Applications of Helical Versus Straight Hollow Fiber Membranes: A Review

flow turbulences inherent to the geometry of helical membranes. These conditions give rise to an uptake of mass and heat transfer coefficients and a reduction of temperature and concentration polarization phenomena. Aside from enhanced flow properties, helical hollow fiber bundles tend to be more robust by design, thus exhibiting better resiliency over long service operations than straight bundles. One persistent shortcoming of the helical fibers seems to be an increase in pressure drop. However, this does not always translate into a higher energy consumption – i.e., versus straight bundles. Given the performance advantage, product robustness, and adaptiveness to a broad range of applications, the adoption of helical hollow fiber technology deserves growing support from the membrane community in academic and industrial settings. functional properties in terms of flow rate-pressure drop profiles, retention efficiencies, and fouling


Introduction
The field of separation sciences has gained increased visibility throughout the years. In particular, the number of articles dedicated to membrane distillation studies has steadily expanded between 2000 and 2021, as depicted in Figure 1 (a). It can be noticed that the publication rate follows two distinct regimes (slopes) during these two decades displaying a slow progression during the 2000-2009 period and followed by a sharp uptake in pace after 2010. More specifically, researchers have sought to leverage hydrodynamic phenomena' simulation and modeling studies to optimize membrane distillation operating parameters [1][2][3][4][5]. Furthermore, the choice of membrane materials and fabrication processes have been widely explored to increase the permeate flux and mitigate fouling phenomena [6][7][8][9][10]. According to Culfaz et al. [11], the helical configuration of the membrane promotes turbulence and therefore causes a significant reduction in concentration polarization. This reduction is attributed to Dean vortices, occurring at a flow rate above the critical Re. Indeed, under these conditions, a secondary flux can be created, and the depolarization of fouling can be established [11][12][13]. In terms of membrane fabrication, the fibers can be produced by spinning a polymeric solution that passes through a hollow cone spray nozzle. Fibers can be formed by precipitating the spun solution in a coagulation bath, followed by a controlled drying phase. Straight parallel fibers can be obtained by cutting and collecting them from the take-up drum of the spinning unit, then packing them in parallel orientation inside a module. Moreover, helically wound fibrous mats can be fabricated by spinning a continuous fiber from a rotating ring, then collecting it onto a core that travels back and forth inside the ring [14][15][16]. Although the capital cost differences between these two filter configurations are hardly discussed by technical experts, it does not seem to be a burden since the engineering designs are not drastically changed, and the fabrication steps are not too cumbersome.
Nowadays, a key area of interest lies in coupling carefully selected membrane distillation configurations with renewable energy sources to better compete against other distillation techniques [17][18][19]. Many membrane filter designs can be tested, including hollow fiber, planar, tubular, and spiral modules [20][21][22]. The demand for hollow fiber modules has constantly been rising because their advantageous area-to-volume ratio (relative to flat sheets) facilitates the optimization of process performance, and their low energy consumption contributes to a low operating cost [23,24]. Hence, hollow fibers can be used in different geometries, such as straight and helical hollow fibers [25][26][27]. According to Figure 1(b), the number of published papers discussing straight designs has been greater than that of helical fibers in the past two decades. Yet, the rate of helical hollow fibers publications outperformers that for straight hollow fibers by almost 150% during that same period.
Membrane distillation modules are generally made of fibers assembled in a straight form. Wirth et al. [28] conducted a side-by-side experimental study and tested straight and helical cartridges together. They established that the permeate flux of the helical module was almost 19% higher than that of the straight wound bundle. Indeed, the helical design was thought to enable the occurrence of a turbulent flow stream, which significantly enhances thermal transfer. Mallubhotla et al. [29] also compared these two configurations in a similar fashion, whereby the polymeric membrane was made of polyethersulfone fibers exhibiting an internal diameter of 270 µm and an external diameter of 620 µm. Furthermore, the helically wound hollow fibers had a pitch turn of 0.099 m. The experimentation presented in Figure 2 describes two modules tested under similar operating conditions. The obtained results indicated that the fiber configurations (helical or straight) and the pH of the feed solution did not affect the permeate flow. Moreover, these two designs exhibited comparable pressure drop values in charge circulation inside the fibers for a feed flow rate of 50 ml/min. However, when feed flow reaches a 200 ml/min threshold, the pressure drop caused by helical fibers is 2.4 times greater than that obtained for straight fibers Figure 3

