The Influence of Exogenous Particles on the Behavior of Non-Newtonian Mucus Fluid

Abstract

Every day, approximately 7 m³ of air flows through the lungs of an adult, which comes into contact with 80 m² of the lung surface. This air contains both natural and anthropogenic particles, which can deposit on the surface of the mucus lining the respiratory tract. The presence of particles in the mucus leads to changes in its rheology and, consequently, in its functions. Therefore, this research aimed to determine how a non-Newtonian fluid suspension will behave during flow, illustrating the movement of mucus during coughing. The model mucus was an aqueous solution of carboxymethylcellulose (CMC). The tested particles suspended in a non-Newtonian fluid were Arizona Fine Dust, diesel exhaust particles, polyethylene microparticles, and pine pollen. It was noticed that as the fluid viscosity increases, the number of Kelvin–Helmholtz instabilities increases. The fluid’s expansion angle at the output of the measuring cell decreased, and the values of parameters characterizing the aerosol generated at the outlet decrease for selected particles present in the fluid. The research shows that the deposition of particles from polluted air in the respiratory tract, although they do not enter the bloodstream, may affect the human body. Deposited particles can change the behavior of mucus, which may translate into its functions.

1. Introduction

There are two sources of dust pollution in the environment: natural, such as sea salt, volcanic eruption, and desert, and anthropogenic sources, including domestic heating in households, fuel combustion from vehicles, and thermal power generation. The potential harmfulness of particles to human health due to their deposition in the respiratory tract is determined by particle size, shape, and composition. The larger the particle, the shorter the residence time in the air and the less likely to get into the lungs. Particles larger than five microns are deposited in the mouth and upper respiratory tract, from where they can be removed by coughing or sneezing. However, the smaller the particle, the longer it stays in the atmosphere and the deeper it can penetrate the airways. Nanometric-sized particles can easily travel from the lung alveoli through the bloodstream to all organs and tissues in the body. It was determined that about 5% of deposits in the lung, such as silver, gold, iridium, titanium dioxide, polystyrene, and carbon nanoparticles with a 5–10 nm diameter, may travel via the blood to bones and other organs [1,2,3,4,5]. The influence of nanoparticles on the tissue depends on their chemical composition, size, shape, and electric charge. Geiser and Kreyling [2] indicated a difference in the amount of transported nanoparticles depending on their size. For instance, 10% of 20 nm iridium nanoparticles deposited in the lungs moved to organs and bones.

In comparison, only 2% of 25 nm carbon nanoparticles moved to other organs. Additionally, the smaller the nanoparticles, the greater the ability to translocate to bones and soft tissues. Translocation of inhaled 80 nm iridium nanoparticles is about one order of magnitude less than 20 nm ones. A similar relationship was observed in the movement of gold nanoparticles in the body. 4% of inhaled gold nanoparticles with a diameter of 1.8 nm entered the bloodstream within 24 h of deposition in the lungs. However, only 0.2% of gold nanoparticles with a diameter of 18 nm were found in the blood under the same conditions and timeframe. It is worth noting that the nanoparticle’s shape also influences nanoparticle translocation. Spherical gold nanoparticles with a smooth surface are less easily displaced in the body than similarly sized but dendritic-shaped agglomerates of iridium or carbon.

Depending on their size, particles deposit in different areas of the respiratory tract, where they can be removed during coughing and sneezing or by pulmonary macrophages. Still, they can diffuse through the mucus layer, interact and dissolve in the pulmonary surfactant, or travel via the blood to various body organs [6].

