A near-superhydrophobic surface reduces hemolysis of blood flow in tubes

Abstract

The use of an external mechanical pump to sustain the circulation in a body, also known as extracorporeal circulation, is an integral part of many medical procedures such as hemodialysis and cardio-pulmonary bypass. However, the damage to red blood cells caused by the flow-induced shear stresses in the flow circuit has remained an intractable problem for many years, limiting the operational duration of extracorporeal circulation. In this study, near-superhydrophobic surfaces were investigated as a potential solution to mitigate the hemolysis of blood during extracorporeal pumping through the use of a proof-of-concept flow circuit. It was found that the thin layer of air trapped by the near-superhydrophobic surface due to the Cassie–Baxter state reduced the wall shear stress exerted on the blood flow, resulting in a corresponding decrease in the rate of hemolysis. For blood that undergoes an oscillatory flow, this reduction in the hemolysis was shown to be directly related to the mean shear rate and shear rate amplitude of the flow.

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Introduction

Extracorporeal circulation, a process in which the circulation of blood in a body is sustained with the aid of a mechanical pump in an external circuit, is crucial for medical procedures such as cardiopulmonary bypass and hemodialysis.^1–5 A major limitation of the process, however, is that it introduces hemolysis (i.e. mechanical destruction of red blood cells), which constrains the duration of its operation.^6–11

Although the main cause of this blood damage had already been ascertained to be the shear stresses exerted on the blood as it flows through the extracorporeal circuit,^7,8,11,12 few solutions have been proposed to mitigate the hemolytic activities of the external pumping circuit. Current research efforts aimed at lowering hemolysis rates are focused mainly on developing low shear pump designs and optimizing operating parameters such as rotation speed, flow rate and pump head.^13,14 The most practical and promising suggestion to date involves lowering the occlusion level of roller pumps,^3,4 a common extracorporeal circulation pump. The reduction in hemolysis achieved using this technique, however, comes at the cost of decreased flow rates and pumping inefficiency. In addition, it cannot be implemented for centrifugal pumps, which have found widespread use in extracorporeal circulation as well.^2,9,15

All these limitations, however, can potentially be circumvented by the use of superhydrophobic or near-superhydrophobic surface coatings in the extracorporeal circuit. Such surfaces are highly water repellent, and generally depend on the deposition or fabrication of hydrophobic micro- and/or nano-structures on the surface to work.^16–21 Because of the low surface energy of these structures, water or water-based solutions/suspensions cannot seep in between the structures, but remain suspended and supported only by the tip of the structures.²¹ As a result, the fluid effectively sits on a surface made up of air and the top of the micro-/nano-structures, which is also known as the Cassie–Baxter state.^22,23

Due to this unique arrangement, water droplets have very low adhesion to near-superhydrophobic/superhydrophobic surfaces and tend to roll or bounce off these surfaces easily.^16,19,20 In addition, it has been shown that near-superhydrophobic/superhydrophobic surfaces impart very low wall shear stresses to flowing fluids because it enabled deviations from the “no-slip” flow condition of fluid near to the surfaces, thus allowing the same amount of fluid to be delivered from one point to another using a lower pressure (i.e. improved pumping efficiency).^24–26 This diminished wall shear stress should, in theory, also lead to a lower hemolysis rate when near-superhydrophobic/superhydrophobic surfaces are incorporated into an extracorporeal circuit.

The objective of this report, therefore, is to quantitatively characterize the hemolytic potential of a near-superhydrophobic surface with respect to a regular surface, and relate the observed difference to the reduction in wall shear stress induced by the near-superhydrophobic surface through the use of an established mathematical model. It should be emphasized that the current report documents a proof-of-concept study and hence, the flow circuit used for the experiments was not reflective of those currently employed by medical professionals for actual extracorporeal circulation.

Materials and methods

Blood

Fresh porcine blood (Primary Industries Pte Ltd, Singapore) was obtained and used in accordance to the rules and regulations of the Agri-Food and Veterinary Authority of Singapore. Every 10 parts of the blood was mixed with 1 part of an anticoagulant to prevent blood clots from forming. The anticoagulant was obtained by adding 1.975 g of sodium citrate tribasic dihydrate (Sigma Aldrich C8532) and 1 g of HEPES (Sigma Aldrich H3375) for every 50 ml of deionized water.

