CO₂ driven diffusiophoresis and water cleaning: similarity solutions for predicting the exclusion zone in a channel flow

We investigate diffusiophoretic separation of negatively charged particles in a rectangular channel flow, driven by CO₂ dissolution from one wall. Since the negatively charged particles create an exclusion zone near the boundary where CO₂ is introduced, we model the problem by applying a shear flow approximation in a 2D configuration. From the form of the equations we define a similarity variable to transform the reaction-diffusion equations and particle distribution equations to ODEs. The definition of the similarity variable suggests a characteristic length scale for the particle exclusion zone. We consider height-averaged and different orientation of the flow behaviors in rectangular channels to rationalize and connect our experimental observations with the model. Our observations and the theoretical model provide design parameters such as flow rate, channel dimensions and CO₂ pressure for the in-flow water cleaning systems.