We examine the motion of a liquid-air meniscus advancing into a microchannel with chemically heterogeneous walls. We consider the case where a constant flow rate is imposed, so that the mean velocity of the interface is kept constant, and study the effects of the disorder properties on the apparent contact angle for each microchannel surface. We focus here on a large diffusivity regime, where any possible advection effect is not taken into account. To this end, we make use of a phase-field model that enables contact line motion by diffusive interfacial fluxes and takes into account the wetting properties of the walls. We show that in a regime of sufficiently low velocities, the contact angle suffers a hysteresis behavior which is enhanced by the disorder strength. We also show that the contact line dynamics at each surface of the microchannel may become largely coupled with each other when different wetting properties are applied at each wall, reflecting that the dynamics of the interface is dominated by nonlocal effects.

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