Hematocrit measurements

Blood samples were drawn from the flow circuit and placed in 15 ml test tubes. The samples were separated into plasma and blood cells through the use of the centrifuge, Sartorius Sigma 3-18K, at 9000 rpm for 5 minutes. The hematocrit can be calculated as the volume ratio of blood cells to the entire blood sample.

Hemolysis characterization

The degree of hemolysis was quantified by measuring the concentration of hemoglobin in the blood plasma using a commercial hemoglobin assay kit (Sigma Aldrich MAK115). 200 μl of the hemoglobin assay reagent was first mixed with 50 μl of blood plasma, obtained using the centrifuging process described above, and left to incubate for 5 minutes at room temperature. The concentration of plasma hemoglobin was then determined from absorbance measurements of the mixture at a wavelength of 400 nm, using a spectrophotometric multiwall plate reader (Tecan Infinite M200 Pro). The damage to the red blood cells were also qualitatively verified by acquiring optical microscopy images of the red blood cells before and after they were subjected to extracorporeal pumping using Olympus Microscope CX41.

Fabrication of near-superhydrophobic surface

Near-superhydrophobic surfaces were obtained by depositing a commercial liquid repellent coating²⁷ (Rust-Oleum Neverwet), consisting of micro- and nano- particles suspended in a polymeric binder, on the inside of a PVC (polyvinyl chloride) pipe. This was accomplished by first pouring the base coat solution of the Neverwet coating onto the inside surface of a PVC pipe inclined at approximately 60° to the horizontal, and rotating the pipe as the base coat dried to ensure an even coating. An hour after the application of the base coat, the top coat was applied to the inside surface of the pipe in the same manner and left to set for another hour.

Surface characterization

The wettability of the near-superhydrophobic surface and a regular PVC surface were quantified using contact angle measurements of at least 5 different droplets for each type of surface. Scanning electron microscopy (SEM) pictures were obtained using FEI Inspect F50 after the samples have been coated with 20 nm of aluminum by means of an Edwards Auto 360 thermal evaporator, in order to improve the electrical conductivity of the surface. Surface roughness measurements were made using a surface profilometer, Alpha Step 500 (Tencor Instruments), at 4 different locations on the inside surface of a coated, as well as an uncoated, PVC pipe. The pipes were sawn in half to facilitate the measurements. The thickness of the coating was similarly measured by means of microscopy images.

Flow loop

To generate mechanical damage to the blood in the extracorporeal circuit, a closed flow loop containing about 800 ml of blood was used (Fig. 1a). The flow loop consists of an open reservoir (blue), a flow probe (black), a rigid pipe with either a near-superhydrophobic inner surface or regular PVC inner surface (gray), and a commercial medical pump (Kamoer CK-15) which drove the blood flow. The pipe had a length of 30 cm, an inner diameter of 14 mm and a thickness of 2 mm, and connections between the various circuit elements were made using elastic silicone tubes (yellow) with an inner diameter of 8 mm and a thickness of 2 mm. The total length of the silicone tubes was 1 m, which was sufficiently long to avoid the formation of kinks in the tubes as they form a close loop in the circuit. PTFE tape were used, where necessary, to prevent leaks. The flow probe was connected to a flow meter (model 501, Carolina Medical Electronics Inc.) and data acquisition unit (National Instruments, USB X series) which sampled the real time flow rate at a frequency of 2000 Hz.

Fig. 1 Schematic diagrams illustrating (a) the setup of the closed flow loop and (b) the operation of the medical roller pump with an elastic tube.

The medical pump is a fully occluded roller pump that provides pulsatile flow. It works by squeezing the blood-filled silicone tube with a roller and moving the roller along the elastic tube to push the fluid forward (Fig. 1b). As one roller finishes its course of motion and releases the tube, another takes its place. In such pumps, the mean flow rate can only be increased by raising the frequency of roller movement.³

The hemolytic performance of a near-superhydrophobic surface was investigated by inserting a rigid pipe with the liquid repellent coating into the flow circuit. The coating was applied to the inside of rigid PVC pipes rather than that of the elastic silicone tubes as the latter tend to flex significantly during operation, which can cause spalling of the coating. Blood was then driven through the circuit at different flow settings by systematically increasing the roller frequency from 0 Hz to 15.7 Hz, the maximum setting on the pump. The mean flow rate obtained using these frequencies covers the full spectrum of flow rates commonly used in hemodialysis^28–30 and the lower end of spectrum used in cardiopulmonary bypass surgeries.^31,32 For the control experiments, the pipe with the liquid repellent coating was replaced by a regular uncoated PVC pipe with everything else remaining constant, and the experiments were repeated with the same flow settings. This ensured that any difference in hemolysis observed between the variable and control experiments was due solely to the flow over the different surfaces on the inside of the PVC pipes.

