Static mixers are an e cient means to mitigate membrane fouling as they deﬂect the ﬂuid, thus increasing the shear rate at the membrane surface and enhancing back-transport of rejected matter. However, inserting static mixers in the ﬂow channel of a membrane imposes an additional pressure drop. To decrease this detrimental e ect of static mixers, we shorten twisted tape mixers and investigate how this shortening translates into a reduction of fouling mitigation. We follow two approaches known from heat transfer enhancement: i) shorten the total length of the twisted tape and ii) use regularly spaced short twisted tape elements which are kept at their position by smooth rods placed in between the twisted elements. Computational ﬂuid dynamics (CFD) is applied to analyze the ﬂow pattern, the shear rate at the membrane and the resulting pressure drop. The results allow for the selection of modiﬁed twisted tape mixers with lower pressure loss, but su cient ﬂow properties for fouling mitigation. The most promising mixer designs were selected according to the CFD study, 3D-printed, and their fouling mitigation e ect experimentally investigated using silica suspensions. Additionally, the e ect of foulant concentration in this system is analyzed. For low silica concentrations (0 :03g=L) the short and spaced twisted tapes mitigate fouling as e ciently as the full-length twisted tape. At high silica concentrations and ﬂuxes, the full-length mixer mitigates fouling more strongly than the short and spaced twisted tapes. However, the modiﬁed twisted tapes prove to be more energy-e cient up to a certain fouling exposure. Keywords: Turbulence Promoters, Static Mixers, CFD - Computational Fluid Dynamics, Fouling Mitigation, Pressure Drop 1. Introduction Ultraﬁltration processes are often a ected by mem- 1 brane fouling. Fouling can be caused by (a) foulants 2 adsorbed at the membrane surface or in the membrane 3 pores, (b) by foulants forming a gel layer at the mem- 4 brane surface, and (c) by particles constricting or block- 5 ing the pores. Various countermeasures aiming at foul- 6 ing reduction are applied in industry, and many more 7 have been investigated in research. Mostly, these foul- 8 ing countermeasures inﬂuence the hydrodynamics in- 9 side the membrane module, trying to impose ﬂuid insta- 10 bilities [1] resulting in chaotic and turbulent-like ﬂow 11 conditions. This ﬂow destabilization can either be gen- 12 erated actively, for instance by rotating or vibrating the 13 These authors contributed equally to this work. Corresponding Author: M. Wessling Email address: manuscripts.cvt@avt.rwth-aachen.de (Matthias Wessling)membrane or the membrane module, or by passive tech- 14 niques. Passive measures require less additional energy 15 and have no moving parts. Often, they aim at creat- 16 ing secondary ﬂows. Such secondary ﬂows can be in- 17 troduced by Dean vortices which can evolve in curved 18 channels [2]. Another approach to destabilize the ﬂuid 19 ﬂow is the application of static inserts in a ﬂow chan- 20 nel. These static inserts, also called static mixers or 21 turbulence promoters [3, 4, 5], deﬂect the ﬂuid in the 22 ﬂow channel. Thus, they induce secondary ﬂows and 23 increase the actual crossﬂow velocity in the channel as 24 well as the shear rate at the wall. For this reason, inserts 25 have long been used to improve heat transfer in heat ex- 26 changers [6, 7, 8, 9]. Static mixers also enhance mixing 27 of the boundary layer. This way concentration polar- 28 ization is reduced, mass transport ampliﬁed and particle 29 back-transport into the bulk promoted. In membrane ﬁl- 30 tration, static inserts are applied as all these phenomena 31 - ﬂuid deﬂection, increased shear rate, enhanced mixing 32 Preprint submitted to Journal of Membrane Science May 7, 2019 - help to decrease membrane fouling [3]. 33 2. Background 34 Research on the application of static mixers in mem- 35 brane ﬁltration dates back at least to the 1970s [10]. 