Continuous Laminar Flow Aeration and Oxygenation

AIRFLOW IN THE RESPIRATORY SYSTEM

Andrew Davies MA PhD DSc , Carl Moores BA BSc MB ChB FRCA , in The Respiratory System (Second Edition), 2010

The major determinant of flow – radius

Laminar flow has been extensively investigated by scientists, one of whom, Poiseuille, defined the relationship between driving pressure (Δ P) and flow ( $\dot{\text{V}}$ ) as:

$\dot{\text{V}}=\frac{(\mathrm{\Delta }P)\pi {\text{r}}^4}{8\mathrm{\eta }1}$

where r is the radius of the tube, η is the viscosity of the gas, and l is the length of the tube. This relationship applies to gas flow in the long straight smooth tubes under stable conditions – hardly conditions that apply to the lungs. However, it can be roughly applied to breathing, and you may notice that the most important factor affecting airflow in this equation is the radius of the tube, which is raised to the fourth power (r⁴). This means that if you reduce the radius by half and keep everything else constant, the flow will be reduced to ${\frac{1}{16}}^{\text{th}}$ .

Laminar flow in a tube can be represented as a series of cylinders moving down the tube, with the central cylinder moving fastest. The outermost cylinder is stationary and is in fact a layer of the original gas in the tube left behind as the new gas moves forward, as shown in Figure 4.4.

These apparently esoteric considerations have important consequences in respiratory medicine. For example, adequate ventilation of the alveoli of the lungs can be achieved with a surprisingly small tidal volume, provided a high enough frequency of 'breathing' is used. This phenomenon is seen in clinical conditions when high-frequency artificial ventilation of the lungs is used where we want to avoid movements of the chest wall – in trauma victims with a crushed chest, for example. The patient is successfully artificially ventilated with a tidal volume less than his or her anatomical dead space (see p. 64) and frequencies up to 50   Hz. A 'spear' of fresh air in the centre of the airways penetrates deeper into the lungs than might be expected and provides adequate ventilation.

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The Heart as a Pump

Joseph Feher , in Quantitative Human Physiology, 2012

Additional Turbulence Causes Heart Murmurs

Laminar flow is streamlined flow, and it is silent. Chaotic flow is also called turbulent flow, and it is noisy. The occurrence of turbulent flow is often estimated from the Reynolds number, named after Osborne Reynolds, who studied the patterns of flows in tubes by injecting a thin stream of visible dye into the moving fluid. The Reynolds number is given as

[5.4.7] $Re=\frac{2a<V>\rho }{\eta }$

where Re is the Reynolds number, a is the radius of the tube, <V> is the average velocity, ρ is the density, and η is the viscosity. Thus, the Reynolds number is a dimensionless number that is a ratio of the inertial forces to the viscous forces. Turbulence normally occurs when Re ~2000. Abnormal movement of fluid can produce turbulence in the heart, causing additional sounds that can be heard by auscultation. These are heart murmurs. Examples include aortic regurgitation. In this case, the aortic valve incompletely seals the left ventricle from the aorta during ventricular relaxation. Blood squirts back through the leaky valve into the ventricle, driven by the higher pressure in the aorta. The squirting produces a noise, or bruit.

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Cardiovascular Physiology

George J. Crystal , ... Kai Kuck , in Pharmacology and Physiology for Anesthesia (Second Edition), 2019

Turbulent Flow

Unlike laminar flow, the resistance of a tube for turbulent flows is not easily calculated. Owing to the chaotic and unpredictable nature of turbulent flow, resistance of a tube is dependent on the volumetric flow itself; thus, it is not possible to calculate the resistance without knowing the flow beforehand. When flow is turbulent, a larger pressure difference between points is required compared to laminar flow.

Most fluid flows relevant to anesthesia, such as blood flow and gas flow during normal respiration, exhibit laminar flow. There are a few exceptions, however. Many patients experience momentary turbulence in blood flow in the ascending aorta depending on the compliance of the vascular walls. Additionally, patients suffering from bronchospasm can also exhibit turbulent air flow in the lungs owing to the narrowing of the bronchial lumen. When delivering a mixture of oxygen and helium (known as Heliox), the overall density of the fluid dramatically decreases since helium has 1/8 the density of oxygen. As a result, the Reynolds number also decreases, making the fluid flow more laminar and allowing a higher volumetric flow to the lungs, counteracting the constriction due to bronchospasm.