Use Of Helical Hollow Fibers in Desalination
Helical hollow fibers were recently introduced in membrane desalination processes, as summarized in the following overview in Table 1.  (*) Permeate enhancement for helical fiber compared to straight fiber (**) Increment of pressure drop for helical fiber compared to straight fiber A numerical study was conducted to analyze the difference in distillation efficiency between helical and straight hollow fibers for sweeping gas membrane distillation applications [30]. The upstream flow is reported to increase distillation efficiency (permeate flux) by 11%, with a decrease in the friction coefficient (pressure drop) by 28%. Additionally, distillation efficiency varied negatively with the increase of Reynolds number. Indeed, a rise in turbulence leads to higher heat transfer coefficient values, which translates to faster trans-membrane heat exchanges. A bench scale of direct contact membrane distillation set-up, presented by Teoh et al. [31], was tested to study the effects of baffles, spacers, and different fiber geometries on the permeate flux. According to this study, the heat transfer coefficient for the feed side increased from 2600 W/m²K with the un-baffled module to 3750 W/m²K in the presence of helical baffles, which reflects a flux gain of 28%. When hollow fibers exhibiting wavy geometries were tested, the flux enhancement reached nearly 40% without introducing any external turbulent promoter. This boost was explained by the fact that for the fibers with un-straight geometry, an increase of turbulence in the shell-side flow leads to a rise in mass transfer and permeate flux. In another study, Ali et al. [32] assessed the effect of wavy/helical/straight hollow fiber configurations on permeate flux and energy consumption for the case of direct contact membrane distillation and running with permeate flow of 100 ml/min at 20°C. They established that higher feed flows (fiber shell region) combined with helical and wavy modules would yield the highest permeate flux values. Such enhancement is related to thermal polarization improvements on both feed and permeates sides of the membrane. The progression of permeate flux for wavy and helical hollow fibers with Reynolds number was similar. However, when the value of Reynold numbers exceeded 1,500, the helical modules showed better energy efficiency than the straight designs. When these two configurations were used to concentrate whey, the concentrations were 13.7% and 18.6% for straight and helical hollow fibers, respectively. In terms of pressure drop, helically wound fibers exhibited the highest value but their energy pumping cost per unit flux was 17% lower that of straight fibers.
Vacuum membrane distillation experiments were also carried out with helical fibers to improve process efficiency. It was expected that the occurrence of Dean vortices would increase mass and heat transfer coefficients, thereby causing a drop in temperature and concentration polarization [34]. Indeed, this configuration led to a 20% increase in permeate flux by 20% compared to the obtained value for straight fibers. However, the impact of flux gain derived from Dean vortices is limited when the temperature and concentration polarization phenomena are not very strong.

Use of Helical Fiber in Extraction
Hollow fiber cartridges can be used in membrane extraction, and their interfacial area can be 10-fold superior to stirred tanks [35]. Dominguez-Tello et al. [36] used a 3D printer to print a device to facilitate extraction while preserving the helically wound bundle shape. This technique gives the flexibility to perform the extraction with long fibers and to operate with a small sample volume. In addition, good reproducibility and repeatability of all experiments can be ensured, and easy handling of the cartridges can be guaranteed when mounting on the manifold. Another study by Liu et al. [37] compared the efficiencies of both types of design. In this investigation, a helically wound bundle was prepared by winding fiber around a metal rod of constant diameter and maintaining a constant pitch between turns to obtain a helical spiral shape. This fiber was subsequently immersed in a tank filled with a solvent solution made of water saturated with n-butanol. The final phase ended with a drying period spanning a couple of days.
This preparation method produced a robust fiber capable of retaining its helical shape after 20 days of use. Cross-sectional views of these two designs -imaged via scanning electron microscopy-depict a more uniform structure for the straight fiber than the helical fiber [37]. These experimental studies established that the helical fiber's mass transfer coefficient (MTC) values were between 2 and 2.5 higher than straight fibers Figure 4. This rise can be justified by the increase of turbulence leading to a reduction of the boundary layer on the fiber shell, thereby causing the improvement of the mass transfer coefficient. Therefore, the helical fibers preparation technique, presented by Liu S. H. et al. [37], is very promising since the helical fibers produced maintained their geometrical characteristics after an extended service time while the mass flow properties can be further optimized.
Liu et al. [38] reported the uptake of mass transfer for the helical hollow fiber, considering both its shell and lumen sides. Under the same operating conditions, the helically hollow fibers offer an improved mass transfer coefficient, which is about 3.5 times higher than straight fibers. This improvement was attributed to the secondary flow created inside helical fiber elements and the turbulence generated on the shell side. Similar findings have been presented by Kong et al. [39]. This research work combined a simulation study and some experimental analyses. The membrane module comprised five polypropylene hollow fibers, each having a porosity of 45%, an inner diameter of 0.39 mm, and a length of 0.20 m. These characteristics are the same for the helical and straight modules. These cartridges are tested for a lab-scale installation designed to separate the aromatic impurity p-toluic acid in wastewater, using p-xylene (PX) as an extractant. It was found that the helically wound bundle exhibited an extraction efficiency twice as high as the straight fiber bundle. In addition, for inside-out fiber cartridgesi.e., feed stream flows inside the lumen section of fiber-the helical configuration exhibited higher-pressure drop values versus the straight design, but without additional energy input.