The easy spread of particles of various sizes throughout the body raises questions about the consequences of exogenous particles in tissues and body fluids. Many previous works have shown that multiple particles in body fluids affect their rheology [7,8,9], which may lead to disturbances in the body fluids’ function. It was shown that the presence of desert dust particles in model mucus and model saliva causes an increase in its apparent viscosity, which may translate into difficulties in expectorating mucus from the respiratory tract and problems in swallowing saliva. At the same time, the presence of desert dust particles did not change the diffusion coefficient of Rhodamine R through mucus, which may suggest that the protective functions of mucus in the particle size range corresponding to the size of Rhodamine R particles are not disturbed [7]. Przekop et al. showed that the presence of microplastics (polystyrene and polyethene) in the model saliva solution increases its apparent viscosity [9]. However, changes in the rheological properties of body fluids due to the presence of exogenous particles concern only those body fluids that have the characteristic of non-Newtonian fluids. Our previous study indicated that exogenous particles, such as desert dust and soot aggregates, do not change the rheological properties of model tears or cerebrospinal fluid (both are Newtonian fluids). Still, at the same concentration, they affect the rheology of nasal-bronchial mucus and saliva (both are non-Newtonian fluids) [8]. The study of the impact of exogenous particles on humans is based on in vitro studies using cell lines or body fluid models. Using models with the same composition and properties allows for obtaining repeatable results and drawing correct conclusions, which allows for a better understanding of the mechanisms. The multi-parameter nature of processes occurring in living organisms somehow forces the use of simplifications to draw correct conclusions. Since solid particles in the air cause a significant threat to health, and the first line of defense in our body is bronchial mucus, which is a non-Newtonian fluid, we created a model research system that examines the reaction of a non-Newtonian fluid containing particles to intense airflow above its surface. This situation can be compared to the behavior of bronchial mucus during sneezing or coughing. The viscoelastic properties of mucus are strongly related to the proportions of its components. Infections or diseases leading to changes in the proportions of mucus components also cause changes in its rheological properties, which may lead to thickening or thinning of mucus, resulting in, for example, difficult bronchial clearing. Also, exogenous particles strongly affect the mucus’s apparent viscosity. During a rapid flow of air through the respiratory tract, the mucus-air interface is deformed and, as a result of this deformation, an aerosol is formed. From the point of view of fluid mechanics, high-speed airflow over a medium of higher density/viscosity generates shear at the interface between air and fluid. Fluid particles on the interfacial surface, which are set in sinusoidal motion, begin to move in a vorticity motion, which generates rotational velocity at the peak of the sinusoidal wave, causing the appearance of Kelvin–Helmholtz instability (K-H instability) (primary instability). K-H instability is influenced by the physicochemical properties of the fluid (e.g., viscosity), as well as by flow characteristics (shear) and external forces (gravity) [10]. At a later stage, this instability transforms into secondary instability, leading to the formation of drops due to the detachment of the liquid stream (Rayleigh–Taylor (R-T) instability) [11]. A detailed description of K-H and R-T instability can be found in the literature, along with mathematical models describing the phenomenon [12]. Vadivukkarasan indicated that droplets generated during respiratory events such as coughing and sneezing, but also speaking and breathing, result from three hydrodynamic instabilities: Kelvin–Helmholtz, Rayleigh–Taylor, and Plateau–Rayleigh, which occur at the mucus-air interface [13]. Droplet generation due to the deformation of the interfacial surface is one of three mechanisms responsible for the formation of droplets in the respiratory tract. The other two mechanisms are related to the opening and closing of the bronchioles during breathing and the vibrations of the respiratory tract, which arise as a result of the pressure changes in the chest during the movements of the diaphragm [14]. Droplets generated during respiratory incidents range from 0.01 to 500 µm, and their size is influenced by the type of respiratory activity (sneezing, talking, coughing), current respiratory infections, gender, age, and hydration [15]. It has been noticed that respiratory infections cause an increase in the average diameter and number of the generated droplets [16]. At the same time, it was indicated that inhalation of isotonic saline reduces the number of particles generated [17]. The above observations show that the size and number of droplets generated will be influenced by the apparent viscosity of the bronchial mucus, which is higher during infection, causing the formation of larger drops. At the same time, after hydration, it is lower, contributing to a reduction in the number of drops. It is also known from aerosol mechanics that the size of droplets generated in the atomization process is influenced not only by the viscosity of the solution but also by surface tension. As the surface tension increases, the Sauter Mean Diameter increases [18]. The size of droplets generated during respiratory events is essential for their spread in the air. The larger the drop, the faster it falls and the shorter the distance it is transported, while the smaller the drop, the slower it evaporates and the longer it may pose a potential threat to others [14].

Knowing that exogenous particles influence the rheology of the mucus and that the rheology of the fluid is vital in the aerosol generation process, we set the research goal to determine whether changing the rheological properties of the non-Newtonian fluid will result in a change in the instabilities appearing at the interfacial surface and a change in the characteristics of the generated aerosol. The research analyzed the rheological properties (apparent viscosity, storage, and loss modules) of a non-Newtonian fluid suspension with particles of natural (desert dust, pine pollen) and anthropogenic origin (diesel exhaust particles, microplastics) and their impact on K-H and R-T instabilities. Droplet size distributions and characteristic aerosol parameters were determined. It is shown that the behavior of a non-Newtonian fluid containing exogenous particles acted upon by a high-velocity air stream is different from that of a pure fluid. However, the change mechanism is complex and difficult to define clearly at this research stage. These studies may help to understand the behavior of bronchial mucus during respiratory events.