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Chemical Partitioning and Transport in the Environment

Brian L. Murphy , in Introduction to Environmental Forensics (Third Edition), 2015

7.5.1.2 Turbulent Diffusion

Laminar flow becomes turbulent when the Reynolds number, Re, is large compared to one. The Reynolds number is the ratio of inertial to viscous forces:

(7.50) $R_e=\frac{\rho vd}{\mu }$

where ρ and μ are the fluid density and dynamic viscosity, v is a typical velocity, and d is a typical length scale. In cgs units, ρ = 1.2×10⁻³ g/cm ³ and μ = 1.8×10⁻³gm/cm-s (0.18 centipascals, or cP) for air.

In outdoor air, wind speeds are high enough (>100 cm/s) that, over a macroscopic plume dimension, the flow is turbulent. Even in indoor air, diffusion is usually dominated by turbulence. For example, Baughman et al. (1994) released a neutrally buoyant tracer into a 31 m ³ low-air-exchange-rate room under nearly isothermal conditions. The tracer was mixed in the room within about 80 to 100 minutes, corresponding to a diffusion rate of 31^2/3/(80 to 100) ∼0.11 m²/minute = 20 cm²/sec, about 100 times greater than the molecular diffusion rate.

For water, ρ = 1 g/cm³ and μ = 0.01 gm/cm-s. Diffusion in flowing surface water is turbulent. A shallow (10 cm) slowly flowing stream (10 cm/s) has Re = 10⁴. Even shallow lagoons that may appear quiescent can be dominated by turbulence. For example, a 1 m deep lagoon that turns over once per day due to diurnal heating has an effective velocity of about 0.001 cm/s, giving Re = 10.

In porous media such as soil or concrete, the length scale and velocity scales are generally small. For example, the permeability of gravel is about 10⁻⁴ cm², corresponding to a length scale, d, of 10⁻² cm. For a groundwater flow of 100 m/year (0.00032 cm/s), this gives a Reynolds number of 0.00032. According to Bear (1972), all groundwater flow through granular material is laminar.

To see how turbulent diffusion arises in air and surface-water problems, replace the velocity and concentration in Eq. 7.46 with time average and instantaneous values: U→U+u and C → C + c. By definition, the time averages of the fluctuating quantities are zero and hence do not contribute to the terms that are linear in C. The nonlinear term is $\mathbf{\nabla }\mathbf{.}\mathit{u}\mathit{c}$ , so that Eq. 7.46 can be rewritten as:

(7.51) $\frac{\partial C}{\partial t}+\mathbf{\nabla }\mathbf{·}\mathbf{\left(}\mathit{UC}\mathbf{\right)}=\mathbf{\nabla }·(D_{mol}\mathbf{\nabla }C+\mathit{u}\mathit{c}),$

where we have used the subscript to indicate that the diffusion coefficient is due solely to molecular diffusion. It is customary to represent the last term by eddy diffusion coefficients:

(7.52a) $u_{x}c=-D_x\frac{\partial C}{\partial x}$

(7.52b) $u_{y}c=-D_y\frac{\partial C}{\partial y}$

(7.52c) $u_{z}c=-D_z\frac{\partial C}{\partial z},$

which is consistent with the assumption that turbulent diffusion, like molecular diffusion, moves material from regions of higher concentration to regions of lower concentration. By taking different diffusion coefficients in different directions we also take into account the effect that gravity can have in suppressing turbulence.

From Eq. 7.52, the eddy diffusivities add to the molecular diffusion term in Eq. 7.51; for example, the x component of the effective dispersion is (D_mol + D_x) $\frac{\partial C}{\partial x}$ .

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Respiratory System Resistance

Andrew B Lumb MB BS FRCA , in Nunn's Applied Respiratory Physiology (Eighth Edition), 2017

Physical Principles of Gas Flow and Resistance

Gas flows from a region of high pressure to one of lower pressure. The rate at which it does so is a function of the pressure difference and the resistance to gas flow, analogous to the flow of an electrical current (Fig. 3.1). The precise relationship between pressure difference and flow rate depends on the nature of the flow which may be laminar, turbulent or a mixture of the two. It is useful to consider laminar and turbulent flow as two separate entities but mixed patterns of flow usually occur in the respiratory tract. With a number of important caveats, similar basic considerations apply to the flow of liquids through tubes, which is considered in Chapter 6.