36 Since then, various geometries and shapes of inserts 37 have been investigated. The simplest geometry is a rod, 38 which is mostly equipped with a wire around its axis to 39 further deﬂect the ﬂuid [11, 12, 13]. Hence, the number 40 of turns of the wire around the rod can be varied. Either 41 4 turns per 25 mm[11] or per 50 mm[13] appears to be 42 the optimal design in terms of ﬂux enhancement when 43 ﬁltering Baker’s yeast. 44 Another quite simple insert is a twisted tape or double 45 helix as it is referred to in some literature [13, 5]. Com- 46 parable to the wired rod, the so-called pitch length of the 47 twisted tape can be varied. The pitch length corresponds 48 to the length of one full twist. The pressure drop, as well 49 as the fouling reduction, depend on the pitch length. De- 50 creasing pitch length translates to higher pressure drop, 51 but increased fouling reduction [5, 14]. 52 Modiﬁcations of twisted tapes are abundant in litera- 53 ture, especially in the ﬁeld of heat transfer [15]. Twisted 54 tapes with drilled holes are one example. Such a perfo- 55 rated tape was used, for instance, by Rahimi et al. [16] 56 in heat transfer studies. The aim of perforating the tapes 57 is to decrease the pressure drop which they impose on 58 the system [16, 17]. In this case, this is achieved since 59 the ﬂuid can ﬂow through the openings in the insert. 60 Perforated tapes also proved to be beneﬁcial in the mi- 61 croﬁltration of milk [17]. 62 Similarly, not only the surface of the inserts can 63 be perforated, but also the edges of the twisted tape 64 can be corrugated, notched or serrated [9, 18, 19, 14]. 65 Notches can be u-shaped, v-shaped, rectangular or cir- 66 cular [9, 20, 21]. Moreover, the cut tape can also 67 be bend such that a wing-like structure evolves [8, 9]. 68 These modiﬁcations of twisted tapes have mainly been 69 investigated in heat transfer [8, 9]. In membrane ﬁl- 70 tration, twisted tapes with a wavy-like edge only had a 71 minor inﬂuence on the fouling of humic acid when com- 72 pared to a standard twisted tape [14]. 73 Twisted tapes usually have a constant diameter along 74 their length. To reduce their pressure drop and the loss 75 of membrane area, static inserts with varying diameters 76 have been investigated. The diameter can decrease lin- 77 early with the mixer length and increase sharply in a 78 step [14], or it can increase and decrease regularly, e.g. 79 in a sinusoidal shape [14] or a cone-like structure [22]. 80 An axially varying diameter reduced the pressure loss 81 of the insert. However, tapes with constant diameter 82caused a higher ﬂux increase than the tapes with vary- 83 ing diameter [14]. When cone-shaped inserts were com- 84 pared to smooth rods, they reduced fouling to a greater 85 extent than the rods [22]. 86 More complex structures such as Kenics static mixers 87 [4], screw-threaded [23] or blade-type inserts [17] have 88 also been successfully used to improve micro- and ul- 89 traﬁltration applications. Additive manufacturing, com- 90 monly known as 3D printing, enables the fabrication of 91 advanced designs of static inserts. Thus, helically mi- 92 crostructured spacers [24] or spacers based on triply pe- 93 riodic minimal surfaces [25] have been developed for 94 ﬂat sheet applications in ultraﬁltration. Furthermore, 95 static inserts for tubular membranes have been fabri- 96 cated using additive manufacturing [14]. 97 Another approach to decrease the pressure drop asso- 98 ciated with the insertion of static mixers is to reduce the 99 length of the mixer. Thus, the volume of the ﬂow chan- 100 nel occupied by the static insert is decreased. Yadav and 101 Padalkar [26] used this approach to enhance the heat 102 transfer of air ﬂow. Applying CFD simulations, they 103 found that the full-length twisted tape gave the highest 104 Nu numbers, but also the highest friction factors for all 105 investigated Re numbers. The half-length twisted tape 106 considerably reduced the friction factor compared to the 107 full-length tape. However, the heat transfer enhance- 108 ment due to the half-length tape was also lower than 109 that of the full-length tape. Still, the half-length tape 110 showed a 847 % higher heat transfer coe cient than 111 the tube without a tape inserted. This was attributed 112 