2. Materials and Methods

2.1. Non-Newtonian Fluid and Particles

Low-viscosity carboxymethylcellulose (CMC) (Sigma Aldrich, Poznań, Poland) was used to prepare non-Newtonian fluid with a concentration of 3.5%, 4.0%, and 4.5% (w/w). CMC was dissolved in water. The solution was stirred on a magnetic stirrer (100 rpm) for 48 h. The pH was adjusted to 7.4 with HCl and NaOH. The CMC solution was prepared each time, two days before the measurement, and on the day of measurement, only the pH of the sample was determined. The solution was not stored. Three concentrations of CMC were used in the research to check how a non-Newtonian fluid with different apparent viscosity would behave under the tested conditions.

To determine the impact of exogenous particles on the behavior of the non-Newtonian fluid, four types of particles were selected: two of natural origin (desert dust particles and pine pollen) and two of anthropogenic origin (diesel exhaust particles (soot particles present in diesel engine exhaust) and polyethylene microparticles).

Desert dust particles—Arizona Fine Dust (AFD) (Powder Technology, Arden Hills, MN, USA) come from the Salt River Valley and, after processing and classification, are commonly used for filtration testing. The average diameter of an AFD particle in the air is 1.968 µm and in water 0.513 µm [7]. The particles consist of over 68% of SiO₂ (a detailed composition can be found on the manufacturer’s website). An SEM photo of AFD is shown in Figure 1A. (SEM photos were taken on a scanning electron microscope [Ultra Plus Zeis, Potsdam, Germany]) AFD is successfully used in research as a model of a particle of natural origin [7]. AFD particles were added to the CMC solution at 6 mg/mL concentration one hour before each test and placed on a magnetic stirrer at 100 rpm to create a homogeneous suspension. AFD and diesel exhaust particles were added to the CMC solution at 6 mg/mL. The concentration was chosen taking into account the results of our previous studies [19] in which we determined the deposition of soot particles in the human respiratory tract (up to 1.7 mg/min of intense exercise) and the daily production of mucus, which ranges from 10 mL to 300 mL per day [20].

Pine pollen (PiPo) particles were obtained from Pinus sylvestris and were collected directly from male inflorescences during the pine flowering period. Pine pollen was chosen as the second example of natural particles present in the air because, during the flowering period of the pine tree, their concentration in the air reaches very high values. Yellow residue on sidewalks, cars, benches, and windows in May indicates the presence of pine pollen in the air. An SEM photo of PiPo is shown in Figure 1B (SEM photos were taken on a scanning electron microscope [TM-1000, Hitachi, Tokyo, Japan]). The average diameter of PiPo particles is 34 µm. PiPo was added to the CMC solutions at 0.032 mg/mL one hour before the test and left on a magnetic stirrer at 100 rpm. PiPo concentration was determined considering the highest recorded concentration of pine pollen in the atmosphere (4954.56 grains/m³ [Institute of Biology UJK, Kielce, Poland, 2013]), the number of pollen grains in 1 g of pine pollen, and the daily air flow through the lungs of an adult human.

Soot particles—diesel exhaust particles (DEP)—were obtained from the exhaust gases of a diesel engine (Mercedes-Benz 1982, not equipped with a catalytic converter or particulate filter) running at idle speed on Ecoverva fuel (Orlen, Warsaw, Poland). A detailed description of the method of obtaining DEP and its chemical composition can be found in [21,22]. An SEM image of DEP aggregates is shown in Figure 1C (SEM photos were taken on a scanning electron microscope [Ultra Plus Zeis, Potsdam, Germany]). The average diameter of DEP aggregates in air is 0.111 µm and in water 0.250 µm [8]. DEP aggregates were added to the CMC solution at 6 mg/mL one hour before the tests. The sample was placed on a magnetic stirrer at 100 rpm to obtain a homogeneous suspension.

Microspherical polyethylene microparticles (PE) (Cosphereic LLC, Goleta, CA, USA) with a size range of 38–45 µm were added to the CMC solution at 6 particles/mL concentration. This concentration was obtained by assuming, based on the catalogue card, the number of PE microparticles in 1 g of the product. Considering that bottled water contains an average of 6000 particles/L [23], it was assumed that such a particle concentration could be achieved in saliva, an example of a non-Newtonian fluid. Like all other tested particles, PE microparticles were added to the CMC solution one hour before the measurement and left on a magnetic stirrer at 100 rpm to obtain a homogeneous suspension.