Each hemolysis experiment was carried out for 90 minutes under ambient conditions (temperature = 20 °C, relative humidity = 30%), with the pump running continuously for the full duration. 15 ml blood samples were drawn from the flow loop and tested for plasma hemoglobin at 30 minute intervals. Following the procedure of Noon et al.,¹ at least 3 different plasma hemoglobin readings were taken for each time point. Other than one outlier at t = 30 min for the flow setting, VI (N.S.H), all the readings were included in the results analysis.

Computational fluid dynamic (CFD) simulations

CFD simulations were carried out to evaluate the wall shear stresses exerted on the blood for each flow setting. This was done by modeling the pipe using 12 000 axisymmetric elements in ANSYS Workbench (ANSYS, Inc., Canonsburg, PA, USA). The flow waveforms, obtained with the flow probe for different pump settings, were then applied at the pipe inlet as a boundary condition. The boundary condition for the outlet is pressure = 0 Pa and the no-slip boundary condition was applied to the pipe walls to simulate the PVC surface. Flow across the near-superhydrophobic surface cannot be simulated as easily, however, and therefore, the corresponding shear stresses will be calculated through analytical means, based on the simulation results for the PVC surface instead.

FLUENT 15.0 (ANSYS, Inc., Canonsburg, PA, USA) was used to perform the CFD simulations for 6 complete cycles (20 time steps/cycle) of each flow waveform to remove the transient effects and achieve steady state before the shear stresses on the model were acquired. A non-Newtonian model (Carreau) was used for the dynamic viscosity of blood in the simulations, which is given by³³

where G refers to the shear rate, η_∞ is the dynamic viscosity for a Newtonian model, 0.0035 Pa s, η₀ is the dynamic viscosity at zero shear, 0.056 Pa s, and λ and n are constants equivalent to 3.31 s and 0.357 respectively.

Results

Near-superhydrophobicity

The liquid repellent coating was found to cover the inner surface of the rigid pipe uniformly with a thickness of 53.0 ± 6.7 μm and an average roughness of 2.34 ± 1.07 μm. This roughness was mostly due to the components within the liquid repellent coating and not imparted by the original, uncoated PVC surface which was comparatively smooth, with an average roughness of 0.21 ± 0.12 μm.

The coating works by creating a rough surface composed of silanized micro- and nano-particles embedded in a polymeric matrix²⁷ (see ESI†). Because of the highly hydrophobic nature of these particles, water was not able to imbibe the rough surface to wet the micro- and nano-structures, but instead, lie on the top of these structures on a composite surface of solid and air, which is also known as the Cassie–Baxter state. Additional experiments had been performed to demonstrate this, and can be found in the ESI.†

The effect of the liquid repellent coating on PVC can be seen in Fig. 2, where the contact angle of a blood droplet can be observed to rise from 85.5° ± 3.2° for a flat, regular PVC surface to 140.6° ± 4.1° for a flat, coated PVC surface. These values are close to contact angle measurements obtained using water droplets (82.8° ± 2.5° for PVC; 138.4° ± 3.0° for coated PVC).

Fig. 2 (ai) Photo of a 6 μl blood droplet exhibiting a contact angle of 85° on a flat PVC surface and a schematic diagram illustrating the state of the droplet. (aii) Sequential images showing the sticking and spreading of a 6 μl blood droplet deposited onto a PVC surface. (bi) Photo of a 6 μl blood droplet exhibiting a contact angle of 140° on a flat PVC surface with a near-superhydrophobic coating and a schematic diagram illustrating the Cassie–Baxter state of the droplet. Green – PVC surface; orange – hydrophobic micro-/nano-structures. (bii) Sequential images showing a 6 μl blood droplet bouncing off a near-superhydrophobic surface. Note that the pipes in (aii) and (bii) were inclined at 45° to the horizontal.