to the preservation of the swirl ﬂow behind the twisted 113 tape. [26] 114 The approach to use several short twisted tape ele- 115 ments with free space in between as turbulence pro- 116 moter is based on the same idea as the application of 117 shortened twisted tapes. The swirl ﬂow introduced by a 118 twisted tape is preserved for a certain length behind the 119 twisted tape. Therefore, another twisted tape element 120 is placed behind the ﬁrst twisted tape, but with some 121 free space in between. Optimally, the free space cor- 122 responds precisely to the length within which the swirl 123 ﬂow decays. CFD simulations could deliver data for 124 this optimization to decrease the experimental e ort and 125 ﬁnd optimal solutions. Wang et al. [27] optimized the 126 conﬁguration of short-length twisted tapes regarding the 127 heat transfer of turbulent air ﬂow. As optimization pa- 128 rameters, the heat transfer enhancement e ciency and 129 the evolution of the swirl ﬂow were considered. In their 130 case, the optimal free space between two twisted tape 131 elements was 28 - 33 times the inner diameter of the 132 tube which is a very high free space ratio. 133 The aim of applying spaced twisted tape is again to 134 2 Figure 1: Graphical representation of the approach followed in this study: Using full-length, short and spaced twisted tapes to mitigate membrane fouling. The helical ﬂow pattern remains behind the shorter tape parts. This way the fouling mitigating hydrodynamics continue, but pressure drop is reduced. reduce the pressure loss induced by the inserts and si- 135 multaneously, to maintain the heat or mass transfer en- 136 hancement of the full-length twisted tape. Ferroni et 137 al.[28] found that regularly spaced twisted tapes de- 138 creased the pressure drop by at least 50 % compared 139 to full-length twisted tapes when using liquid water as 140 the medium. Spaced twisted tapes have been success- 141 fully tested for improving heat transfer [29, 30, 15, 31]. 142 Eiamsa-ard et al. [15], for instance, compared the 143 heat transfer e ciency of full-length and several spaced 144 twisted tapes using a hot and a cold water stream. They 145 found that the full-length tape led to the highest Nu 146 numbers, but also had the highest friction factors. The 147 Nu number and the friction factor of spaced twisted 148 tapes was in between the full-length tape and the empty 149 tube. 150 As mentioned before, CFD simulation is often used to 151 optimize ﬂuid ﬂow regarding pressure loss [32, 33, 34]. 152 Flow simulations also have the advantage of supplying 153 additional information that is otherwise hard to mea- 154 sure in experiments, e.g. shear stress [35, 36, 37, 38]. 155 Another advantage of ﬂow simulations is the possibil- 156 ity to investigate complex insert structures which might 157 be complicated to fabricate. Jung and co-workers [39] 158 analyzed numerically the fouling mitigation of barrier- 159 embedded partitioned pipe mixers in cross-ﬂow ﬁltra- 160 tion using the concentration boundary layer thickness 161 and the wall concentration as parameters to measure the 162 e ectiveness of the inserts. 163 To the best of our knowledge, neither short nor spaced 164twisted tapes have been investigated in the ﬁeld of mass 165 transfer. The combined experimental and simulation 166 study presented below analyzes how short and spaced 167 twisted tapes a ect membrane fouling in comparison to 168 a full-length twisted tape. CFD simulations are per- 169 formed where twisted tapes with various lengths and 170 di erent free space ratios are investigated to reduce the 171 experimental e ort. The di erent tapes are compared 172 regarding shear rate, ﬂow pattern and pressure drop. 173 The most promising short and spaced twisted tapes are 174 fabricated via 3D printing and experimentally investi- 175 gated using silica colloids as model foulants. Further- 176 more, the silica concentration is varied to study its in- 177 ﬂuence on membrane fouling and the fouling mitigation 178 by the static mixers. Fig. 1 shows a graphical represen- 179 tation of the approach followed in this study. 