Laminar Flow

With laminar flow, gas flows along a straight unbranched tube as a series of concentric cylinders that slide over one another, with the peripheral cylinder stationary and the central cylinder moving fastest, the advancing cone forming a parabola ( Fig. 3.2, A ).

The advancing cone front means that some fresh gas will reach the end of a tube but the volume entering the tube is still less than the volume of the tube. In the context of the respiratory tract, there may be significant alveolar ventilation when the tidal volume is less than the volume of the airways (the anatomical dead space), a fact that is very relevant to high-frequency ventilation (page 462). For the same reason, laminar flow is relatively inefficient for purging the contents of a tube.

In theory, gas adjacent to the tube wall is stationary, so friction between fluid and the tube wall is negligible. The physical characteristics of the airway or vessel wall should therefore not affect resistance to laminar flow. Similarly, the composition of gas sampled from the periphery of a tube during laminar flow may not be representative of the gas advancing down the centre of the tube. To complicate matters further, laminar flow requires a critical length of tubing before the characteristic advancing cone pattern can be established. This is known as the entrance length and is related to the diameter of the tube and the Reynolds number of the fluid (see later).

Quantitative Relationships

With laminar flow the gas flow rate is directly proportional to the pressure gradient along the tube ( Fig. 3.2, B ); the constant is thus defined as resistance to gas flow:

$\Delta P=\text{flow rate}\times \text{resistance}$

where ΔP = pressure gradient.

In a straight unbranched tube, the Hagen–Poiseuille equation allows gas flow to be quantified

$\text{Flow rate}=\frac{\Delta P\times \pi \times {(\text{radius})}^4}{8\times \text{length}\times \text{viscosity}}$

by combining these two equations:

$\text{Resistance}=\frac{8\times \text{length}\times \text{viscosity}}{\pi \times {(\text{radius})}^4}$

In this equation the fourth power of the radius of the tube explains the critical importance of narrowing of air passages. With constant tube dimensions, viscosity is the only property of a gas relevant under conditions of laminar flow. Helium has a low density but a viscosity close to that of air; therefore it will not improve gas flow if the flow is laminar (page 36).

In the Hagen–Poiseuille equation, the units must be coherent. In CGS units, dyn.cm⁻² (pressure), ml.s⁻¹ (flow), and cm (length and radius) are compatible with the unit of poise for viscosity (dyn.sec.cm⁻²). In SI units, with pressure in kilopascals, the unit of viscosity is newton.second.metre⁻² (see Appendix A). However, in practice it is still customary to express gas pressure in cmH₂O and flow in l.s⁻¹. Resistance therefore continues to usually be expressed as cmH₂O per litre per second (cmH₂O.l⁻¹.s).

Turbulent Flow

High flow rates, particularly through branched or irregular tubes, result in a breakdown of the orderly flow of gas described earlier. An irregular movement is superimposed on the general progression along the tube (Fig. 3.3, A ), with a square front replacing the cone front of laminar flow. Turbulent flow is almost invariably present when high resistance to gas flow is a problem.

The square front means that no fresh gas can reach the end of a tube until the amount of gas entering the tube is almost equal to the volume of the tube. Turbulent flow is more effective than laminar flow in purging the contents of a tube, and also provides the best conditions for drawing a representative sample of gas from the periphery of a tube. Frictional forces between the tube wall and fluid become more important in turbulent flow.

Quantitative Relationships

The relationship between driving pressure and flow rate differs from the relationship described earlier for laminar flow in three important respects:

1.

The driving pressure is proportional to the square of the gas flow rate.

2.

The driving pressure is proportional to the density of the gas and is independent of its viscosity.

3.

The required driving pressure is, in theory, inversely proportional to the fifth power of the radius of the tube (Fanning equation).

The square law relating driving pressure and flow rate is shown in Figure 3.3, B . Resistance, defined as pressure gradient divided by flow rate, is not constant as in laminar flow but increases in proportion to the flow rate. Units such as cmH₂O.l⁻¹.s should therefore be used only when flow is entirely laminar. The following methods of quantification of 'resistance' may be used when flow is totally or partially turbulent.

