# Calibration

Calibration of Flow Speed

# Calibration of fluid flow velocity

To visualize the flow profile, rainbow beads (SPHERO^{TM} Rainbow Calibration Particles, Cat No. RCP-60-5, Lot No. AB01, diameter: 6um^{[1]}) were dissolved in the cell culture medium, which contained some dead cells. A series of pumped flow rate(5μl/min, 15μl/min, and 45μl/min) were applied to generate a steady fluid flow. The length of the streakline (shown as a gray line in picture) represents the total traveling distance of the beads during the exposure time of 100ms . Fig. 1 shows a typical image of a bead trace(fastest microfluidics channel with the flow rate of 5ul/min). To minimize hydraulic effects of the PDMS walls, the pictures were taken from the midplane of the channel providing the maximum flow velocity. Note that the traveling direction of the beads was left. Each streak was measured separately, and the average length of all streaks in one particular channel divides the exposure time was regarded as the maximum flow velocity of this channel. ^{[2]}

## Experiment

To minimize the error, we took pictures on fast microfluidics channel when pumped flow rate was 5μl/min; on mid microfluidics channel when pumped flow rate was 15μl/min; on slow microfluidics channel when pumped flow rate was 45μl/min, considering that fluid flow velocity is proportional to pumped flow rate.

Data collection blow:

channel | flow rate(μl/min) | length①(um) | length②(um) | length③(um) |
---|---|---|---|---|

fast | 5 | 630 | 455 | 610 |

mid | 15 | 180 | 160 | 180 |

slow | 45 | 48 | 75 | 80 |

## Result

We wrote a MatLab program to calculate the maximum flow velocities. Codes were shown below:

#### MatLab Code:

ex_fast=[630,455,610]*90;

% align the data to um/s by multiply 10 and convert to 45μl/min

ex_mid=[180,160,180]*30;

ex_slow=[48,75,80]*10;

ex_fast_mean=mean(ex_fast); ex_fast_std=std(ex_fast);

ex_mid_mean=mean(ex_mid); ex_mid_std=std(ex_mid);

ex_slow_mean=mean(ex_slow); ex_slow_std=std(ex_slow);

variable | mean(um/s) | variable | std(um/s) |
---|---|---|---|

ex_fast_mean | 50850 | ex_fast_std | 8600 |

ex_mid_mean | 5200 | ex_mid_std | 350 |

ex_slow_mean | 676 | ex_slow_std | 170 |

The ratio of maximum velocities in 3 different channels is 13:100:978.

# Reference

- ↑ Rainbow beads official website, Retrieved from http://www.spherotech.com.
- ↑ Maneshi MM, Sachs F, Hua SZ,
*A Threshold Shear Force for Calcium Influx in an Astrocyte Model of Traumatic Brain Injury.*J Neurotrauma. 2015 Jul 1,**32**(13) : p. 1020-9.