Microfluidic viscometer for measuring the viscosity of microliter-volume liquid samples
A microfluidic viscometer measures the viscosity of a microliter-volume fluid sample using a microfluidic chip having a microchannel with a high aspect ratio (˜10), allowing the microflow therein to be approximated as a rectangular slit flow. The microfluidic chip is fabricated by stacking rigid sheet materials that can be laser cut to specified shapes and sizes. The microchannel, rendered smooth and hydrophobic by a repellant coating, provides a straight flow path for the sample to approach flow equilibrium as it moves through. By applying corrections related to the visual bias from the camera and the capillary pressure difference at the air-liquid interface, the viscosity of the fluid sample can be calculated based on differential pressure data, sample length, velocity, volumetric flow rate, and contact angle from captured video, and the channel dimension, given that the sample has reached a flow equilibrium condition.
1. A viscometry sample holder comprising:
a sample channel configured to flow a liquid sample under pressure, the sample channel having an upstream end and a downstream end opposite the upstream end along a length of the sample channel;
a viewing window providing optical access to the liquid sample in the sample channel; and
a plurality of ports comprising:
a loading port fluidly coupled to the sample channel proximal the upstream end of the sample channel for loading the liquid sample into the sample channel;
a gas injection port fluidly coupled to the sample channel proximal the upstream end of the sample channel for injecting a gas into the sample channel;
an exhaust port fluidly coupled to the sample channel proximal the downstream end of the sample channel;
an upstream pressure port proximal the upstream end of the sample channel and coupled for measuring an upstream pressure in the sample channel adjacent the upstream pressure port; and
a downstream pressure port proximal the downstream end of the sample channel and coupled for measuring a downstream pressure in the sample channel adjacent the downstream pressure port.
2. The viscometry sample holder of claim 1 , wherein the downstream pressure port is between the upstream pressure port and the exhaust port along the length of the sample channel.
3. The viscometry sample holder of claim 1 , wherein the gas injection port is fluidly coupled to the sample channel at the upstream end of the sample channel.
4. The viscometry sample holder of claim 1 , wherein the gas injection port is the upstream pressure port.
5. The viscometry sample holder of claim 1 , wherein the gas injection port is different from the upstream pressure port, and the upstream pressure port is between the gas injection port and the downstream pressure port along the length of the sample channel.
6. The viscometry sample holder of claim 1 , wherein the sample channel has a sample channel height of 75 nm to 200 μm.
7. The viscometry sample holder of claim 1 , wherein the sample channel has a sample channel width of 500 nm to 1500 μm.
8. The viscometry sample holder of claim 1 , comprising a sample chip, the sample chip comprising a plurality of sample chip layers comprising:
a base layer;
a cover layer; and
a sample channel layer sandwiched between an upper surface of the base layer and an opposing lower surface of the cover layer,
wherein:
the sample channel layer comprises a sample channel slit opening traversing a thickness of the sample channel layer, wherein the sample channel slit opening is defined by a sample channel wall;
the viewing window comprises at least a part of the cover layer adjacent the sample channel; and
for each one of the plurality of ports, independently, at least one of the base layer or the cover layer comprises that one of the plurality of ports.
9. The viscometry sample holder of claim 8 , wherein the upper surface of the base layer, the sample channel wall, and the lower surface of the cover layer together define the sample channel.
10. The viscometry sample holder of claim 8 , wherein the plurality of sample chip layers further comprises:
a loading channel layer comprising a loading channel fluidly coupled:
to the loading port at a loading port end of the loading channel; and
to the upstream end of the sample channel at a sample channel end of the loading channel,
wherein an upper surface of the sample channel layer, the sample channel wall, and the lower surface of the cover layer together define the sample channel.
11. The viscometry sample holder of claim 8 , wherein the cover layer comprises each one of the plurality of ports.
12. The viscometry sample holder of claim 8 , wherein the plurality of sample chip layers comprises alignment structures configured for alignment of the plurality of sample chip layers.
13. The viscometry sample holder of claim 8 , further comprising a sample chip case configured to enclose the sample chip, the sample chip case comprising a sample chip case base and a sample chip case cover, wherein:
the sample chip case base and a sample chip case cover are respectively configured for assembly to define an interior space sized and shaped to fittingly enclose the sample chip;
the sample chip case cover comprises a window opening sized, shaped, and positioned for alignment with the at least the part of the cover layer adjacent the sample channel, to provide the optical access to the liquid sample in the sample channel when the sample chip is enclosed in the sample chip case and the sample chip case is assembled, wherein the viewing window further comprises the window opening; and
for each one of the plurality of ports, the sample chip case comprises a corresponding port coupler configured for fluid coupling with the corresponding port.
14. The viscometry sample holder of claim 13 , wherein for each one of the plurality of the ports, the corresponding port coupler forms an airtight seal with the port when the sample chip is enclosed in the sample chip case and the sample chip case is assembled.