Following scientific convention, the coated PVC surface is termed as near-superhydrophobic, since superhydrophobic surfaces require the static contact angle to be greater than an arbitrarily defined value of 150°.^18,34 Nonetheless, it is worth noting that the coated PVC surface displayed a high degree of non-wettability (roll-off angle/contact angle hysteresis ≈ 0°) and trapped liquid in the Cassie–Baxter state, which are characteristics of superhydrophobic surfaces.^20,34 Thus, the results of this study are not expected to differ significantly even if a fully superhydrophobic surface had been used instead.

As further proof that the non-wetting property persisted even when the coating was on the inside of the rigid pipe, pipes with and without the hydrophobic coating were sawn open and 6 μl of blood droplets were deposited onto them. The blood droplets were observed to stick and spread out on the regular PVC surface (Fig. 2aii) but bounced off the near-superhydrophobic coated surface rapidly (Fig. 2bii).

Flow rates and shear stresses

Fig. 3a shows a typical pulsatile flow waveform produced by the roller pump. The waveform is approximately sinusoidal, and can be expressed as

F(t) = F₀ + F_a sin ωt (2)

where F(t) is the instantaneous flow rate, F₀ is the mean flow rate, F_a is the amplitude of flow, t is time and ω refers to the angular velocity of the flow, which is given by 2πf where f is the frequency of the pulsatile waveforms generated by the rollers. The waveform was checked every 30 minutes during the experiments and were found to be stable and consistent for all flow settings.

Fig. 3 (a) Instantaneous flow rate detected by the flow probe for flow setting II. (b) Variation in wall shear stress for the different flow settings over a single period for the PVC surface obtained using CFD simulations. Note that the direction of net flow by the fluid is taken to be positive here. Since the shear stress exerted on the fluid by the pipe wall was always in the opposite direction to the flow, the average shear stresses are negative. (Inset) Representative CFD result showing the uniform spatial distribution of wall shear stress on the model of the pipe for flow setting VI.

Using the flow waveforms in CFD simulations, the instantaneous wall shear stress experienced by the PVC surface for each type of flow waveform was obtained. From Fig. 3b, it can be seen that the wall shear stress followed the sinusoidal character of the flow waveform, and was spatially uniform throughout the wall of the symmetrical PVC pipe (Fig. 3b inset).

In addition, the magnitude of τ₀, the mean wall shear stress, can be observed to increase with the mean flow rate, F₀ (see Table 1). The amplitude of the shear stress waveform, on the other hand, remained mostly the same, as the amplitude of the flow oscillations did not vary significantly for the different flow settings. The instantaneous wall shear stress can be given by

τ(t) = τ₀ + τ_a sin ωt (3)

where τ(t) is the instantaneous flow rate and τ_a is the amplitude of the oscillating shear stress. Table 1 documents the various properties of the different flow waveforms tested, including the shear rate values, G₀ and G_a, that correspond to the respective values of τ₀ and τ_a.

Table 1 Parameters for the 6 different flow settings used. τ₀ and τ_a are tabulated based on data shown in Fig. 3b. Note that G₀ = −τ₀/η and G_a = −τ_a/η

Flow setting	I	II	III	IV	V	VI
f (Hz)	0.00	4.30	7.10	10.0	12.80	15.70
F0 (l min^−1)	0.00	0.35	0.74	1.00	1.27	1.47
Fa (l min^−1)	0.00	0.97	1.07	0.79	0.94	1.00
τ0 (Pa)	0.00	−0.14	−0.26	−0.37	−0.49	−0.59
G0 (s^−1)	0.00	19.3	46.0	73.5	104	130.5
τa (Pa)	0.00	0.60	0.65	0.58	0.58	0.55
Ga (s^−1)	0.00	131.50	145.70	126.30	127.50	118.00

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Hemolysis

It is known that the level of hematocrit present in the blood influences the rate of hemolysis³⁵ and thus, normalization had to be carried out to ensure a fair comparison between the results of the experiments. To do so, blood of different hematocrit levels, achieved by diluting the blood with phosphate buffered solution (1×), were subjected to the same flow condition (flow setting III) in the experimental setup for 60 minutes. The plasma hemoglobin for each sample was then measured and plotted in Fig. 4a to obtain the normalization curve. It was found that for the range of hematocrit tested, the rate of increase of plasma hemoglobin (ΔH/t^0.785, in mg dl⁻¹ min^−0.785) is a quadratic function of hematocrit (hct, in %),

