Inducing secondary ﬂows and vortices is known to enhance mass transport. They can be imposed by structured ﬂow channels for instance. In particular, these vortices reduce fouling and concentration polarization. In this work we present a new method of producing hollow ﬁber membranes with a sinusoidal change in diameter over the ﬁber length. We engineered a pulsation module that imposes a sinusoidally ﬂuctuating bore liquid ﬂow rate. Harmonic bore ﬂow conditions can be varied over a wide range. The ﬂuctuating bore liquid ﬂow rate translates into axial membrane properties varying with respect to inner bore diameter and wall thickness. The resulting narrowing and widening of the membrane lumen channel are hypothesized to induce secondary vortices to the liquid inside the membrane lumen known as the Bellhouse e ect. Improved oxygen transport from shell-to-lumen side prove superiority over straight hollow ﬁber membranes in G /L absorption process. We anticipate the dynamic ﬂow module to be easily integrated into currently existing hollow ﬁber membrane spinning processes. Keywords: Bellhouse e ect, secondary ﬂow, sinusoidal shaped ﬁbers, hollow ﬁber Todo list 1. Background 1.1. Importance of hollow ﬁber geometry Hollow ﬁber membranes o er important advantages over other membrane conﬁgurations. They show well-deﬁned ﬂow conditions on the inside of the ﬁber. Packing densities are su- perior over ﬂat sheet based membrane modules. In fact, appli- cations requiring mass production of membranes mainly rely on hollow ﬁbers as their production and assembly into mod- ules is highly scalable. This is particularly true for medical applications such as hemodialysis and blood oxygenation [1]. While commonly assumed to be done only by spiral-wound modules [2], even seawater desalination is done with hollow ﬁber membranes [3] at a scale as important as spiral-wound modules. Parallelization and high degrees of production au- tomation allows for scalable spinning processes [4]. 1.2. Hollow ﬁber spinning In industrial hollow ﬁber fabrication the ﬁber is extruded through a spinneret [5]. The extrusion of the inner lumen ﬂow channel is done parallel to the main ﬂow direction of the poly- mer solution by engineering parallel ﬂow inside the spinneret.Although radial stress may occur due to die swell, the result- ing geometry is a constant lumen channel cross-section along the main direction of the ﬁber. This indisturbed tubular ge- ometry causes close to perfect laminar ﬂow proﬁles in later applications. However, in applications like hemodialysis, the ﬁbers are slighly undulated to maintain a good dialysate ﬂow on the ﬁber shell side [6], while lumen side ﬂow is assumed to remain undisturbed laminar. In membrane contactor modules, shell side ba es and other means are integrated into the hollow ﬁber module to allow for ﬂuid ﬂow perpendicular to the main ﬁber direction [7]. This allows for increased mixing on the shell side of the ﬁber only. No increased mixing is possible with this method on the ﬁber inside. 1.3. Mass transport in furrowed channels The ﬂuid ﬂow in furrowed or grooved ﬂow channels has been reported in literature since the work of Bellhouse [8] in 1973. These studies revealed that periodic geometrical ﬂow distur- bances can lead to increased mixing inside the ﬂow channels. This can be transferred into an increase in transfer rate (either heat or mass transfer) across the ﬂow channels surface [9, 10]. Early numerical and experimental studies agreed well [11, 12]. Recently, Kasisteropoulou [13] investigated the ﬂuid ﬂow in periodically grooved microchannels. Nishimura et al. in- vestigated the ﬂuid ﬂow in wavy channel in numerous publi- cations as early as 1991. They used both experimental [14– 1 T. Luelf et al. /Journal of Membrane Science 00 (2016) 1–8 2 20] and numerical methods [14, 16–18, 20, 21] to investigate the ﬂow behavior in wavy ﬂat channels [14–18, 21] and wavy walled tubes [19, 20]. In both cases the formation of vortices have been reported. When comparing both geometries they conclude, that the mass transfer increment in the studied ﬂow regime (50 <Re<1000) is larger for the wavy-walled tube than the wavy-walled ﬂat channel [19]. Neusser and cowork- ers recently attempted to transfer the concept of furrowed ﬂow channels to new biohybrid membranes. They developed a setup to transfer a ﬂat sheet oxygenation membrane into a membrane having furrows and seeded them with endothelial cells [22, 23]. Unfortunately, all these principles have not entered the fabri- cation process of hollow ﬁber preparation yet. It is the aim of this work to establish evidence that continuous preparation of hollow ﬁbers having furrowed lumen channels is possible and o ers the anticipated improvements in mass transport. 