Use of Helical Hollow Fibers in Gas/Liquid Applications
The presence of membranes in gas/liquid applications has become increasingly significant, as reflected by the many studies conducted. Singh et al. [40] benchmarked straight and helical fibers for an oxygenation case study. This membrane equipment can be used to deliver oxygen to blood inside the human body. According to this study, the helical fibers exhibited 2.7 times higher permeate flux than the straight fibers. This dramatic augmentation of mass transfer coefficients and permeate flux can be correlated with the effect of secondary flow inside fibers, which leads to an intensification of the mixing of fluids. Additionally, the pressure drop was 2.46 times higher for the helical membrane modules compared to the straight fiber cartridges. This pressure drop uptake increases power consumption, which consequently undermines the benefits of helically wound bundles for this application.
Nagase et al. [41] also experimented with these helical fibers for oxygen transfer from water. This study tested four modules with different arrangements of hollow polypropylene fibers. Helical fibers showed a clear improvement in the mass flow compared with straight fibers due to the increased turbulence. Furthermore, this improvement in flow allowed for a reduction in membrane surface area at the module.
Kaufhold et al. [42] tested the use of hollow fibers with (straight/meander/helical/twisted configurations) in some experiments focused on oxygen separation. It was established that the oxygen mass transfer coefficient for a Reynolds number of 141 was 2.4 times higher for the helical module versus the straight element. This improvement was noticeable, with hollow fibers exhibiting a curvature diameter below 4 mm. For larger diameters, these designs led to a reduction in fiber packing density inside the modules. Luelf et al. [43], who investigated both straight and helical cartridges, reported some sharp advantages that the latter due to reduced concentration polarization, lower surface membrane fouling, and higher mass transfer coefficient values An artificial gill is a device transporting oxygen from water to air. It enables humans to breathe underwater, thereby extending the time that humans can be spent underwater. Nagase et al. [41] experimented with helical fibers for oxygen transfer from water seeking to utilize them in artificial gill in artificial gill. These researchers benchmarked four modules with different arrangements of polypropylene hollow fibers. As a result, the mass flow coefficients were drastically improved for helically wound bundles compared to straight fiber bundles due to increased flow turbulence. Furthermore, this outcome led to an optimization of permeate flux and reduced the membrane surface area inside the filter cartridges.
Jani et al. [44] tried optimizing the design of a gas-liquid micro-mixer. For this purpose, they developed a gas-liquid separator made of a helical fiber membrane. This micro-contactor presented in Figure 5 is composed of a polypropylene fiber that is helically around a glass tube and characterized by an outer diameter of 2.7 mm, an inner diameter of 1.8 mm, and an average pore diameter of 0.27 µm. This tube is inserted into another tube, thereby forming the shell side. It was shown that for a Reynolds number higher than 60, a mass flow improvement greater than 80% was achieved when comparing the helical versus straight fiber type.