2.2. Rheological Measurement

Pure CMC solutions and all suspensions were subjected to rheological analysis. The analysis was performed on an oscillating rheometer (MCR 102, Anton Paar, Graz, Austria) equipped with a Peltier system in a plate-plate arrangement (the diameter of the plate is 50 mm) with a 1 mm gap at 36.6 °C. The dependences of the apparent viscosity as a function of shear rate and the loss modulus and storage modulus were determined. An amplitude sweep test was performed to determine the linear viscoelastic regime in the strain range of 0.01 to 100%, with a constant oscillation frequency of 3 rad/s. Then, a frequency sweep test was conducted at a constant value of the deflection amplitude. A frequency sweep test was also performed at a set oscillation frequency range from 0.1 to 500 rad/s. Determining the course of the loss modulus and storage modulus allowed for checking whether the tested fluid was dominated by viscous properties (loss modulus dominates) or elastic properties (storage modulus dominates). Rheological measurements were repeated at least three times. The results presented in the charts are the average of the implementations with error bar values marked.

2.3. Experimental Set-Up

The system for generating fluid movement consisted of the following elements: compressed air supply pipe, pressure tank, manometer, solenoid valve, test chamber with measurement cell, UV lamp, and camera. The experimental setup is shown in Figure 2A. The test chamber was a cuboid with dimensions (400 mm × 400 mm × 500 mm) with a black interior without a front wall. The measurement cell was a cuboid with dimensions (15 mm × 15 mm × 140 mm) with a viewing window of 11 mm × 90 mm (Figure 2B). 3.5 mL of the tested solution/suspension at 36.6 °C containing a drop of UV dye (UV Coloris, Mościska, Poland) was introduced into the measurement cell and evenly distributed over the lower surface. The UV dye did not affect the rheology of fluid. The pressure tank was filled with air to a pressure of 5 bar. Then, the solenoid valve was opened for 76 ms. Opening the valve triggered an airflow through the measurement cell with the characteristics shown in Figure 3. The airflow dynamics through the measuring cell are similar to airflow dynamics in front of the mouth during coughing. Gupta et al. [24] showed that the airflow during coughing reaches its maximum value of 2 to 8 L/s at a time of 0.04 to 0.012 s, depending on age, gender, physical condition, lung capacity, etc. A camera placed in front of the measuring cell recorded the movement of the fluid inside and at the outlet from the measuring cell in slow motion in 1080p quality at a rate of 240 frames/s. The size distribution of droplets formed at the outlet from the measuring cell, dv10 (10% of the droplets in the aerosols volume are at or below in reported diameter), dv50 (50% of the droplets in the aerosols volume are at or below in reported diameter, and d32 (Sauter mean diameter) were analyzed using a laser particle counter (Spraytec, Malvern, UK). The experiment was repeated ten times for each suspension. The results presented in the article are the average of the implementations.

The movies were edited using VSDC Video Editor (version 9.1). Each video was processed individually to achieve the best image quality. The quality of the videos was improved by adjusting the contrast and brightness. The number of waves/instability were counted when the first waves/instability disappeared or reached the end of the measurement cell. A photo illustrating the waves/instability occurring during the flow is shown in Figure 4A. The maximum angle of aerosol spread at the outlet from the measurement cell was also determined based on the films (Figure 4B).

3. Results and Discussion

3.1. Rheology of Fluid

An aqueous solution of CMC is a non-Newtonian, shear-thinning fluid. As expected, an increase in CMC concentration causes an average of 40% increase in viscosity at each of the three analyzed concentrations. The apparent viscosity of pure CMC solution is within the range of the apparent viscosity measured for bronchial mucus from a person without a respiratory infection. The apparent viscosity of bronchial mucus ranges from 0.04 Pas to 0.49 Pas [25], while the apparent viscosity of CMC ranges 0.032–0.095 Pas, depending on the CMC concentration. The addition of exogenous particles does not change the nature of the fluid. It is still a non-Newtonian, shear-thinning fluid (Figure 5).

However, depending on the type of particles, a decrease and an increase in apparent viscosity are observed compared to pure CMC. A reduction in apparent viscosity occurred for AFD particles for all CMC concentrations and DEP particles for a concentration of 3.5%. However, an increase in apparent viscosity was observed for DEP particles at a concentration of 4.0% and 4.5% CMC and PE microparticles at 4.5% CMC. PiPo does not affect the apparent viscosity of CMC. The presence of exogenous particles in the CMC solution causes a change in its apparent viscosity, but this effect decreases with an increase in the shear rate. The more significant impact of particles on the apparent viscosity at low shear rates may result in slower diffusion of active substances introduced into the respiratory tract during inhalation (e.g., during an asthmatic attack). The lower impact of the presence of exogenous particles at high shear rates may mean that their presence will not impede the movement of mucus during coughing and sneezing and, therefore, will not interfere with the respiratory clearance process.

