Bolus Cohesivity

Dimensionless numbers are commonly used in fluid mechanics to quantify complex flow behavior and to compare fluids with different properties. In this context they can be used to quantify the cohesivity of the bolus. Although a loose term, we here relate cohesivity to the breakup of the bolus into smaller drops, which is a structural definition that has functional implications such as increased risk of aspiration. Please note that bolus cohesivity has nothing to do with “cohesivity” used in other areas to describe stickiness such as for adhesives and in texture profile analysis. The main goal of thickening is to slow the flow of the bolus to give the impaired physiology time to react. The flow through the pharynx is a complex flow and in addition to slowing the flow, thickening also affects bolus cohesivity. The forces acting on the bolus are viscous, elastic, and inertial in nature, and surface tension plays an important role in droplet formation. The relevant parameters of the fluid passing through the pharynx are thus viscosity, velocity, the relaxation time, density, and the surface tension. These were determined for the model fluids, and the relaxation times were taken from literature, and are presented in Table 1.

 | Fun Light | Newtonian | Boger | Shear‐thinning
Density [kg/m3] | 1000 | 1240 | 1220 | 1000
Viscosity at 50 s−1 [Pa s] | 0,001 | 0,15 | 0,15 | 0,15
Surface tension [N/m] | 0,058 | 0,052 | 0,051 | 0,057
Relaxation time [s] | 1E‐11 | 0,001 | 0,5 | 1
Reynolds number | 2500 | 21 | 20 | 17
Ohnesorge number | 0,00093 | 0,13 | 0,13 | 0,14
Weissenberg number | 5E‐10 | 0,05 | 25 | 50
Ohnesorge × Weissenberg/Reynolds | 2E‐16 | 3E‐04 | 0,17 | 0,42

The longest relaxation time in the shear‐thinning fluid (0.45% xanthan) could be estimated from previously published results to 0.3–3 s (Berta et al. 2018; Choppe et al. 2010). The longest relaxation time of the Boger fluid could be estimated from a similar system, xanthan in syrup (Zirnsak et al. 1999) where it was found to be 0.3–3 s. Compensating for the relatively higher viscosity of the syrup system compared to the 50% maltodextrin fluid, scaling arguments would push the relaxation times more to 0.1–1 s (Sousa et al. 2017). The relaxation time of water (here Fun Light) at room conditions is very low, in the order of picoseconds. The exact value can be discussed, but for this context it is enough to conclude that it is much smaller than that for the model fluids. The addition of the lemonade caused the surface tension to drop from that of water at 20°C of 0.072 N/m to 0.051–0.058 N/m. The maltodextrin and xanthan may also have a small effect.

The Reynold's number predicts whether a flow is laminar or turbulent or transitional, that is, a mix between the two. The regimes can be expressed in terms of the Reynold's number as laminar for Re < 2300, transitional for 2300 < Re < 4000 and turbulent for Re > 4000. All model fluids displayed laminar flow and Fun Light transitional which correlates well with the observed flow shown in Figure 5.

The Ohnesorge number is mainly used to analyze free‐surface flows to predict droplet breakup as when the fluid passes the epiglottis where the channel is only partly filled. A low Ohnesorge number indicates droplet breakup whereas a high number indicates high viscosity and stable flow resisting breakup. The model fluids have similar Ohnesorge numbers due to having the same viscosity at 50 s−1 and similar surface tension and densities, as opposed to Fun Light where droplet breakup is evident (c.f. Figure 5). As the model fluids do not all have the same constant viscosity, the Ohnesorge number does not represent the full picture.

The Weissenberg number relates elastic to viscous forces and shows a difference between Newtonian as compared to the Boger and the Shear‐thinning fluids. For Fun Light it is very low primarily due to the lack of elasticity. The Weissenberg number clearly shows the effect of adding xanthan to the maltodextrin, that is, going from Newtonian to Boger behavior, which likely is why the Boger fluid does not enter the airways as opposed to the Newtonian fluid (Figure 5).

There is no clear indication on bolus cohesivity from a single dimensionless number, but by multiplying the two numbers promoting bolus cohesivity, Ohnesorge × Weissenberg and dividing by the Reynolds number that impairs cohesivity, a “bolus cohesivity number” could be formed:As viscous and inertial forces are part of several of the dimensionless numbers, the bolus cohesivity number is linearly dependent on elastic and viscous forces and inversely proportional to surface forces and inertial forces squared. Table 1 shows a clear difference in the bolus cohesivity number, especially for the Boger and Shear‐thinning fluids as compared to the Newtonian fluid and to Fun Light, and it correlates well with the observed differences in fluid entering the airways. A high bolus cohesivity number means safe swallowing in that aspiration is avoided. The physical interpretation of the bolus cohesivity number is that it describes how well a bolus keeps together when it is subjected to elastic, viscous, inertial, and surface forces.

(4) Bolus cohesivity number=OhxWiRe