2. Materials and methods 2.1. Transient ﬂow conditions in membrane spinning To allow for a membrane geometry that combines static mix- ing by furrowed channel geometry with a hollow ﬁber mem- brane fabrication process, we choose to design a sinusoidal variation in ﬁber lumen diameter along the ﬁber length. The variation is realized by adding a ﬂuctuation in ﬂow to a con- stant bore ﬂuid ﬂow rate as shown in Figure 1. The constant ﬂow of the polymer solution was induced by a HARV ARD sy- ringe pump. Pulsation was induced by a custom made pulsation module shown in Figure 2: through a T-piece, liquid volume is pressed and withdrawn alternatively into and from the lumen pipe to reach the desired pulsation. This volume was pumped using a microliter syringe incorporated into the pulsation mod- ule. Using the variable rotational speed of an electrical stepper motor, the rotation is transferred into a linear motion by a linear slider attached to a disk with multiple eccentric drillings. The linear slider allows for the attachment of the syringe plunger. Now the frequency of ﬂuid ﬂow can be adjusted by the rotation speed of motor while the amplitude can be varied by the choice of eccentricity on the turning plate. The amplitude of pulsation can also be varied by the selection of the microliter glass sy- ringe (Hamilton), thus pulsation volume can be selected from the whole spectrum of microliter syringes available. Due to the mechanical design, the bore pulsation was sinu- soidal, as can be derived by transformation of rotational move- ment with constant frequency towards linear movement. The superposition of a constant bore ﬂow rate with a sinusoidal pul- sation allows for a decoupled net ﬂow rate from pulsation fre- quency and amplitude, thus o ering all desired degrees of free- dom for the pulsating ﬂow manipulation, namely: Amplitude aof pulsation Frequency fof pulsation Net bore ﬂow rate Figure 1: Pulsation concept for the production of sine shaped hollow ﬁbers. The ﬂow rate of polymer solution is constant whereas bore liquid ﬂow rate is a function of time, leading to variable axial ﬁber diameters Figure 2: Custom made pulsation module consisting of: 1: Luer Lock con- nector for plug and play use in state-of-the-art spining lines, 2: HAMILTON gastight glass syringe, 3: turning plate with discrete eccentric drillings for am- plitude manipulation, 4: linear slider for transformation to linear movement, 5: Motor coupling, 6: Mounting plate for NEMA connection to stepper motor. Stepper motor not shown. 2 T. Luelf et al. /Journal of Membrane Science 00 (2016) 1–8 3 Solution PVDF LiCl NMP Ethanol H 2O [wt:%] [wt:%] [wt:%] [ wt:%] [ wt:%] Polymer 17 4 79 - - Bore - - - 50 50 Table 1: Composition of polymer and bore solution applied in the spinning experiments 2.2. Pulsation calculation Assuming ideal incompressible ﬂuid behaviour of the bore ﬂuid, a superposition of two ﬂows by a T-piece results in a mathematical superposition of ﬂow rates. The ﬂow rate can be quanitiﬁed by equation 1: ˙Vbore;out(t)=˙Vbore;conti+˙Vbore;pulse(t): (1) The time dependant pulsating contribution is deﬁned by the radius rpulse set at the turning plate and the syringe plunger diameter in combination with the constant rotational speed. Rewriting equation 1 results in: ˙Vbore;pulse=Apulsecpulse=Apulse2nrpulsecos(2nt);(2) Integrating the ratio of bore and polymer solution ﬂow rate and the ﬁber drawing velocity an ideal spinning process with no change in dimensions over the air gap distance would result in ﬁber dimensions as follows: dh f;i=s 4˙VBore ch f(3) dh f;o=2s ˙VDope ch f+d2 h f;i 4; (4) with dh f;ibeing the inner ﬁber diameter and dh f;obeing the outer diameter. The pulsating membrane segments are deﬁned by each full sinusoidal run. The period of the sine wave trans- fers to a length of the wave in the ﬁnal membrane diameter. l=1 2ch fT=1 2ch fn1; (5) with T=n1. 