180 3. Materials and Methods 181 3.1. Chemicals and membrane 182 Colloidal silica (Ludox HS40, Sigma Aldrich) was 183 used as model foulant. Concentrations of 0 :03g=L, 184 0:12g=L, 0:24g=Land 0:60g=Lcolloidal silica in a 185 20mM phosphate bu er at pH 8 were applied in the 186 fouling experiments. The tubular ceramic ultraﬁltration 187 membrane (atech innovations GmbH, Germany) had a 188 nominal cut-o of 100 kDa, an inner diameter of 6 mm 189 and a length of 0 :25m. One of the membranes had 190 an active ﬁltration area of 0 :0043 m2and a pure wa- 191 ter permeability of 450 LMH=bar, the second mem- 192 brane of the same type had an active area of 0 :0041 m2193 3 Figure 2: Photo of three experimentally investigated static mixers. Above, the full-length twisted tape, in the middle a short twisted tape and beneath a spaced twisted tape having twisted tapes with a length of 25 mmand 50 mmlong rods in between. and pure water permeability of around 650 LMH=bar. 194 In between fouling experiments, the membranes were 195 cleaned by ﬂushing the ﬁltration system with 10 Lof 196 hot water (temperature around 50C) at a ﬂow rate of 197 60L=hand a subsequent ﬂushing step using deionized 198 water at the same ﬂow rate. During cleaning, the reten- 199 tate was not recycled. 200 3.2. Static mixers 201 All static mixer geometries are based on a twisted 202 tape shape. The diameter of all mixers was 5 :5mm 203 and their thickness 1 mm. The pitch length, which 204 corresponds to the length of one twisted element, was 205 13:75mm. Two types of twisted tapes were investigated. 206 The ﬁrst type represents twisted tapes of di erent length 207 ranging from 100 mmto 250 mmin 50 mmsteps. The 208 second type were so-called spaced twisted tapes. They 209 consist of multiple shorter twisted tapes connected by 210 smooth rods that had a diameter of 2 mm. The primary 211 function of the rods is to connect the mixer sequences 212 and keep them at deﬁned positions. However, they also 213 have a small inﬂuence on the ﬂow proﬁle, shear rates 214 and consequently fouling reduction. They decrease the 215 area of the ﬂow channel and impose a doughnut-shape 216 on the ﬂow. The following three designs of the spaced 217 twisted tapes were used: 218 combination 50 /50: alternating 50 mmtwisted tape 219 and 50 mmsmooth rod 220 combination 25 /25: alternating 25 mmtwisted tape 221 and 25 mmsmooth rod 222 combination 25 /50: alternating 25 mmtwisted tape 223 and 50 mmsmooth rod (see Fig. 2) 224Fig. 2 exemplary shows three static mixer geome- 225 tries which were experimentally investigated. The full- 226 length twisted tape is the uppermost tape with a length 227 of 250 mm, beneath, a short twisted tape and one type 228 of spaced twisted tape are displayed. 229 In total, seven twisted tape geometries, a smooth rod 230 (diameter: 2 mm, length: 250 mm), and the empty ﬂow 231 channel of the tubular membrane were investigated us- 232 ing CFD. Based on the CFD results, ﬁve of the seven 233 static mixer geometries were selected for fabrication 234 and experimentally investigated. These were the twisted 235 tape with full length (250 mm, corresponding to the 236 length of the membrane), a twisted tape with a length of 237 200mmand one with a length of 150 mm. In addition, 238 two of the spaced twisted tapes were fabricated: combi- 239 nation 25 /25 and combination 25 /50. The mixers were 240 manufactured in-house by polyjet 3D printing (Strata- 241 sys, Objet Eden 260V , resolution: 32 m) and consist 242 of a photosensitive acrylate-based polymer (Stratasys, 243 RGD810). A second polymer (Stratasys, SUP705) is 244 printed to support the mixers during the printing pro- 245 cess. Subsequently, this support structure was removed 246 in a bath of 1 MNaOH solution. 247 3.3. Filtration Set-Up 248 All ﬁltration experiments (pure water permeability, 249 fouling, cleaning) were carried out using a Titan Osmo 250 Inspector (Convergence Industry B.V ., The Nether- 251 lands). A simpliﬁed ﬂow sheet of the system is shown 252 in Fig. 3. The pressures of feed, retentate, and permeate 253 can be measured. In the feed and permeate, two Cori- 254 olis mass ﬂow controllers measure and control the ﬂow 255 rates by controlling the diaphragm pump and the pres- 256 4 Membrane ModuleP-75 P PF F P-56P B01Feed Tank P-56 P-86Figure 3: Flow sheet of the experimental set-up. Permeate and reten- tate were collected in the feed tank and fully recycled. sure retention valve in the retentate line, respectively. 