In this article, the author describes a set of models of particle transport in microchannels that has been recently developed at FUJIFILM Dimatix for design and optimization inkjet print heads. The models are used to estimate the modes of particle transport in horizontal channels, the times for particles to settle at the bottom of a channel, and the fluidization flow velocity. The Rouse number is commonly used to estimate the mode of sediment transport in horizontal turbulent flow with large Reynolds number. However, in microchannels such as in modern inkjet systems, the liquid flows are usually laminar. In this article, the author uses a modified Rouse number that is expanded to the case of weakly turbulent and laminar flows. To illustrate the applicability of the modified Rouse number, he applies it to the transport of pigment particles in a horizontal channel in the FUJIFILM inkjet print head and compares theoretical results with experimental observations. In the article, he also constructs a model to estimate two settling times in rectangular channels: the time of formation of a monolayer of particles at the bottom of a channel and the required time for all particles to settle at the channel bottom. In design and optimization of a print jet head, it is also important to know the critical fluidization flow velocity of the ink to prevent sedimentation of ink pigment particles in vertical channels. In this article, the author constructs a simple model to estimate the maximum fluidization flow velocity as well. The modified Rouse number constructed in this article, as well as presented models, can be used in other applications as well.