2.3. Membrane fabrication Hollow ﬁber membranes have been produced on a single ﬁber spinning line. Polymer solutions have been prepared on the basis of Solvay Solef 6010 PVDF according to Table 1. LiCl (Cas.-Nr. 7447-41-8) was supplied by Carl Roth, NMP (Cas.-Nr. 872-50-4) was supplied by Fisher Scientiﬁc. The spinning line was adapted to pulsating spinning by adding the pulsation module described above without further modiﬁcations. In order to maintain comparability, hollow ﬁbers have been spun with active pulsation and without pulsation. Spinning conditions are listed in Table 2. A Hamilton gas tight syringe with 250 µl holdup and plunger diameter of 2.3 mm was used on the pulsation module.Sample VBore VPolymer cWheel [mL=min] [mL=min] [cm=s] 1-8 0.6 0.9 2 9-10 0.6 1.35 2.33 Table 2: Conventional spinning parameters used in this work dBore dpolindpolout [mm] [ mm] [ mm] 0.51 0.82 1.12 Table 3: Spinneret dimension 2.4. Image analysis Membrane geometries have been measured with an optical device speciﬁcally designed for determining ﬁber dimensions. The digital information was further analyzed via MATLAB® image analysis if not stated otherwise. Fiber walls were made transparent by soaking with octanol, to introduce a ﬂuid of sim- ilar refractive index into the pores of the membrane matrix. Af- ter soaking the ﬁber became transparent [24]. H 2O colored with red dye was added into the ﬁber lumen to create contrast be- tween the lumen and membrane matrix. In order to prevent re- fractive distortion, the photographic image was taken with the ﬁber submerged in a petri-dish ﬁlled with octanol, thus provid- ing a planar liquid surface. 2.5. Gas-liquid contacting To evaluate the potential of mass transfer enhancement inside the hollow ﬁber lumen, mass transfer experiments have been performed. Gas absorption into a ﬂowing liquid has been cho- sen as experimental system. Experiments have been performed via oxygen-water gas-liquid contacting. The experiments were performed in a setup as illustrated in Figure 3. Water is pumped from a glass vessel through the metal tub- ing through the membrane module and back into the glass ves- sel. Oxygen atmosphere was applied on the shell side of the module at ambient pressure. The oxygen level inside the ves- sel was continuously measured via a Pyroscience Robust Probe OXROB10. Between each measurement run the vessel has been Membrane n r puls ID [Hz] [mm] 1 1.17 7.5 2 0 - 3 0.78 7.5 4 0 - 5 1.17 7.5 6 1.56 7.5 7 0.78 7.5 8 1.17 10 9 1.17 7.5 10 0 - Table 4: Frequency and amplitude bore ﬂow conditions used to obtain di erent membrane geometries 3 T. Luelf et al. /Journal of Membrane Science 00 (2016) 1–8 4 N2 O2 O2 PT Figure 3: Flowpath of gas-liquid contacting experimental setup. The oxygen content in the stirred vessel is measured over time. Nitrogen or oxygen are connected to the membrane module as demanded. Speciﬁc ﬂow rates are set with a controllable gear pump. degassed by nitrogen both inside the vessel and on the out- side of the membrane module. Control measurements to en- sure no oxygen transfer through tubing and sealing have been performed regularly with a metal tube instead of the membrane module. 3. Results 3.1. Pulsation evaluation The behaviour of the pulsation module was tested during membrane preparation by pressure measurements in the bore channel of the spinneret assembly. As bore liquid is considered to be a Newtonian, incompressible ﬂuid, a sinusoidal pulsation in ﬂow rate should directly correlate to a sinusoidal pulsation in pressure, as given by Bernoulli’s law. The resulting pressure variation is shown in Figure 4. The data points represent actual measurements of pressure, whereas the lines are ﬁtted sine functions. Double data points directly next to each other are caused by the restricted time resolution of the data acquisition device. Triangle points are measurement data from a standard spinning process with the same spinning conditions. Squared data points were obtained during pulsating operation. The pressure ﬂuctuations correlate well with the an- alytical sine functions and only little to no damping is observed due to sti tubing and incompressible medium and parts. At this point we conclude that the pulsation induction into the bore ﬂuid line of the spinning setup is technically viable. 