ΔH/t^0.785 = 0.0005(hct)² − 0.0047(hct) (4)

Fig. 4 (a) Plot of ΔH/t^0.785 vs. hct. The data points represent the experimentally measured values while the dotted trend line represents eqn (4). (b) Plot of ΔH vs. t for the different flow settings. The data points represent experimentally measured values while the trend lines represent the best fit curves of the data points to the relationship of ΔH ∝ t^0.785. The best fit curve and data points for the same flow setting are given the same color. Best fit curves of the near-superhydrophobic surface (N.S.H) are represented by dashed lines whereas that of the regular PVC surface are represented by solid lines. The units for ΔH and t are mg dl⁻¹ and min respectively. Error bars represent standard deviations. (c) Bright field optical microscopy images of red blood cells (i) before and (ii) after being subjected to extracorporeal pumping through a regular PVC pipe at flow setting VI for 60 min. The dotted white arrow points to a red blood cell with deformed cell membrane while the solid white arrow points to a red blood cell with spiky protrusions. Scale bars represent 10 μm.

Note that the units of the constants, 0.0005 and 0.0047, in eqn (4) can be shown to be mg dl⁻¹ min^−0.785 by balancing the scientific units on both sides of the equation.

Using eqn (4), the concentration of plasma hemoglobin at each time point for the different experiments were then adjusted to a hematocrit of 40% (average hematocrit of all samples = 38.2% ± 8.6%) and plotted as data points in Fig. 4b. Data for Fig. 4b in the tabulated form can be found in the ESI.† The magnitude of ΔH is consistent with those reported for similar experiments,¹ providing validation for our results. It had also been shown previously³⁶ that ΔH is proportional to t^0.785, and it can be observed that the data points fit closely to this trend, indicated as dashed lines (near-superhydrophobic surface) and solid lines (PVC surface) in Fig. 4b, with an average R² value of 0.92 ± 0.08. However, because of the low levels of hemolysis involved, the ΔH ∝ t^0.785 fitting was statistically insignificant (p > 0.05) for the cases I (PVC), II (PVC), III (PVC), I (N.S.H) and II (N.S.H).

From Fig. 4b, it can be observed that the rate of hemolysis, indicated by the gradient of the trend lines, was always greater for regular PVC surfaces as compared to near-superhydrophobic surfaces for any given flow condition, other than flow setting I (no flow; static condition). For flow setting I, there was no discernible increment in ΔH over time for both the near-superhydrophobic and PVC surfaces, implying that there were no chemical reactions between the blood with the PVC or liquid repellent coating that led to hemolysis i.e. the PVC surface and liquid repellent coating were biocompatible and not toxic to blood.³⁷

To account for the difference in hemolysis rates between regular and near-superhydrophobic surfaces, the mechanical force acting on the blood flow, which is a well-known source of hemolysis,^7,8,11 was examined. It was found that for the experimental parameters of this study, hydrodynamic pressure was not the cause for hemolysis. This is because Blackshear et al.⁷ had previously shown that hemolysis only takes place if the pressure, relative to the atmosphere, is greater than 2000 mmHg, but in all the experiments performed for this study, the hydrodynamic pressure did not even exceed 50 mmHg (see ESI†).

In addition, it can be observed from Fig. 4b that the hemolysis rates generally rise from flow setting I to VI, which is associated with increased mean flow rates and higher wall shear stresses (Table 1 and Fig. 3b). This is consistent with previous studies which showed that exposure to shear stresses can lead to red blood cell damage.^7,8,11 To further confirm this, the microscopy images of the red blood cells before and after being subjected to extracorporeal pumping were examined. From Fig. 4c, it can be seen that after extracorporeal circulation, the red blood cell membranes were deformed (dotted arrow in Fig. 4cii) or had spiky protrusions (solid arrow in Fig. 4cii), a phenomenon that was also observed in previous studies³⁸ detailing the effects of shear stresses on red blood cell damage (see ESI† for more microscopy images of the damaged red blood cells). These evidence indicate that shear stresses were the main cause behind the hemolysis observed in the experiments.