Use of Helical Hollow Fibers in Membrane Filtration Applications
The utilization of helical hollow fibers is also prevalent in filtration processes. It has been reported that their permeate flux can reach 300%-400% of values typical for straight fiber elements. In addition, the pressure drop uptake measured for helical designs was 200%-300% higher relative to straight fiber configurations [45]. Other filtration studies concluded that the permeate flux of helical hollow fiber membranes was five-fold that of straight hollow fibers [46]. This increase can be attributed to secondary flows caused by Dean vortices, which can occur for fluid motion produced in curved channels and above certain critical Reynolds numbers.
Kuakuvi et al. compared the performance behavior of helical and straight hollow fibers while running some ultrafiltration experiments [47]. The membrane modules were made of 20 fibers, corresponding to a full membrane area of 2.0510 -2 m 2 . The inner fiber diameter was 0.7 mm, and its length was 470 mm. The pressure drop was expected to be lower for straight hollow fiber geometries, as highlighted in the above studiesi.e., mainly because of Dean vortices. However, these researchers established that the larger the coil diameter (fiber) for helical membranes, the lower the pressure drop. Moreover, for similar energy consumption levels, membrane modules built with helical fibers gave the highest permeate flux A comparison between helical and straight hollow fibers was made in the case of filtration of bovine serum albumin (BSA) [48]. The experimental filtration setup is depicted in Figure 6. Helical hollow fibers gave a membrane permeability of 227 l/h m² bar for pure water filtration, which is 72% higher than measured for straight hollow fibers. The effect of hollow fiber configurations on filter fouling during BSA filtration has been investigated, with the protein feed stream passing inside or outside the hollow fiber bundles. Results depicting the variation of pressure drop for helical cartridges (PDH) and straight hollow cartridges (PDS) are reported in Figure 7. For all designs, the progression of fouling as a function of time exhibited an upward trend. For the helical modules, the fouling profile was almost unchanged between inside-out and outside-in BSA feed streams. However, BSA feed stream orientation impacted the fouling behavior for straight modules. When comparing both configurations, helical hollow fibers yielded the highest level of protein fouling, corresponding to a high decrease in permeate flux, an increase in production cost, and a shortened membrane life cycle with time, increasing the production cost and reducing the lifespan of the membrane [13,49,50].
In Table 2, we summarize the comparison between helical and straight hollow fibers for the case of the effects of fiber configurations on permeate flux and pressure drop.

Long-Term Application of Helical and Straight Hollow Fibers
When exploring the long-term use of both hollow fiber configurations (straight and helical types), Baldridge et al. [51] concluded that there was no significant change in efficiency after a couple of days of air filtration. However, Liu et al. [29] established that after running an extraction process for more than 20 days, straight modules experienced an increase in the fiber length, which caused some performance loss because of the distorted bundle [37]. Conversely, the membrane characteristics of helical modules remained unchanged after 20 days of operation. In summary, these two research programs suggest that gentle processes (e.g., air filtration) have a lesser impact on membrane properties during extended service operations. But more intrusive (liquid) processes will yield greater mechanical stress on the membranes; in this case, the helical design proves to be the preferred optioni.e., versus straight fibers Liu et al. [37].

Conclusion
The interest in membrane processes has been steadily growing for several decades due to many attractive features such as their ability to separate or concentrate species, modularity, controllable footprint, ease of operation, and compliance with other technologies. However, the most outstanding challenge is balancing the minimization of fouling phenomena and energy consumption with increased permeate flux and membrane retention properties. Many studies have explored several types of hollow fiber membranes to address these shortcomings, including the straight and helical hollow fiber designs. A comparative analysis between these two configurations targeted several applications, including extraction, desalination, gas/liquid applications, and filtration processes.
The attractiveness of helically wound fiber membranes highlighted by this review results from their mechanical robustness and intrinsic ability to promote flow turbulence. These attributes often lead to faster permeability rates, reduced concentration polarization, and fouling propensity stable performance over the extended service life, thus favoring the helical modules over the straight ones. Future work should consider a more systematic exploration of the relationship between the helical fiber structure and its pressure drop in targeted applications. Furthermore, the adoption of modeling tools could be extremely beneficial in correlating the hollow fiber membrane structure (straight and helical types) with their functional properties in terms of flow rate-pressure drop profiles, retention efficiencies, and fouling characteristics

Funding
This research received no specific grant from any funding agency in the public, commercial, or not-for-profit sectors.

Data availability statement
The data that support the findings of this study are available on request from the corresponding author.

Conflicts of interest
Authors declare that their present work has no conflict of interest with other published works.