3.2. Membrane morphology During the spinning process, it became immediately clear that the lumen volume dilation and contraction modiﬁed the ge- ometry of the hollow ﬁber after coagulation. Fiber dimensions will be analyzed below in more detail. Figure 5 shows the cross Figure 4: Bore ﬂuid pressure as indication for sinusoidal ﬂow rate with min- imal damping e ects at the spinneret. NMeasurement of constant ﬂow rate operation;Measurement of pulsating ﬂow section of Sample 5 at axial positions near maximum and min- imum diameter. It is apparent that the ﬁber wall thickness is higher for the smaller inner diameter section. This redistribu- tion of wall thickness is a direct result of a radial conservation of mass distributed over larger cross-sectional area of the ﬁber wall. Whether there is also a redistribution of mass in the axial wall direction cannot be concluded at this stage. The corrugated inner morphology was studied in detail by Bonyadi et al. [25]. Di erent conditions under which corrugated cross-sectional ar- eas occur are suggested. Among other hypothesises possibly leading to a corrugated inner cross-section, the contribution of elastic and buckling instability is enhanced in our process. In addition to an inward radial force induced by a shrinkage of polymer dope, the ﬂuctuating bore ﬂuid adds a contribution to this force. 3.3. Membrane geometries Figure 6 shows the ﬁber diameters gained by optical image analysis. Table 5 shows the results of the corresponding sine function ﬁtting. The ﬁber diameters were ﬁt to comply with equation 6. The periodical shape of the ﬁbers is visible. Higher pulsation rates during membrane fabrication are represented by higher frequency of diameter-change in ﬁber measurements. In- dications of some non-ideal sinusoidal shape in the samples of Figure 6 b) are visible. Also ﬁbers with the same pulsation set- ting (Sample 3 and 7) in some cases show di erent amplitudes in the diameter measurement, resulting from unequal pulsat- ing over the circumference of the ﬁber. These e ects of non- ideal behavior require further deeper analysis and are beyond the scope of the current manuscript. f(x)=asin(2fx)+dm (6) Figure 7 presents the inner ﬁber lumen of Sample 4, 6 and 9, spun with induced bore pulsation. A sinusoidal variation 4 T. Luelf et al. /Journal of Membrane Science 00 (2016) 1–8 5 Figure 5: FESEM images of ﬁber sample 5 cross-sections taken on the thick (1) and thin (2) element of the ﬁber. Figure 7: Fiber lumen of Sample 4, 9 and 6 spun with induced bore pulsation. Membrane wall is transparent due to refractive index matching of PVDF with octanoleasin(2fx)+dm # a [mm] f [1 /mm] dm[mm] 1 0.243 0.139 1.00 3 0.215 0.092 0.81 5 0.211 0.136 1.06 6 0.149 0.187 1.10 7 0.220 0.092 1.02 8 0.248 0.141 1.01 9 0.039 0.13 1.06 Table 5: Fitted parameters of ﬁber outer diameter calculated from image anal- ysis in inner ﬁber diameter can be observed with an connect lu- men channel between wide and narrow sections. The geom- etry is regular without visible distortions from sinusoidal di- ameter variation for ﬁber 9 with relatively low pulsation fre- quency of 1.17 Hz compared to 1.56 Hz of Sample 6. Sample 6 shows non-idealities of the bore channel of the ﬁnal ﬁber. The small diameter regions are narrow ﬂow channels with diameter changes that do not follow a sine function. As the pulsation rate is 1.56 Hz and thus signiﬁcantly higher than for sample 9 the ﬂow rate of the pulsation device leaving the bore ﬂuid line overcompensated the constant ﬂow rate of the syringe pump, leading to partial backﬂow through the nascent ﬁber into the spinneret maintaining an open channel with minimal diameter. 