Determining zeta potential of a core sample

A core testing system comprising:

• a first fluid;
• a second fluid that is less conductive than the first fluid, wherein the first fluid and the second fluid are immiscible;
• a core holder comprising a first end and a second end, the core holder configured to hold a core plug;
• an upstream reservoir fluidly coupled to the first end of the core holder and a downstream reservoir fluidly coupled to the second end of the core holder;
• an upstream trap fluidly coupled to the first end of the core holder and a downstream trap fluidly coupled to the second end of the core holder;
• an upstream external electrode cell comprising a first port and a second port, the first port of the upstream external electrode cell fluidly coupled to the upstream reservoir and the upstream trap, and the second port of the upstream external electrode cell fluidly coupled to the first end of the core holder;
• a downstream external electrode cell comprising a first port and a second port, the first port of the downstream external electrode cell fluidly coupled to the downstream reservoir and the downstream trap, and the second port of the downstream external electrode cell fluidly coupled to the second end of the core holder;
• a multimeter electrically coupled to the upstream external electrode cell and the downstream external electrode cell;
• a data acquisition system fluidly coupled between the first end and the second end of the core holder, the data acquisition system configured to measure a differential pressure across the core holder;
• a controller configured to perform operations comprising:
• receiving a signal representing the differential pressure across the core holder from the data acquisition system;
• receiving a signal representing a voltage across the core holder from the multimeter;
• and
• based on the differential pressure and the voltage, determining a zeta potential of the core plug;
• wherein each of the upstream reservoir, the downstream reservoir, the upstream trap, and the downstream trap contain some of the second fluid;
• and
• wherein the first fluid fills the core holder and separates the second fluid from the core holder.