257 The system allows for constant ﬂux ﬁltration monitor- 258 ing a feed-side pressure increase as indicator for con- 259 centration polarization and fouling. 260 3.4. Computational Fluid Dynamics 261 For the design of shortened mixers that exhibit a sim- 262 ilar ﬂow pattern and fouling mitigation at reduced pres- 263 sure loss, detailed knowledge of the hydrodynamics in- 264 side the membrane is needed. The developing ﬂow pat- 265 tern, resulting shear rates and the pressure loss were 266 therefore evaluated using the CFD software COMSOL 267 Multiphysics. 268 For simulation, the inner membrane diameter was as- 269 sumed to match the diameter of the twisted tapes 270 (5:5mm) to improve mesh construction and conver- 271 gence properties. Additionally, an inﬂow section of 272 10mmwas added for laminar ﬂow proﬁle development. 273 For modeling ﬂuid ﬂow along a membrane, it is reason- 274 able to neglect the transport through the membrane, as 275 the permeate ﬂux is small compared to feed ﬂow [40]. 276 Hence, it is widely acknowledged in the literature to 277 assume the membrane as impermeable for simulation 278 [41]. In the system used in this work, the ratio of per- 279 meate to feed ﬂow was 4 :7 % at maximum allowing for 280 the same assumption. Silica particles were neglected as 281 well since they do not inﬂuence the ﬂuid properties at 282 low concentrations, as was shown in rheology experi- 283 ments. 284 The Reynolds number is Re2060 for pure water prop- 285 erties at 30C, atmospheric pressure, a tube diameter 286 of 5:5mmand an inlet velocity of 0 :3m=s. Hence, a 287 stationary laminar ﬂow model with incompressible ﬂow 288 was applied. 289 For single phase incompressible laminar ﬂow, COM- 290 SOL solves the Navier-Stokes equations. These equa- 291 tions describe the conservation of momentum (Eq. 1) 292 and mass (Eq. 2). 293Table 1: Measured viscosity of deionized water and silica suspen- sions with the indicated concentrations at 30C. Given are the vis- cosity values averaged for shear rates from 10 s1to 100 s1. The standard error SE of triplicate measurements is stated in addition. DI silica concentration water 0:12g=L0:24g=L0:60g=L [mPas] 0:761 0:772 0:836 0:838 SE [mPas] 0:017 0:024 0:057 0:082  ~v t+~vr~v! =rp+r~v+~F (1) r~v=0 (2) Hereis the density, ~vthe velocity, pthe pressure, 294 the dynamic viscosity and ~Fis the sum of external 295 forces applied to the ﬂuid. The ﬁnite element method 296 with linear shape functions was used in COMSOL for 297 discretization. 298 The meshing was successively reﬁned by increasing the 299 degrees of freedom until a stable result was obtained. 300 The pressure drop along the module was used as a con- 301 trol parameter. A number of mesh elements above 3 105302 was found to be su cient, see supplementary material. 303 3.5. Viscosity Measurements 304 The viscosity of the silica suspensions was measured 305 in a double gap system at 30Cusing a Discovery Hy- 306 brid Rheometer HR3 (TA Instruments, USA). 12 mL 307 sample of each solution was measured at shear rates 308 ranging from 1 s1to 4000 s1. The viscosity of DI 309 water was measured in comparison. 310 The viscosity was found to be constant in a wide 311 range of shear rates, and similar to water for all sus- 312 pensions. Hence, an average value for the viscosity of 313 each ﬂuid was calculated from the measured values at 314 shear rates from 10 s1to 100 s1. The mean viscosi- 315 ties are given in Tab. 1 and used to calculate the ﬁltration 316 resistance (Eq. 3). 