Diffusion against convection

I read with great interest the recent paper entitled " Con-vective washout reduces antidiarrheal efficacy of entero-cyte surface–targeted antisecretory drugs " by Jin et al. (2013) in the February 2013 issue of the Journal. In this paper, the influence on drug diffusion of adverse fluid convection was modeled by solving a diffusion convec-tion equation with appropriate boundary conditions. In effect, the paper models the likelihood that solute can travel from the mucosal surface to the crypts in the face of adverse fluid secretion. The concept of normal intestinal secretion from the enterocytes has been advocated many times, but its existence and function have periodically been questioned, as early as the late nineteenth century (Hoppe-Seyler, 1879). The need for luminally directed movement of fluid specifically to flush material or harmful bacteria away from the mucosal surface was advocated by Pavlov (1897) as itself confirming the existence of fluid secretion as a normally occurring physiological event. Although it can also be argued that secretion has no obvious normal physiological function (Lucas, 2010), the concept of an antibacterial purpose to secretion arises often (Barrett and Keely, 2000), as well as a putative need for secretion to transport in a timely way crypt cell products to the tips of the villi. Despite this, there are very few published solutions to this diffusion–convection problem , and the present authors are to be commended for providing one. If their input values are accepted, it seems clear that normal secretion rates close to those observed in extreme cases of cholera (Fig. 2 of Jin et al., 2013) would be required to keep the mucosal surface free of bacteria. This is evident when the diffusion coefficient for bacteria is taken into account, as this can be of the order of 10 5 cm 2 sec 1 (Kiørboe et al., 2002) for some bacteria. At rates of fluid velocity that are allegedly normal, i.e., required by the premise that the small intestine normally secretes one liter of fluid per day, the Péclet number is likely to be far less than that assumed by the authors and insufficient to keep bacteria off the mucosal surface. The argument for normally occurring rates of secretion having a hygienic function seems fatally undermined by the calculations provided by the authors. However, a concern that should be expressed is that the theoretical values selected by the authors may vary by an order of magnitude …