Mass Transfer from Mobile to Immobile Regions in Irregularly Shaped Micro-Channels at Low Reynolds Number

Transient mass transfer in rough-walled micro-channels was investigated experimentally. We conducted experiments using rough-walled channels with various irregularities at small Reynolds number conditions. Mass transfer in the mainstream (mobile region) and dead water region (immobile region) were quantified using an image analysis technique based on absorption photometry. The experimental results showed that the solute dispersion in the mobile region was influenced by the irregular shape of the channel wall complicatedly. In contrast, mass transfer in the immobile region occurred by molecular diffusion independently on the wall roughness in our experimental conditions. The irregular shape of channel wall may enhance the mass transfer in mobile region by distorting the velocity distribution (Togi et al., 2020), while the solute redistribution to immobile region may suppress it in streamwise direction, just on a longer time scale. We developed a mass transfer model analogous to Mobile-Immobile model (MIM model) proposed by previous studies. The concept of the model is the same as the previous study (Zhou et al., 2019) and the coefficients of the model describing mass transfer in each region were quantified from the experimental results as functions of geometric characteristics of the rough-walled channel. In addition, mass transfer coefficient from mobile to immobile regions were derived mathematically based on the experimental results. The MIM model with the coefficients derived in this study well describes solute dispersion in variously shaped irregular channels quantitatively.