Step 1: Problem Definition.
The evaporator's capacity is 4000 kg of solid caustic soda daily. The concentration shifts from 10% to 35% solids. The water removed is the difference between the initial and final water quantities.
Step 2: Calculation.
The mass of solids remains constant. The water evaporated is calculated as the initial water mass minus the final water mass.\[\text{Water evaporated} = \text{Initial water} - \text{Final water} = 4000 \times \left( \frac{10}{90} \right) - 4000 \times \left( \frac{35}{65} \right)\]\[\text{Water evaporated} \approx 28571 \, \text{kg per day}.\]
Final Answer: \[\boxed{\text{A) 28571}}\]