# A Systematic Review of Computational Fluid Dynamics Models in the Stomach and Small Intestine
## 3 Results
### Small Intestine
Laminar flow was present across all CFD models of the small intestine with specific flow patterns being dependent on the motility prescribed in the model. Similar to the stomach, in contracting regions, flow is opposite to the direction of peristaltic wave propagation, and vortices/vort flow is present in regions upstream and/or downstream of the contraction [55; 56; 60; 63; 64]. These studies all highlight the importance of vortical flow in enhancing digestion and absorption of nutrients within the intestines. Vortices were also observed with segmentation contractions (Figure 6), with no net movement of fluid along the length of the intestine and the authors concluded that these contractions may serve to transport nutrients from the lumen to the intestinal wall [56; 57; 59; 62]. The resulting flow patterns from pendular/longitudinal contractions were dependent on the specific type of intestinal wall motion i.e., oral (intestinal wave moving in the oral direction), stretching or compression [58]. In their paper, [PERSON] et al. [62] observed non-steady vortices within contractile regions while more ordered axial flow was present in [58]. These differences are likely due to the specific ex-vivo recordings of longitudinal motion used to define the contraction patterns. Colliding peristaltic waves resulted in swirling flow regions [67] and high-velocity fluid jets exiting the colliding region [61]. Several studies have investigated the effect of fluid viscosity on the flow behavior within the intestine. Chyme within the small intestine is a complex suspension of undigested particulate matter, solubilized nutrients, secreted enzyme, bile and mucin [69]. Most studies have used arbitrary viscosities of fluids such as water (\(\approx\)1 mPa s) and honey (\(\approx\)1 Pa s), with only a few studies using experimentally recorded viscosities of the liquid phase of digesta (after filtering out particulate matter), represented as a Newtonian fluid [60; 67]. Whole digesta has been experimentally observed to be more viscous and non-Newtonian due to the particulate matter and exhibits pseudoplastic behavior where  
Figure 5: Anatomically realistic model of duodenum motility developed by [PERSON] et al. [67], (**a**) Model of slow-wave propagation used to derive peristaltic contractions within the duodenum, and (**b**) computed mixing of a glucose bolus (red sphere) with digesta visualized using an isosurface. Reproduced with permission from [PERSON] et al., Physics of Fluids; published by AIP Publishing, 2023. Figure 6: Streamlines generated due to a single (**top**) and double (**bottom**) segmental contractions within a segment of the small intestine simulated by [PERSON] et al. [59]. Adapted with permission from [PERSON] et al., Journal of Food Engineering; published by Elsevier, 2015.  
the apparent viscosity decreases with increased shear rate [70]. Two CFD models have considered the effect of representing digesta as a non-Newtonian fluid [56; 67]. The modeling framework of [71] used particle-based techniques, SPH and Discrete Element Method (DEM), to predict collisional and hydrodynamic interactions between the fluid and solid phases of digesta. This model allows for simulating the non-Newtonian behavior based on system mechanics rather than a rheology model, and this also separates the simpler Newtonian behavior of the fluid phase from the more complex behavior of the solid phase. Mixing within the intestine occurs at several length scales, and most CFD models studied macroscale mixing using several approaches. The passive transport of a scalar/species was computed, the variance in concentration [55] and mixing of a glucose bolus [57; 67] (Figure 5b) provided a metric of intestinal mixing. The displacement of massless particles [62; 72], area of vortices [56], and stretch of fluid elements (deformation gradient tensor) [58] were also used to assess the macroscale mixing occurring within the small intestine. [PERSON] et al.