# Source code for dclab.features.emodulus.viscosity

```"""Viscosity computation for various media"""

import warnings

import numpy as np

from ...warn import PipelineWarning

#: Media for which computation of viscosity is defined
KNOWN_MEDIA = ["CellCarrier", "CellCarrierB", "water"]

[docs]class TemperatureOutOfRangeWarning(PipelineWarning):
pass

[docs]def get_viscosity(medium="CellCarrier", channel_width=20.0, flow_rate=0.16,
temperature=23.0):
"""Returns the viscosity for RT-DC-specific media

Media that are not pure (e.g. ketchup or polymer solutions)
often exhibit a non-linear relationship between shear rate
(determined by the velocity profile) and shear stress
(determined by pressure differences). If the shear stress
grows non-linearly with the shear rate resulting in a slope
in log-log space that is less than one, then we are talking about
shear thinning. The viscosity is not a constant anymore (as it
is e.g. for water). At higher flow rates, the viscosity becomes
smaller, following a power law. Christoph Herold characterized
shear thinning for the CellCarrier media :cite:`Herold2017`.
The resulting formulae for computing the viscosities of these
media at different channel widths, flow rates, and temperatures,
are implemented here.

Parameters
----------
medium: str
The medium to compute the viscosity for; Valid values
are defined in :const:`KNOWN_MEDIA`.
channel_width: float
The channel width in µm
flow_rate: float
Flow rate in µL/s
temperature: float or ndarray
Temperature in °C

Returns
-------
viscosity: float or ndarray
Viscosity in mPa*s

Notes
-----
- CellCarrier and CellCarrier B media are optimized for
RT-DC measurements.
- Values for the viscosity of water are computed using
equation (15) from :cite:`Kestin_1978`.
- A :class:`TemperatureOutOfRangeWarning` is issued if the
input temperature range exceeds the temperature ranges given
by :cite:`Herold2017` and :cite:`Kestin_1978`.
"""
# also support lower-case media and a space before the "B"
valmed = [v.lower() for v in KNOWN_MEDIA + ["CellCarrier B"]]
medium = medium.lower()
if medium not in valmed:
raise ValueError("Invalid medium: {}".format(medium))

# convert flow_rate from µL/s to m³/s
# convert channel_width from µm to m
term1 = 1.1856 * 6 * flow_rate * 1e-9 / (channel_width * 1e-6)**3 * 2 / 3

if medium == "cellcarrier":
temp_corr = (temperature / 23.2)**-0.866
term2 = 0.6771 / 0.5928 + 0.2121 / (0.5928 * 0.677)
eta = 0.179 * (term1 * term2)**(0.677 - 1) * temp_corr * 1e3
if np.min(temperature) < 16 or np.max(temperature) > 26:
# see figure (9) in Herold arXiv:1704.00572 (2017)
warnings.warn("For CellCarrier, the temperature should be in "
+ "[18, 26] degC! Got min/max of "
+ "[{:.1f}, {:.1f}] degC.".format(
np.min(temperature), np.max(temperature)),
TemperatureOutOfRangeWarning)
elif medium in ["cellcarrierb", "cellcarrier b"]:
temp_corr = (temperature / 23.6)**-0.866
term2 = 0.6771 / 0.5928 + 0.2121 / (0.5928 * 0.634)
eta = 0.360 * (term1 * term2)**(0.634 - 1) * temp_corr * 1e3
if np.min(temperature) < 16 or np.max(temperature) > 26:
# see figure (9) in Herold arXiv:1704.00572 (2017)
warnings.warn("For CellCarrier B, the temperature should be in "
+ "[18, 26] degC! Got min/max of "
+ "[{:.1f}, {:.1f}] degC.".format(
np.min(temperature), np.max(temperature)),
TemperatureOutOfRangeWarning)
elif medium == "water":
if np.min(temperature) < 0 or np.max(temperature) > 40:
# see equation (15) in Kestin et al, J. Phys. Chem. 7(3) 1978
warnings.warn("For water, the temperature should be in [0, 40] "
+ "degC! Got min/max of "
+ "[{:.1f}, {:.1f}] degC.".format(
np.min(temperature), np.max(temperature)),
TemperatureOutOfRangeWarning)
eta0 = 1.002  # [mPa s]
right = (20-temperature) / (temperature + 96) \
* (+ 1.2364
- 1.37e-3 * (20 - temperature)
+ 5.7e-6 * (20 - temperature)**2
)
eta = eta0 * 10**right
return eta
```