In the pure CMC solution, the storage modulus dominates over the loss modulus, which is also observed for bronchial mucus [26]. Exogenous particles also reduce the storage modulus, which is consistent with literature data. Hattori noticed a significant reduction in the storage modulus of nasal mucus when exposed to house dust [27].

In 3.5% CMC, exogenous particles, caused a clear dominance of the loss modulus over the storage modulus. Therefore, the suspensions acquire the characteristics of a viscous fluid (Figure 6).

Additionally, stabilization of the CMC sample with DEP particles can be observed (no kinks in the curves illustrating the modules), and destabilization in the presence of PE microparticles (breaks in the curves appear at lower angular frequencies). The kinks in the curves representing the module results from the disruption of fluid movement in the rheometer measuring gap. The forces of viscosity and elasticity are much lower than the inertia force of the tested sample and characteristic kinks appear in the curves illustrating the module [28]. As a rule, samples should be analyzed until such kinks occur.

Similar dependencies are observed for the other two CMC concentrations (Figure 7 and Figure 8), and the modulus values themselves, as expected, increase with increasing CMC concentration.

The presence of exogenous particles in the CMC solution causes the loss modulus to dominate over the storage modulus. The dominance of the loss modulus over the storage modulus suggests that the tested fluid behaves more like a viscous liquid than an elastic solid. This may indicate that removing such a suspension from the respiratory tract during coughing/sneezing will be easier. Bronchial mucus from people suffering from cystic fibrosis or COPD is difficult to remove from the respiratory tract because, theologically, it is characterized by a significant increase in the storage modulus over the loss modulus compared to the mucus of a healthy person [26].

3.2. Analysis of Fluids-Free Surface Deformation

The airflow through the measuring cell filled with the tested fluid caused its movement towards the outlet of the measuring cell. It caused waves/instabilities on the surface of the fluid. Depending on the fluid being tested, the maximum number of waves/instabilities is 4.70–7.30 (

Table 1. Number of instabilities during the airflow (SD-standard deviation).

	Number of Instabilities
	Mean	SD
CMC 3.5%	5.00	0.60
+AFD	4.44	0.53
+DEP	6.50	0.76
+PiPo	4.70	0.67
+PE	5.60	0.52
CMC 4.0%	6.17	0.55
+AFD	5.22	0.67
+DEP	6.44	0.53
+PiPo	5.56	0.73
+PE	6.20	1.03
CMC 4.5%	6.60	0.70
+AFD	6.00	0.93
+DEP	7.30	0.67
+PiPo	6.00	0.76
+PE	6.80	1.23

).

An increase in CMC concentration causes an increase in the number of instabilities. When comparing the number of instabilities of pure CMC solution and CMC suspensions with particles, there is a noticeable increase in the number of wave/instabilities due to the presence of DEP aggregates and PE microparticles, and a decrease in the case of AFD and PiPo (Figure 9). The most significant effect is observed at the lowest CMC concentration. As the CMC concentration increases, the effect weakens.

In turn, the angle of fluid ejection from the measuring cell decreases with increasing CMC concentration for all suspensions (Figure 10).

At the highest CMC concentration, the presence of all tested particles reduces the value of the fluid ejection angle compared to pure CMC. As the CMC concentration decreases, this effect becomes less clear.

The ejection of fluid from the measuring cell leads to the formation of an aerosol. The droplet size distributions are shown in Figure 11, Figure 12 and Figure 13. Figure 14 shows parameters characterizing the formed aerosol (dv10, dv 50, and d32).

The presence of desert dust particles and microplastics caused a decrease in the characteristic aerosol parameters (dv10, dv50, and d32) with increasing CMC concentration. The values change for the remaining particles and pure CMC, but are not subject to any trends. When analyzing the droplet size distributions, it is possible to observe a shift in the distributions towards smaller drops due to the presence of exogenous particles in the aerosol. The effect is observed for all particles present in CMC regardless of concentration, excluding PE microparticles in 3.5% and 4.0% CMC and DEP in 3.5% CMC.