15. The viscometry sample holder of claim 13 , wherein the sample chip case base comprises a perimeter ridge proximal a perimeter of the sample chip case base and extending from an upper surface of the sample chip case base opposing a lower surface of the sample chip case cover when the sample chip case is assembled, the sample chip case cover comprises a perimeter groove proximal a perimeter of the sample chip case cover and extending into the lower surface of the sample chip case cover, wherein the perimeter ridge and the perimeter groove are respectively sized, shaped, and configured for nesting of the perimeter ridge in the perimeter groove when the sample chip case is assembled for alignment of the sample chip case cover and the sample chip case base.
16. The viscometry sample holder of claim 13 , wherein the sample chip case base comprises one or more prying grooves formed in the upper surface of the sample chip case base for prying apart the assembled sample chip case cover and the sample chip case base.
17. A viscometry system comprising:
the viscometry sample holder of claim 1 ;
a gas pump fluidly coupled to the gas injection port and operable to inject the gas into the sample channel to flow the liquid sample under pressure in the sample channel;
a pressure gauge coupled to the upstream pressure port and the downstream pressure port and operable to measure a differential pressure based on the upstream pressure and the downstream pressure;
an optical imager operable and positioned to optically image the liquid sample in the sample channel through the viewing window; and
a controller:
coupled to the pressure gauge to receive differential pressure measurement signals from the pressure gauge;
coupled to the optical imager to receive optical sample image signals from the optical imager; and
operable to compute a viscosity of the liquid sample in the sample channel based on the differential pressure measurement signals and the optical sample image signals.
18. The viscometry system of claim 17 , wherein the optical imager comprises a camera operable to generate a video signal of the liquid sample while flowing in the sample channel, wherein the optical sample image signals comprise the video signal.
19. The viscometry system of claim 17 , wherein the optical imager comprises a camera operable to capture a sequence of images of the liquid sample while flowing in the sample channel, wherein the optical sample image signals comprise the sequence of images.
20. The viscometry system of claim 17 , wherein the controller is operable:
to determine an average sample velocity of the liquid sample while flowing in the sample channel based on the optical sample image signals; and
to compute the viscosity of the sample in the channel based on the differential pressure measurement signals and the determined average sample velocity of the liquid sample while flowing in the sample.
21. The viscometry system of claim 20 , wherein the controller is operable:
to determine a length of the liquid sample while flowing in the sample channel based on the optical sample image signals; and
to compute the viscosity of the sample in the channel based on the differential pressure measurement signals, the determined average sample velocity of the liquid sample while flowing in the sample channel, and the length of the liquid sample while flowing in the sample channel.
22. The viscometry system of claim 21 , wherein the controller is operable:
to compute a shear stress of the liquid sample while flowing in the sample channel based on the differential pressure measurement signals, the length of the liquid sample while flowing in the sample channel, and cross-sectional dimensions of the sample channel;
to compute a shear rate of the liquid sample while flowing in the sample channel based on the determined average sample velocity of the liquid sample while flowing in the sample channel, and the cross-sectional dimensions of the sample channel; and
to compute the viscosity of the sample in the channel based on the computer shear stress and the computed shear rate.
23. The viscometry system of claim 22 , wherein:
the optical imager is operable to optically image an upstream air-liquid interface of the liquid sample; and
the controller is operable:
to determine a dynamic contact angle of the upstream air-liquid interface with a sidewall of the sample channel based on the optical sample image signals; and
to compute the viscosity of the sample in the channel based at least in part on the dynamic contact angle.
24. The viscometry system of claim 23 , wherein the controller is operable:
to compute a capillary pressure difference based on the determined dynamic contact angle of the upstream air-liquid interface, a surface tension of the liquid sample, and a hydraulic radius of the sample channel; and
to compute the shear stress based in part on the computed capillary pressure difference.
25. The viscometry system of claim 24 , wherein the controller is operable to compute the viscosity as the ratio of the shear stress τ w and shear rate {dot over (γ)} at the sample channel wall according to:
τ
w
=
H
(
Δ
P
-
Δ
P
capillary
)
2
(
1
+
H
W
)
L
sample
γ
.
=
6
Q
(
1
+
H
W
)
WH
2
where H is a sample channel height of the sample channel, W is a sample channel width of the sample channel, ΔP is the differential pressure measured by the pressure gauge, L sample is the length in the sample channel of the liquid sample, the volumetric flow rate Q of the liquid sample is:
Q
=
HW
v
_
where ν is the average sample velocity ν of the liquid sample flow in the sample channel, and ΔP capillary is the capillary pressure difference according to:
Δ
P
capillary
=
2
σ
cos
θ
R
_
where σ is the surface tension of the liquid sample, σ is the dynamic control contact angle, and R is the hydraulic radius of the sample channel determine by:
R
_
=
1
1
H
+
1
W
.