Local anaesthetics inhibit the generation of electrical impulses and their conduction along the neuronal axon membrane, by reversible blockade of sodium ion channels.
There is a continuous imbalance of sodium and potassium ions between the cytoplasm of neurons and the intercellular fluid.
This is maintained at about 25 times more potassium intracellular and 15 times more sodium in interstitial space.
Local anaesthetics enter the neuron cell by simple diffusion and breaks itself into its components in the acidic intracellular environment thus blocking the sodium influx channel. Once the sodium influx channel is blocked, the neuron cell cannot generate action potential along the neurolemmoma, it cannot conduct any sensation along the nerve sheath. In an inflamed interstitial area where the interstitial fluid becomes acidic, the local anaesthetic agent breaks itself into its components and cannot diffuse along the nerve sheath.
You should always remember that local anaesthetic agent generates its effect from the inside of the nerve cell and not from the outside while it remains in the interstitial fluid.