Furthermore, for the sake of completeness, we also examine the possibility that the liquid repellant coating on the near-superhydrophobic surface may have chemically strengthened the red blood cells against shear stresses and caused a reduction in the rate of hemolysis during flow. While our experiments do not preclude the potential of this happening, the likelihood is extremely low for the following reasons.

Firstly, to the best of our knowledge, there has been no report on any polymer or ceramic that can improve the resistance of red blood cells to hemolysis during blood flow. This is also true for nanoparticles, which have only been shown to be capable of inducing hemolysis, rather than strengthen red blood cells against damage.^39–41 Lastly, if the coating had chemically reacted with the red blood cells, some level of degradation should have taken place. However, there were no observed changes to the appearance and performance of the liquid repellent coating throughout the study. In fact, the blood contact angle of the near-superhydrophobic surface after a hemolysis experiment was measured to be 139.5° ± 4.1°, which is nearly identical to the pre-experimental value of 140.6° ± 4.1°.

Therefore, it is most likely that the difference in hemolysis rates observed between the near-superhydrophobic and PVC surfaces is solely due to dissimilar wall shear stresses exerted on the blood flow by the respective surfaces. To validate this, our results will be quantitatively analyzed and compared to well-established models that describe shear-induced hemolysis in the following section.

Discussion

Considering the hemolysis of blood in the experimental setup shown in Fig. 1a was caused by wall shear stresses generated by the flow of blood through the rigid pipe and the rest of the circuit,

ΔH_PVC = ΔH_p,PVC + ΔH_r (5)

ΔH_N.S.H = ΔH_p,N.S.H + ΔH_r (6)

where ΔH is the total increase in plasma hemoglobin, ΔH_p is the increase in plasma hemoglobin due to the flow through the rigid pipe and ΔH_r is the increase in plasma hemoglobin due to the flow through the rest of the circuit. The subscripts PVC and N.S.H (near-superhydrophobic) denote the surface that the respective variables belong to. From eqn (5) and (6), the reduction in hemolysis enabled by the near-superhydrophobic coating, ΔH_c, can be isolated as

ΔH_c = ΔH_PVC − ΔH_N.S.H = ΔH_p,PVC − ΔH_p,N.S.H (7)

Arora et al.¹² had previously used a strain-based approach, built on Giersiepen et al.’s work,³⁶ to develop a prediction for the hemolysis of blood subjected to a low-intensity oscillating flow. In this model, the viscoelastic character of the red blood cell membrane is taken into account and its failure is brought about when the red blood cell becomes critically deformed. This distortion to the shape of the red blood cell in a pulsatile flow is influenced by G₀ and G_a, which determine the maximum, minimum and net deformation of the red blood cell (Fig. 5a). Within the parameters of this study, the mathematical model can approximately be expressed as¹²

ΔH_p,PVC =kG₀^2.4β^1.6t^0.785 (8)

where k is a proportionality constant that takes into account all other factors influencing hemolysis and β = G_a/G₀. Note that G₀ = −τ₀/η and G_a = −τ_a/η. The values of G_a and G₀ can be computed from Fig. 3b and are documented in Table 1.

Fig. 5 (a) Schematic diagrams illustrating the deformation of a red blood cell subjected to the minimum shear rate, G₀ − G_a and the maximum shear rate, G₀ + G_a, of a pulsatile flow. The cell oscillates between these shapes so that its net deformation is given by the average shear rate, G₀. (b) Plot of ΔH_c/G₀^2.4t^0.785 vs. β. The dashed trend line represents the relationship ΔH_c/G₀^2.4t^0.785 ∝ β^1.6. (c) Plot of ΔH_c/β^1.6t^0.785 vs. G₀. The dotted trend line represents the relationship ΔH_c/β^1.6t^0.785 ∝ G₀^2.4. For (b) and (c), each data point represents 1 flow setting. The units for ΔH_c, G₀ and t are mg dl⁻¹, s⁻¹ and min respectively.