Two constants. This method considers resistance as comprising two components, one for laminar flow and one for turbulent flow. The simple relationship for laminar flow given previously would then be extended as follows:

$\text{Pressure gradient}=k_1(\text{flow})+k_2{(\text{flow})}^2$

k ₁ contains the factors of the Hagen–Poiseuille equation and represents the laminar flow component and k ₂ includes factors in the corresponding equation for turbulent flow. Mead and Agostini ² summarized studies of normal human subjects in the following equation:

$\begin{array}{c}\text{Pressure gradient}(\text{kPa})=0.24(\text{flow})\\ +0.03{(\text{flow})}^2\end{array}$

The exponent n. Over a surprisingly wide range of flow rates, the previous equation may be condensed into the following single-term expression with little loss of precision:

$\text{Pressure gradient}=K{(\text{flow})}^n$

In this equation n has a value ranging from 1 with purely laminar flow, to 2 with purely turbulent flow; the value of n being a useful indication of the nature of the flow. The constants for the normal human respiratory tract are

$\text{Pressure gradient}(\text{kPa})=0.24{(\text{flow})}^{1.3}$

The graphical method. It is often convenient to represent 'resistance' as a graph of pressure difference against gas flow rate, on either linear or logarithmic coordinates. Logarithmic coordinates have the advantage that the plot is usually a straight line whether flow is laminar, turbulent or mixed, and the slope of the line indicates the value of n in the equation above.

Reynolds Number

For long, straight unbranched tubes, the nature of the gas flow may be predicted from the value of the Reynolds number, which is a nondimensional quantity derived from the following expression:

$\frac{\begin{array}{c}\text{Linear gas velocity}\times \text{ tube diameter}\\ \times \text{ gas density}\end{array}}{\text{Gas viscosity}}$

The property of the gas that affects the Reynolds number is the ratio of density to viscosity. When the Reynolds number is less than 2000, flow is predominantly laminar, whereas greater than a value of 4000, flow is mainly turbulent. Between these values, both types of flow coexist. The Reynolds number also affects the entrance length (i.e. the distance required for laminar flow to become established), which is derived from:

$\begin{array}{l}\text{Entrance length}=0.03\times \text{tube diameter}\\ \times \text{Reynolds number}\end{array}$

Thus for gases with a low Reynolds number not only will resistance be less during turbulent flow but laminar flow will become established more quickly after bifurcations, corners and obstructions.

Values for some gas mixtures that a patient may inhale are shown relative to air in Table 3.1. Viscosities of respirable gases do not differ greatly but there may be very large differences in density.

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Biophysical Techniques for Structural Characterization of Macromolecules

S. Mitic , S. de Vries , in Comprehensive Biophysics, 2012

1.22.2.2 Laminar Flow Mixing

Mixing under laminar flow conditions will occur rapidly when the distance over which fluids have to be diffusively mixed is very small. Laminar flow mixing is a good alternative to turbulent mixing, especially when one has limited amounts of reagents. As a result of rapid developments in the fields of micro- and nanomachining and lithography, micromixers with flow channels as small as 1  μm or even smaller have been manufactured. The diffusion time for solutes (t _diff) is given by eqn [6]:

[6] $t_{\text{diff}}=\frac{d^2}{2\cdot D}$

The diffusion time, t _diff, is proportional to the square of the distance or the channel diameter, d, over which molecules have to diffuse. For a small molecule with a diffusion constant, D, of approximately 10⁻⁹  m²  s⁻¹, the diffusion time is approximately 500   μs for a channel of 1   μm. Thus, by decreasing the diffusion distance, the mixing-diffusion time becomes shorter. Based on this principle, different types of diffusive mixers have been developed, such as the glass-silicon-glass mixer (SF FTIR) and the LIGA (lithography, electroplating, and molding) structured stainless-steel mixer (SF FTIR). ^47–49 These laminar-flow systems require small sample volumes and low flow rates of a few nanoliters per second, which is ideal for the study of expensive biochemical samples. The operating pressure is very close to ambient.