3.4. Mass transfer experiments Gas-liquid contacting experiments have been performed with di erent ﬁber batches, both with straight and sine shaped 5 T. Luelf et al. /Journal of Membrane Science 00 (2016) 1–8 6 Figure 6: Plot of ﬁber outside diameters along the ﬁber axis. Diameter maximum values are set to be at zero axis position. Colours and numbers denote di erent samples. geometry. Mass transfer rates as a function of lumen ﬂow rates are plotted in Figure 8. Positive deviation of the transfer rates become clear for higher lumen ﬂow rates. The calculated ﬂow rates are total ﬂow rates. For low ﬂow rates all membrane samples have about the same oxygen ﬂux up to a ﬂow rate of approximately 2 mL /min. At this ﬂow rates the transfer rate of the highly pulsat- ing ﬁber 6 outperforms ﬁbers 9 and 4 e.g. with oxygen ﬂuxes of 8.1 mmol /m2h for ﬁber 6 and 5.4 mmol /m2h and 3.9 x10 mmol /m2h for ﬁbers 9 and 4 respectively. 4. Discussion A pulsation module has been designed to account for a highly scalable and ﬂexible ﬂow pulsation to be applicable as a plug-in solution on an existing membrane spinning line. Pulsation of the bore ﬂuid was successfully transferred to the precipitating polymer solution. The axially variable geome- try was conserved into the ﬁnal ﬁber. The created degrees of freedom in membrane spinning can be used in multiple ways, e.g. to create ﬁbers with non sinusoidal diameter variation by changing the motor movement to a non constant rotation. While the results of mass transfer are promising, the current work can only be considered as a proof of principle. Many potential fur- ther steps can be taken based on the above data, but need to be evaluated in more detail. Transferring the principle to other material systems. Exploration of high frequency to ﬁnd out how the fre- quency inﬂuences geometry and mass transport. Figure 8: Results of oxygen transfer experiments. Membrane batch 6; NMembrane batch 9; Membrane batch 4. Error bars indicate standard devi- ation obtained by at least triplicate measurements. 6 T. Luelf et al. /Journal of Membrane Science 00 (2016) 1–8 7 Applying the proposed ﬁber geometry in membrane ﬁltra- tion applications to inﬂuence polarisation phenomena. Transferring the concept to a multi-spinneret line where one plunger system actuates multiple spinnerets being op- erated out of one block as is found in industrial parallelized spinning processes. Establishing ﬂuctuation conditions of the bore ﬂuid which are asymmetric in nature and thus shape non-sinusoidal geometries. Interaction of pulsatile feed ﬂow with the new structures: Does it improve mass transport even further by inducing non-steady eddies that interfere with the laminar stream lines and di usion resistances. In the past we have reported that strong gradients in the skin of microstructured ﬁbers need to be avoided [26] and only subtle transitions guarantee sharp separation charac- teristics. How does axial rather than radial gradients inﬂu- ence separation skin properties? 5. Conclusion and Outlook The presented work describes the implementation of a novel method to produce hollow ﬁber membranes with passive mix- ing functionalities. The mixing is achieved via a sinusoidal variation in diameter along the ﬁber length. Gas liquid con- tacting with this novel hollow ﬁber membrane shows promis- ing improvements. Transfer rates increased by a factor of about 2.4. While all presented experiments have been performed with a si- nusoidal plunger movement of the pulsation device, the move- ment can be altered in future work. A higher pulsating fre- quency with a smaller microliter syringe would lead to more open ﬁbers with intensiﬁed ﬂow disturbance. On the other hand a time gap between each sine run or a change in pulsating fre- quency (e.g. fast collapsing of ﬁber diameter and slow back- pumping) might lead to even more improved ﬁber properties or ﬁbers with non symmetric structures. Acknowledgements M. W. acknowledges the support through an Alexander-von- Humboldt Professorship. This work was performed in part at the Center for Chemical Polymer Technology CPT, which is supported by the EU and the federal state of North Rhine-West- phalia (grant no. EFRE 30 00 883 02).