Streaming Current - Measurement Method

Measurement Method

A typical setup to measure streaming currents consists of two reversible electrodes placed on either side of a fluidic geometry across which a known pressure difference is applied. When both electrodes are held at the same potential, the streaming current is measured directly as the electric current flowing through the electrodes. Alternatively, the electrodes can be left floating, allowing a streaming potential to build up between the two ends of the channel.

A streaming potential is defined as positive when the electric potential is higher on the high pressure end of the flow system that on the low pressure end.

The value of streaming current observed in a capillary is usually related to the zeta potential through the relation:

.

The conduction current, which is equal in magnitude to the streaming current at steady state, is:

At steady state, the streaming potential built up across the flow system is given by:

Symbols:

• I_str - streaming current under short-circuit conditions, A
• U_str - streaming potential at zero net current conditions, V
• I_c - conduction current, A
• ε_rs - relative permittivity of the liquid, dimensionless
• ε₀ - electrical permittivity of vacuum, F·m−1
• η - dynamic viscosity of the liquid, kg·m−1·s−1
• ζ - zeta potential, V
• ΔP - pressure difference, Pa
• L - capillary length, m
• a - capillary radius, m
• K_L - specific conductivity of the bulk liquid, S·m−1

The equation above is usually referred to as the Helmholtz-Smoluchowski equation.

The above equations assume that:

• the double layer is not too large compared to the pores or capillaries (i.e., ), where κ is the reciprocal of the Debye length
• there is no surface conduction (which typically may become important when the zeta potential is large, e.g., |ζ| > 50 mV)
• there is no electrical double layer polarization
• the surface is homogeneous in properties
• there is not axial concentration gradient
• the geometry is that of a capillary/tube.