Hydrodynamic focusing represents a recent development to employ diffusive micromixers with minimal amounts of sample consumption. Through specific solvent delivery and mixer geometries, a liquid flow is squeezed or 'hydrodynamically focused' into a thin stream, reducing the diffusion distance to 50–100   nm and yielding a diffusive mixing time in the microsecond time range. ^50–55 However, the slow onset of mixing may result in true dead times that might in fact be longer – on the order of approximately 500   μs. ⁵⁵

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Biomedical Transport Processes

Gerald E. Miller PhD , in Introduction to Biomedical Engineering (Third Edition), 2012

14.2.6 Reynolds Number and Types of Fluid Flow

The differences between laminar and turbulent flow are considerable. Laminar flow, sometimes known as streamline flow, occurs when a fluid flows in parallel layers, with no disruption between the layers. It is the opposite of turbulent flow. In nonscientific terms, laminar flow is "smooth," while turbulent flow is "rough." The dimensionless Reynolds number is an important parameter in the equations that describe whether flow conditions lead to laminar or turbulent flow. It indicates the relative significance of the viscous effect compared to the inertia effect, with laminar flow being slower and more viscous in nature, while turbulent flow can be faster and more inertial (accelerating) in nature. The Reynolds number is proportional to the ratio of the inertial force (acceleration) to the viscous force (fluid deceleration). The values of the Reynolds number for various types of flow are as follows:

•

laminar if Re < 2,000

•

transient if 2,000 < Re < 3,000

•

turbulent if 3,000 < Re

These are approximate values. The Reynolds number can be affected by the anatomy/geometry of the fluid flow field, the roughness of the vessel wall, and irregularities in pressure or external forces acting on the fluid. When the Reynolds number is much less than 1, creeping motion or Stokes flow occurs. This is an extreme case of laminar flow where viscous (friction) effects are much greater than the virtually nonexistent inertial forces. Stokes flow was previously described regarding the falling sphere viscometer and is also typical of blood flow in capillaries.

As already noted, the Reynolds number is dimensionless and gives a measure of the ratio of inertial forces (Vρ) to viscous forces (μ/L), and, consequently, it quantifies the relative importance of these two types of forces for given flow conditions. The equation for the Reynolds number is

$\text{Re}=\frac{\rho \text{VD}}{\mu }=\frac{\text{VD}}{\nu }=\frac{\text{QD}}{\nu A}$

where

V= the mean fluid velocity in (cm/s)

D = the diameter (cm)

μ = the dynamic viscosity of the fluid (g/cm-sec)

ν = the kinematic viscosity (ν = μ/ρ) (cm²/s)

r = the density of the fluid (g/cm³)

Q = the flow rate (cm³/s)

A= the pipe cross-sectional area (cm²)

The first form of the equation is the most common form. In the circulatory system, the Reynolds number is 3,000 (mean value) and 7,500 (peak value) for the aorta, 500 for a typical artery, 0.001 in a capillary, and 400 for a typical vein. This corresponds to turbulent flow in the aorta (where the aortic wall is strengthened to overcome the turbulent forces), laminar flow in arteries and veins, and creeping flow in capillaries. Thus, there are added forces, mixing, and momentum transport in the aorta and virtually no momentum transport in capillaries. However, as was noted in the discussion on mass transfer in systemic capillaries, it is the low axial blood flow that allows for the radial mass transfer to occur. This could not happen in arteries, since the fluid velocity is too large to allow any significant radial mass transfer to occur. However, with turbulent flow in the aorta, there is considerable mixing of fluid layers and added wall shear stresses. As a result, there is added mass transfer across the artery walls, which is why arterial disease is prominent in the aorta. Such a disease is caused by mass transfer of lipids across the arterial wall and by distortion of the endothelial cells lining the vessel wall, allowing for such mass transfer to occur in the gaps.

A depiction of the systemic capillaries is shown in Figure 14.39. The Reynolds number is less than 1 and the flow is creeping flow. Such flow produces entirely viscous flow with no inertial effects, no turbulence, and no flow separation. As such, there are no negative effects due to the circuitous nature of the capillary bed nor to sudden sharp turns or bifurcations. In larger vessels, such vessel geometry would produce turbulence and/or flow separation.

Figure 14.39. The network of the systemic capillaries leading from arterioles and ending in venules, with bending and bifurcating elements in the capillary bed that are possible with creeping flow.

