluid. The density and viscosity of the medium fluid were 1012.95 kg m À 3 and 0.00282 kg m À 1 s À 1 , respectively. The tilt surface of the computational domain of the fluid, which is the cone-shaped rotating rod/medium interface, was selected as the "inlet" surface. The velocity of the inlet surface was input in terms of rad/s. The velocity of the remaining surface of the computational domain was set as zero based on no-slip assumption as it was in contact with either the surface of the stationary ring or the wall surface of the culture dish. The SIMPLE (Semi-Implicit Method for Pressure Linked Equations) algorithm was employed to solve the Navier-Stokes equations iteratively. The calculation in double digit precision was used to achieve simulation results with high accuracy. The second-order upwind discretization scheme was selected to avoid the oscillation of the solution. The under-relaxation factors of the pressure, density, body forces, and momentum were set at 0.27, 1, 1, and 0.55, respectively [2]. The solutions were iterated until the specified convergence criterion of 10 À 6 was achieved. The degree of the model discretization was based on the convergence evaluation results. The final model had 397,307 computational polyhedral cells and 72,510 nodes.
The assumptions made in the simulation were (i) the model was under the steady state and isothermal conditions, (ii) the fluid velocity at a fluid-solid boundary was equal to that of the solid boundary (no-slip condition), (iii) the medium was homogeneous and isotropic, and (iv) the cell height at the bottom of the culture dish was negligible [2].
The criterion used to determine how uniformly the shear stress is distributed over the surface of the culture dish bottom is the area-weighted uniformity index (γ a ), where a value of 1 indicates the highest uniformity. The area-weighted uniformity index can be expressed as [3]: where, τ is the shear stress (Pa). τ a is the area-weighted average shear stress, which is calculated by The simulations were performed using an Intel Xeon E5-1650 v2 @ 3.5 GHz processor with 32 GB RAM and 4 GB graphic card memory.