Multi-component mixture flow in the stomach and duodenum allowing for functional disorders: results of numeric modelling for determining acidity

This paper covers certain aspects of mathematic model development for describing mixture flow in the antroduodenum. It details data for numeric research on pH level distribution in the antroduodenal section of the gastrointestinal tract. One-phase multi-component mixture contains components which are dissolved at the molecular level: hydrochloric acid, sodium hydrocarbonate, water, and a product of the reaction between acid and alkaline. The model allows for functional disorders in four antroduodenum sections which result in poorer secretory and motor functions performance. Mathematical tasking includes mass and momentum conservation equations for mixture components taking account mass sources due to components secretion and neutralization reaction. Kinematic boundary conditions are set on antroduodenum walls allowing for peristaltic motion (no slip condition). As for other boundaries of the examined area (inlet/outlet sections), here we set values of the 1st phase mass fractions, pressure, and conditions under which tangent components of stress vector are equal to zero. To determine pH level of the mixture via components concentrations, we obtained two algebraic equations, cubic and quatric ones. Model parameters were identified on the basis of data taken from literature and performed ultrasound research. We discuss various calculated scenarios where we examined impacts exerted by initially increased acidity (for example, due to acidic fluid intake) on dynamic acidity spread in the tract depending on fluid volume and pH level, occurence of functional disorders in alkaline secretion and in antrum motility. We showed that drinks with pH = 2.3 can potentially damage mucous coat of the tract walls, especially if alkaline secretion disorders occur. The approaches we suggest in the paper can in future be used for working out individual recommendations on consuming food and drinks with increased acidity.