317 3.6. Fouling Experiments 318 Colloidal silica (Ludox HS40) was used as a model 319 foulant. The fouling was assessed using the improved 320 ﬂux step method by van der Marel et al. [42]. In this 321 method, the ﬂux is increased stepwise to a maximum 322 ﬂux and decreased to the initial ﬂux. In between the 323 high ﬂux steps, a ﬂux relaxation step is applied. Thus, 324 the reversibility of fouling by ﬂux relaxation can be 325 assessed. During the experiments, the transmembrane 326 pressure (TMP) is measured, and the feed ﬂow rate kept 327 5 constant at 30 L=h. The high ﬂux levels were applied for 328 10minand the ﬂux relaxation steps for 5 min. For the 329 highest silica concentrations of 0 :24g=Land 0:60g=L, 330 transmembrane pressures of up to 20 barwere reached. 331 High ﬂux steps were aborted as soon as a TMP of 17 bar 332 was reached to keep the stability limits of set-up and 333 tubing. An exemplary fouling experiment for a sys- 334 tem without a static mixer and one with a static mixer 335 (twisted tape with 150 mmlength) is shown in Fig. 4. 336 The inﬂuence of the static mixer is already clearly vis- 337 ible as the TMP levels remain constant over almost all 338 ﬂux levels as compared to the TMP increase for the ex- 339 periments without static mixer. 340 The total ﬁltration resistance Rwas calculated ac- 341 cording to Eq. 3. Here, the transmembrane pressure 342 TMP is divided by the viscosity and the permeate 343 ﬂux J. The measured viscosity averaged in the range 344 of 10 s1to 100 s1, was used in the calculations. For 345 the silica suspension with a concentration of 0 :03g=L, 346 the measured viscosity of pure water was applied. 347 R=T MP J(3) Furthermore, the energy dissipated during the ﬁltra- 348 tion process was considered. The dissipated energy 349 Edissconsists of two parts; the energy dissipated due 350 to cross-ﬂow and the energy dissipated due to ﬁltration. 351 Eq. 5 shows the resulting calculation as given by Fane 352 and Chang [43]. The energy dissipated due to cross- 353 ﬂow was calculated by multiplying the pressure drop 354 along the membrane with the feed ﬂow rate (ﬁrst term 355 in Eq. 5). Theoretically, an average ﬂow rate at the 356 feed side should be used instead of the feed ﬂow rate. 357 As, however, the stage-cut in the experiments never ex- 358 ceeded 4:7 %, this di erence was neglected and the feed 359 ﬂow rate used. Additionally, the hydraulic energy dis- 360 sipated by ﬁltration was considered as the second con- 361 tribution to the total dissipated energy. The energy dis- 362 sipated by ﬁltration was obtained by multiplying TMP 363 with permeate ﬂow rate (second term of Eq. 5). 364 Ediss= pQF+T MPQP (4) =(pFpR)QF+pF+pR 2QP (5) Qdenotes the volumetric ﬂow rate, TMP the trans- 365 membrane pressure and pthe pressure. The subscript F 366 refers to feed, Rto retentate and Pto permeate. 367 The dissipated hydraulic energy describes the energy 368 which is lost as it is converted into friction losses, mix- 369 ing and heat. Hence, it can also be considered as the 370energy that reduces fouling. Static mixers obstruct the 371 ﬂow, induce eddies and vortices. Therefore, they in- 372 crease the pressure drop along the membrane. As this 373 pressure drop substantially contributes to the hydraulic 374 dissipated energy, the additional energy required due to 375 the insertion of static mixers is already included in Ediss. 376 By relating the dissipated energy to the obtained 377 amount of permeate, the speciﬁc dissipated energy Esp378 inkWh perm3permeate was received (Eq. 6). Edissis 379 divided by the permeate ﬂow rate QPor by ﬂux Jtimes 380 ﬁltration area A. 381 Esp=Ediss QP=pQF JA+T MP (6) TMP, ﬁltration resistance and speciﬁc dissipated en- 382 ergy during the ﬂux step experiments were analyzed to 383 compare the fouling mitigation capabilities of the dif- 384 ferent mixers. All experiments were carried out in trip- 385 licates, and the standard error is indicated as error bars. 386 4. Results and Discussion 387 4.1. Computational Fluid Dynamic Simulations 388 CFD simulations were conducted for seven di er- 389 ent mixers, the empty tube and a tube with a centered 390 smooth rod. The generated data was an indication for 391 the selection of ﬁve static mixers for experiments. Here, 392 the parameters for ﬁltration performance analyzed are 393 conservation of ﬂow pattern, shear rate enhancement 394 and pressure loss. 395 Twisted tape static mixers enforce a helical ﬂow pat- 396 tern in a tubular membrane lumen. This ﬂow pattern 397 already proved e ective for fouling reduction [5, 14]. 