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Capacitive sensors are widely used in different liquid level sensing applications, including multi-phase thickness measurements. The performance of these sensors usually degrades when dealing with highly viscous liquids under dynamic conditions. In such situations, in what is known as fouling, liquid accumulates on the sensor body causing errors in the measured capacitance. In this paper, we propose a new design for a capacitive sensor that can considerably reduce the effect of fouling on sensor measurements. Our proposed instrument is based on a multi-row parallel-plate structure. The design is first analyzed using finite element simulations, and then experiments are performed to validate the simulations. Results show the superior performance of the suggested design and the ability of our proposed oil thickness instrument to mitigate the problem of oil fouling.