It was also shown previously by Ou et al.²⁴ that the reduced shear stress experienced by fluids flowing past near-superhydrophobic/superhydrophobic surfaces is a direct result of the diminished area of contact between the fluid and solid surface, due to the thin layer of air trapped by the hydrophobic surface roughness. In other words, the fluid in the blood, as well as red blood cells, was effectively flowing past shear-free fluid–air interfaces as well as fluid–solid interfaces where the no-slip boundary condition persisted. Therefore,

ΔH_p,N.S.H = mkG₀^2.4β^1.6t^0.785 (9)

where m is the fraction of the inner surface area of the coated pipe that is in direct contact with the fluid. The value of m can be computed for orderly arrays of micro-/nano-structures²⁰ or measured using techniques such as Raman spectroscopy for disorderly surface roughness.⁴²

It can be observed from eqn (9) that our analysis did not account for the effect that the dissimilar chemistry between the near-superhydrophobic coating and the PVC surface had on hemolysis. The justification for this is based on the observation that the circulating blood had minimal contact with the coating (<15% of total surface area; see ESI†) due to the adoption of the Cassie–Baxter state, and therefore, the difference in the hemolysis rate between the near-superhydrophobic and regular PVC surfaces can predominantly be attributed to their dissimilar surface roughness rather than surface chemistry. Substituting eqn (8) and (9) into eqn (7), it can be shown that

ΔH_c = KG₀^2.4β^1.6t^0.785 (10)

where K = (1 − m)k. It is worth noting that eqn (10) predicts that the reduction in hemolysis brought about by a near-superhydrophobic surface is expected to increase with higher G₀ and β.

To verify our analysis, the experimentally obtained values of ΔH_c/t^0.785 for each flow setting were first computed using

Eqn (11) can be derived from eqn (7). The values of ΔH_p,PVC/t^0.785 and ΔH_p,N.S.H/t^0.785 for each flow setting can be found using the proportionality constant of the trend lines shown in Fig. 4b. Then, using the values of G₀ and β for each flow setting, ΔH_c/G₀^2.4t^0.785 vs. β and ΔH_c/β^1.6t^0.785 vs. G₀ were plotted as data points in Fig. 5b and c respectively.

Since eqn (10) can be re-written as

ΔH_c/G₀^2.4t^0.785 = Kβ^1.6, (12)

the ΔH_c/G₀^2.4t^0.785 vs. β data points in Fig. 5b must adhere closely to the power-law trend of y ∝ x^1.6 (represented by the dashed line in Fig. 5b) for eqn (10) to be valid. Similarly, eqn (10) can also be re-written as

ΔH_c/β^1.6t^0.785 = KG₀^2.4, (13)

and for it to be valid, the ΔH_c/β^1.6t^0.785 vs. G₀ data points in Fig. 5c must follow the power-law trend of y ∝ x^2.4 (represented by the dotted line in Fig. 5c) closely. Moreover, the proportionality constant of the fitted trend lines in both Fig. 5b and c should give the same value for K as indicated in eqn (12) and (13).

From Fig. 5b and c, it can be observed that the data points do indeed fit the expected trend lines. The R² value of fit for Fig. 5b was 0.97 while the R² value of fit for Fig. 5c was 0.96. Furthermore, the value of the proportionality constant, K, derived separately from the trend lines in Fig. 5b and c, was found to be equivalent to 4.1 × 10⁻⁶ in both plots. Fig. 5b and c, therefore, provide strong validation for the above analysis, which demonstrates that the lower hemolysis rates found on the near-superhydrophobic surface can be sufficiently accounted for by considering the diminished shear stresses brought about by the reduced contact area on such surfaces.

Conclusion

The hemolytic potential of near-superhydrophobic surfaces had been investigated and found to be much lower than that of regular surfaces. This result was attributed to diminished contact of the blood with the walls of the pipe due to a thin layer of air trapped by the near-superhydrophobic surface, leading to reduced wall shear stresses acting on red blood cells during extracorporeal circulation. In addition, it was shown through a detailed analysis of the results that near-superhydrophobic surfaces provide a greater reduction of hemolysis when the blood is subjected to more adverse flow conditions (higher mean shear rate and higher shear rate amplitude). These results suggest that near-superhydrophobic surfaces may be useful for reducing hemolysis when incorporated into extracorporeal circuits.

Conflict of interest

The authors declare that there are no competing financial interests.

Acknowledgements

This study was partially supported by the Singapore Millennium Foundation (Grant number: R-397-000-200-592; PI:Yap Choon Hwai). We thank Mr Ivan Loh for his advice and guidance on the use of the plasma hemoglobin test kit.

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Footnote

† Electronic supplementary information (ESI) available. See DOI: 10.1039/c6ra12376g

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