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Jet Health

Elaine C. Jong , in The Travel and Tropical Medicine Manual (Fifth Edition), 2017

Contamination

While the laminar flow serves to minimize spread of passenger-generated contaminants, the major barrier to particulate matter on all modern aircraft is the high-efficiency particulate air (HEPA) filter. This is the standard filter used in most hospital intensive care units, operating rooms, and industrial clean rooms. A rating is given on efficiency based on the ability of the filter to remove particles greater than 0.3 microns. For reference, bacteria and fungi are on the order of greater than 1 micron in size. Viruses, however, may range on the order of 0.003-0.05 microns. Less data exist on these organisms, but it is known that clumping of virus particles facilitates their removal via HEPA filters.

Studies have been done collecting air samples from various locations and assaying for microorganisms. Locations included municipal buses, shopping malls, sidewalks, downtown streets, and airport departure lounges. It was found that microbial aerosols in the aircraft cabin were much less than in other public locations. While there does exist a risk of disease transmission simply based on the number of passengers and the close proximity, it does not appear to be any greater aboard aircraft than that for any of the other modes of public transportation. Interestingly, aircraft cabin microbial aerosols were reported lower during night flights when presumably there was less passenger activity and were higher during daytime flights when passengers were more likely to get out of their seats to walk up and down the airplane aisle.

In addition to pathogenic organisms, the concern over other contaminants exists as well, including carbon dioxide, carbon monoxide, and ozone. Carbon dioxide levels have been equated with poor air quality in buildings and other public spaces. However, data collected on 92 different US flights found carbon dioxide, carbon monoxide, and ozone levels well below maximum Federal Aviation Administration (FAA) and Occupational Safety and Health Administration standards. Thus passenger symptoms of fatigue, headache, nausea, and upper respiratory tract irritation are likely to stem from other factors, including flight duration, noise levels, dehydration, and circadian dysrhythmia. The American Society of Heating Refrigeration and Air Conditioning Engineers has recently proposed Standard 161P, which makes recommendations for cabin air quality for all commercial passenger aircraft carrying 20 or more passengers.

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Principles of Anticoagulation in Extracorporeal Circuits

Rolando Claure-Del Granado , ... Ravindra L. Mehta , in Critical Care Nephrology (Third Edition), 2019

Circuit, Tubing, and Membrane

Improving the laminar flow configuration, minimizing stagnant areas in dialyzer headers, keeping tubing lengths short, avoiding dependent loops, minimizing reservoir volumes, and decreasing air-blood interface in traps all can help prevent clotting. ³ The air-blood interface in the bubble trap can be the initial site for clotting. However, direct heparin injection into the air trap was not found to improve circuit life, although the dose used may have been insufficient. ²⁵ Recently, an experimental model was developed to test biochemical markers of coagulation activation at various times and sites in a dialysis circuit. The authors measured TAT complexes and found that the blood lines alone, without a dialyzer attached, did not activate significantly coagulation during the first 20 minutes of circulation; in contrast, when a dialyzer was included in the system, only 5 minutes of circulation was needed to activate coagulation. ²⁶

Pumped ECC systems have the advantage of ensuring more consistent blood flows, regardless of the patient's blood pressure, which can contribute to circuit life. In non-pumped systems such as continuous arteriovenous hemofiltration (CAVH), membrane geometry may be important, because parallel-plate dialyzers result in greater urea clearance than hollow-fiber configurations in this setting. Parallel plates have less flow resistance, which may result in less unstirred layers at the membrane-blood interface and potentially less clotting. However, in pumped systems such as CVVH, flat-plate dialyzers were not shown to have an advantage over hollow-fiber designs in terms of prolonging circuit longevity, and there was an insignificant trend favoring the latter. ²⁵

The membrane represents approximately 95% of the blood contact area in the circuit. The perfect nonthrombogenic membrane material remains elusive. Membrane failure occurs secondary to red blood cell, platelet, and protein coating of the membrane. The filter can represent the point in the ECC at which the flow is the slowest, creating an environment favorable to red blood cell aggregation, especially if macromolecules such as fibrinogen and artificial plasma substitutes are present and facilitate the creation of molecular bridges. ^3,27 However, when experiments using membranes with larger surface areas were carried out, with the idea that the larger the membrane, the longer the period of time before saturation and failure, no difference was observed in circuit life between membranes of 0.75 versus 1.3 m². ²⁵