Four types of exogenous particles, differing in origin, chemical composition, size, and shape, were chosen for study: large spherical particles of PE microparticles, pine pollen, and small desert dust and dendritic soot aggregates. Considering both the particle size and shape, no similar effects in the behavior of CMC are observed. This may lead to the conclusion that the chemical composition may be more critical for the effect than the shape and size of the particles. Stapper and Samuelsen [29] noted that instabilities should not depend on viscosity and surface tension, but both quantities should affect the size of the generated drops. The droplets obtained at the outlet from the measuring cell are, on average, 500 μm and only for AFD and PE is there a clear decrease in the parameters characterizing the aerosol with the increase in CMC concentration (however, AFD caused a reduction in the CMC viscosity, and PE increased it).

The influence of particles in the CMC solution on aerosolization is ambiguous. Two trends can be observed. For small particles with a diameter below 1 μm, the Sauter mean diameter (d32) decreases with the increase in the particle diameter. In comparison, for large particles above 10 μm, the Sauter mean diameter increases with the increase in the particle diameter (Figure 15A). At the same time, since there is no clear effect of particle size on the apparent viscosity at high shear rate values (100 1/s) (Figure 15B), it can be concluded that the change in apparent viscosity is not the only parameter determining the size of the generated drops.

The apparent viscosity of the suspension, in addition to the particle size, may also be influenced by the chemical composition of the particles. The chemical composition of the particles we use in our research varies. Diesel exhaust particles have numerous polycyclic aromatic hydrocarbons and inorganic compounds adsorbed on their surface. Arizona Fine Dust mainly consists of silicon compounds. The chemical composition of pine pollen depends on the environment it comes from. However, it is assumed to contain only trace amounts of chemicals but is also rich in proteins, amino acids, sugars, and fats. Microplastic particles, in turn, are made of polyethylene. Such a diverse composition of the tested particles does not allow for a clear indication of a specific component’s influence on a given particle’s behavior.

Instead, we can use the general feature of a given particle resulting directly from its chemical composition, i.e., hydrophobicity/hydrophilicity. According to literature data, Arizona Fine Dust, pine pollen, and microplastic particles are hydrophobic, while diesel exhaust particles are not hydrophobic [30,31]. Therefore, taking into account the hydrophobicity/hydrophilicity of the particles, no influence of this feature on the size of the generated drops is observed.

However, it can be noticed that the increase in the viscosity of the suspension causes an increase in the number of instabilities (Figure 16A) and a decrease in the aerosol spread angle (Figure 16B).

This may suggest that a change in the apparent viscosity of a non-Newtonian fluid (regardless of the cause) affects the width of the aerosol stream generated from such a fluid and, thus, the area that the generated drops may contaminate.

Carboxymethylcellulose is a polymer with a high degree of polymerization. Similarly to mucins that form mucus, exogenous particles may change the cross-linking of the structure and create new, or break existing, bonds. The macroscopic behavior of carboxymethylcellulose solution is similar to that of mucus. The value of apparent viscosity and the dominance of the storage modulus over the loss modulus are also identical to those of mucus. This allows us to assume that a mucus model based on carboxymethylcellulose can be used to draw conclusions about the behavior of natural mucus. The mucus’s viscosity, spinnability, and surface properties (like adhesivity) influence its clearability. Optimal values of the above parameters enable correct movement of cilia, proper mucus-epithelium interaction, and the formation of waves on the mucus surface, supporting clearability [32,33,34]. Even a subtle change in apparent viscosity, as our research has shown, can cause changes in the behavior of a non-Newtonian fluid. If this fluid is bronchial mucus, it may result in disrupting its function in the form of easier flow (not staying on the surface of the respiratory tract).

4. Conclusions

Our studies have shown that increased viscosity of pure CMC increases the number of instabilities. However, it cannot be concluded that particles causing an increase in viscosity will also cause a predictable rise in the number of instabilities. The influence of particles on the emerging instabilities is observed, but the mechanism of this influence is more complex than a simple change in viscosity. Therefore, numerical analysis using computational fluid mechanics tools may be helpful in this case. To obtain reliable computational results, it is necessary to get experimental data describing the measurement system, including the physicochemical characteristics of the fluid and particles. The conducted research made it possible to obtain such data, meaning it will be possible to perform numerical analyses in the future.

It has been shown that exogenous particles affect the behavior of non-Newtonian fluid in conditions like coughing. This effect depends on the type of particle. The obtained results can be translated into the behavior of mucus in the respiratory tract, thus indicating that the deposition of particles in the mucus is not without significance for its movement and, therefore, for its function.