398 Therefore, the development and preservation of this pat- 399 tern is a key aspect when estimating the e ectiveness of 400 di erent twisted tape conﬁgurations. The magnitude of 401 the velocity perpendicular to the membrane axis acts as 402 a quantitative measure for the preservation of the heli- 403 cal ﬂow pattern. Fig. 5a shows the ﬂow pattern for three 404 representative twisted tapes, a full-length tape, a shorter 405 150mmtape and a spaced tape with 25 mmtape and 406 50mmconnector. 407 The ﬂow pattern and rotational velocity in a tube with 408 inserted 250 mmtwisted tape were used as a reference in 409 the analysis. If a twisted tape does not cover the whole 410 tube, the helical ﬂow pattern exponentially decreases 411 behind the twisted tape parts. For example, behind a 412 150mmtwisted tape it is still su ciently strong for a 413 distance of around 50 mm. The transition to laminar 414 tubular ﬂow is after a distance of about 100 mm. There 415 is a direct correlation between ﬂow pattern and velocity 416 6 Figure 4: Flux step method. In a), a fouling experiment for the conventional ﬁltration system without a static mixer is displayed (silica concentration: 0:03g=L). In b), the same ﬂux steps are applied for a system with a static mixer. Exemplary, an experiment is shown where a twisted tape with a length of 150 mmwas applied, and 0 :03g=Lsilica were used. perpendicular to the membrane surface. The decrease 417 of the velocity perpendicular to the surface velocity be- 418 hind a 25 mmtwisted tape and a 150 mmtwisted tape 419 is compared in Fig. 6. The ﬂow pattern develops in the 420 same way for both mixers. The distance until the veloc- 421 ity declines to 30 % of its maximum value is used for 422 the development of a spaced static mixer. Based on this 423 result, a combination of 25 mmtwisted tape parts con- 424 nected by 50 mmsmooth rods with 2 mmdiameter is 425 chosen. With this design, the ﬂow pattern is preserved 426 over the whole membrane length, see Fig. 5a. 427 The average wall shear rate is a major quantity for 428 evaluating the anti-fouling potential of a static mixer 429 [43]. It represents forces that lift particles o the 430 membrane surface. A comparison of the simulated 431 average shear rates potentially deduces the mixers 432 e ectiveness. Fig. 5b shows the average wall shear rate 433 for a full length twisted tape, a shorter 150 mmtape and 434 a spaced tape with 25 mmtape and 50 mmconnector. 435 The minimum value corresponds to the shear rate of 436 719 s1at the wall of an empty membrane lumen. 437 The average shear rate is 2543 s1when inserting a 438 full-length twisted tape. For the rest of the twisted 439 tapes, only the shear rate at membrane wall sections 440 without tape is considered. Behind a 150 mm tape, 441 the averaged shear rate decreases to 1190 s1. The 442 spaced approach exhibits higher shear rates between 443 twisted tape parts. In this case, the average shear rate 444 is 1683 s1. The sections behind twisted tapes show 445the preservation of the helical ﬂow pattern similar to 446 Fig. 5a. 447 448 Five twisted tapes were selected for further exper- 449 iments based on the previous results. The shortened 450 200 mmmixer is promising, because the helical ﬂow 451 pattern and, thus, the wall shear rate is maintained 452 until the end of the membrane. However, increased 453 shear rates over the whole module can also be seen in 454 the simulation of the 150 mmtwisted tape. The tape 455 and rod combination all introduce high shear rates at 456 decreased pressure losses. The 25 /50 combination is 457 chosen, because it has the lowest pressure loss, and the 458 25/25 combination generates the highest average wall 459 shear rates. The full length 250 mmmixer is used as a 460 reference. 