Figure 3. Geometry optimization and benchtop evaluation of sweat conductivity channels and electrodes.

a. Typical capacitance spectra for a sweat conductivity sensor comprising a pair of coplanar electrodes integrated with microfluidic systems (pad area $\text{p}=27{\text{mm}}^2$, channel length ${\text{L}}_{\text{c}}=3\text{mm}$) at room temperature in air. The initially empty channels (dashed black line) are filled with different conductive solutions (solid colored lines) with conductivities ranging from 0.000179 (red line) to 1.04 S m-1 (orange line). Those liquids (also used for Figure 3e and f measurements) include DI water, NaCl solutions with multiple concentrations, as well as commercial artificial sweat. The capacitance behavior varies distinctively from 2 kHz to 3 MHz in response to the different conductive liquids. At a given frequency within the range of the sharp decrease of capacitance, the values recorded for different conductivities are different and thus allow a measurement of conductivity through capacitance.

b. Corresponding FEA results of the capacitance for different conductive solutions using the sensor geometry (inset) with channel length ${\mathbf{\text{L}}}_{\mathbf{\text{c}}}=3\text{mm}$ and channel width ${\mathbf{\text{W}}}_{\mathbf{\text{c}}}=0.2\text{mm}$, with same color code as in part a of this figure. The results show excellent agreement with experimental results without any parameter fitting.

c. FEA contour of maximum sensitivity based on a parametric study of the connecting channel width ${\mathbf{\text{W}}}_{\mathbf{\text{c}}}$ and length ${\mathbf{\text{L}}}_{\mathbf{\text{c}}}$ (shown in the schematic on the left) between circular channels in a simplified model of the actual geometry. The size of the circular channels is adjusted to maintain a constant volume while the connecting channel dimensions vary. To maximize the sensitivity, the results suggest that the dimensions of ${\mathbf{\text{W}}}_{\mathbf{\text{c}}}$ and ${\mathbf{\text{L}}}_{\mathbf{\text{c}}}$ must be small.

d. FEA contour of the value of the frequency when the sensor reaches maximum sensitivity. The connecting channel width ${\mathbf{\text{W}}}_{\mathbf{\text{c}}}$ and length ${\mathbf{\text{L}}}_{\mathbf{\text{c}}}$ are varied, as explained in part c of this figure. For given dimensions of the connecting channel, the sensitivity is maximum at the simulated frequency, which corresponds to ideal frequency for the measurement.

e. Experiments showing the influence of geometry (pad size p, length of connecting channel l) on the relationship between the capacitance difference between filled and empty channels and the conductivity of the liquid. Measurements are taken at 25 kHz, and the highest sensitivity is achieved with $\text{p}=27{\text{mm}}^2$, l=3 mm (for a total sensor size at the cm scale).

f. Results with the final stack of materials for the sensor to be used on skin including a additional layer of PDMS (as shown in Fig. 1f) that allows for a back-shielding (shielding plane in between skin and electrodes). The difference in capacitance between filled and empty channels is linear as a function of liquid conductivity for the geometry chosen ($\text{p}=27{\text{mm}}^2$, l=3 mm) and the influence of skin is small as shown by the difference between blue (on skin) and green (in air) curves in the presence of a shielding plane. Sensitivity on skin is 13.9 pF (S.m⁻¹)⁻¹.