The degree of biocompatibility may affect the thrombotic potential of a membrane. Cellulosic and synthetic polymer membranes activate the complement system, but synthetic membranes adsorb the activated products more readily, leading to less overall stimulation of the system. ²⁸ It has been difficult to determine whether thrombogenicity differs between cellulose and synthetic membranes; the results have been contradictory, possibly because of the variety of anticoagulation methods chosen. Polyacrylonitrile (PAN) membranes have been found to be associated with a higher clotting frequency than polyamide membranes in a number of studies. ^14,29 This may have to do with the high negative charge of a PAN membrane, which has been shown to correlate with the degree of activation of Hageman's factor, kallikrein, and bradykinin. In keeping with this hypothesis, a study comparing polyamide and PAN membranes showed that the latter was associated with a greater effect on the levels of TAT. ³⁰ Membranes with higher porosity may lead to removal of the anticoagulant (e.g., r-hirudin), whereas an unmodified cellulosic membrane may result in its accumulation.

Some membranes can be precoated with heparin (e.g., AN69-ST [Hospal, Lyon, France], Hemophan [Akzo, Wuppertal, Germany]), which allows circuits to remain patent longer with either no anticoagulant or with reduced anticoagulant. ³¹ Grafting of polyethyleneimine onto an AN69 PAN membrane decreases surface electronegativity, and the surface then repels cationic plasma molecules, including high-molecular-weight kininogen. Conversely, strongly anionic heparin is bound tightly to the modified membrane and is included in the blood-derived membrane coating the synthetic polymer. ³¹ Multiple studies have looked at the increased biocompatibility of heparin-coated surfaces and have found a decreased adsorption of fibrinogen, diminished platelet activation and aggregation, decreased complement activation, and less formation of platelet-leukocyte aggregates. ^32–34 In a recent retrospective study, the combination of a heparin-grafted AN69ST dialyzer with a citrate-enriched dialysate found no differences in the amount of ultrafiltation and the prescribed treatment time between dialysis sessions using this strategy and sessions were anticoagulation was employed. The effective blood flow was significantly higher in patients with no anticoagulation. ³⁵ A single-center, prospective, randomized, double-blind controlled trial with crossover design comparing filter survival with the AN69ST membrane and the original AN69 membrane in 39 patients treated with CVVH without additional heparin found no differences in terms of filter survival. ³⁶ Similar results were found in a more recent study with similar design. ³⁷

Low-molecular-weight heparin (LMWH)–coated circuits also were shown to be effective, without additional anticoagulation, in intermittent hemodialysis patients with normal coagulation parameters. ³⁴ This study confirmed the increased biocompatibility of heparin-coated surfaces, although TAT levels rose after the fourth hour of dialysis if no additional dalteparin was given. There remains some controversy as to the relative importance, in regard to hemocompatibility, of the interaction of surface-bound heparin with ATIII (and subsequent inactivation of key coagulation factors), compared with the adsorption and cleavage of plasma proteins with these coated membranes. ³² Studies have shown that, to produce valid results, in vitro experiments evaluating the thrombogenic potential of membranes using platelet adhesion and protein adsorption measurements always should use nonanticoagulated blood. ³³

The optimal life requirement of a filter used for CRRT remains controversial. Some studies show that high-flux membranes become maximally coated with proinflammatory molecules by 24 hours, and if attempts are made to extend the life beyond that point, these molecules are released back into the circulation. ³⁸ A low dialysate pH can contribute to dialyzer clotting, although data are scarce since the initial mention of this problem in 1977. ³⁹

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Flowing Water, Turbulent and Laminar Flows⁎

Alexander N. Sukhodolov , ... Bruce L. Rhoads , in Reference Module in Earth Systems and Environmental Sciences, 2022

Abstract

This chapter reviews laminar and turbulent flows in the context of flowing waters. It starts with the examinations of balances of forces and introduces the concept of Reynolds averaging for turbulent flows. These are followed by outlines of the basic methods of modeling, which are based on the Boussinesq hypothesis and different assumptions about turbulent viscosity. Turbulence modeling for flowing waters is illustrated by examining generic turbulent flows: boundary layer, mixing layer, jet and wake. Predictions of turbulence modeling are compared to the results of field-based experiments completed on natural rivers. Although the turbulent flows in flowing waters are always considered difficult to understand and predict, the knowledge of these flows has greatly advanced during past decades and can be used for coupling abiotic and biotic factors in complex ecological models.

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