461 462 4.2. Pressure Drop 463 Pressure drop is an important quantity for ﬁltration 464 performance since it correlates directly with the dissi- 465 pated hydraulic energy. The application of twisted tapes 466 increases the axial pressure drop over the length of the 467 membrane. To determine the pressure drop of the static 468 mixers, the pressure loss of the empty tube was sub- 469 tracted from the total pressure loss of the systems with 470 a mixer (see Eq. 8). Inlet and outlet pressure were mea- 471 sured at the same positions as feed and retentate pres- 472 sure during ﬁltration. 473 7 (a) Flow pattern (b) Shear rate Figure 5: Simulated ﬂow pattern and shear rate for the full length tape (250 mm), the shorter tape with a length of 150 mmand the spaced tape with 25 mmtape and 50 mmconnector. The helical ﬂow and the shear are preserved for around 50 mmafter the mixers’ end. The last 100 mm of the tubular membrane are displayed. Darker colors represent lower rotational velocities or shear rates, lighter colors higher velocities and shear rates. pmixer= ptotal;mixerpempty (7) =(pinpout)total;mixer(pinpout)empty (8) The pressure loss over the length of the module was 474 used to validate the CFD simulations. To have similar 475 conditions for simulations and experiments, the pres- 476 sure loss for the di erent twisted tapes was measured 477 with pure water under no permeation (closed perme- 478 ate outlet). In Fig. 7, simulated and measured pressure 479 losses of di erent static mixers are compared. Assum- 480 ing ideal conditions in the CFD approaches lead to a 481 distinguishable di erence between simulation and ex- 482 periment. For example, the tubing before and behind 483 the module, the surface roughness of the membrane, and 484 the inﬂuence of the silica are not taken into account in 485 Figure 6: Maximum value of velocity component perpendicular to the ﬂow direction depending on the distance to the twisted tape element. Overlapping simulation results for a 150 mmtwisted tape and a 25 mm long twisted tape. /s50/s53/s48 /s50/s48/s48 /s49/s53/s48 /s50/s53/s47/s50/s53 /s50/s53/s47/s53/s48/s53/s48/s48/s49/s48/s48/s48/s49/s53/s48/s48/s80/s114/s101/s115/s115/s117/s114/s101/s32/s76/s111/s115/s115/s32/s91/s80/s97/s93 /s83/s116/s97/s116/s105/s99/s32/s77/s105/s120/s101/s114/s69/s120/s112/s101/s114/s105/s109/s101/s110/s116/s115 /s83/s105/s109/s117/s108/s97/s116/s105/s111/s110/s115 Figure 7: Pressure loss of the di erent static mixers as obtained numerically (CFD simulation, open symbols) and experimentally (closed symbols). The numbers on the x-axis denote the length of the twisted tapes, and for the spaced twisted tapes, the numbers indicate the length of the twisted elements /length of free space. The pressure loss was measured with pure water and without permeation in the ex- periments. Error bars are standard error of triplicate measurements. 8 the CFD simulations. However, both the measured and 486 the simulated pressure drop data show the same trend 487 and are in agreement regarding the order of magnitude 488 (see Fig. 7). 489 As expected, the shorter the twisted tape, the smaller 490 is the additional pressure drop of the insert (see Fig. 7). 491 This trend is visible for both the measured and the 492 simulated pressure drop. Additionally, the 25 /25- 493 combination of spaced twisted tapes shows a higher 494 pressure loss than the 25 /50-combination, again both 495 for the experimental and simulation results. The di er- 496 ent pressure loss of the two spaced twisted tapes can be 497 explained by the di erence in ‘free’ space in between 498 the twisted elements, the di erent number of twisted 499 elements and the di erent total length of the combina- 500 tions. The 25 /25-combination consists of ﬁve twisted 501 tape elements (each 25 mmlong) and four ‘free space’ 502 elements in the form of a smooth rod (2 mmin diam- 503 eter, 25 mmlong). In contrast, the 25 /50-combination 504 has only three twisted tape elements (also each 25 mm 505 long) and two smooth rods (50 mmlong) keeping the 506 twisted elements apart. Hence, the 25 /50-combination 507 shows a smaller total length and less twisted elements 508 as well as a smaller total twisted length compared to the 509 25/25-combination. These di erences in shape explain 510 the lower pressure drop of the 25 /50-combination. 511 4.3. Filtration Resistance 512 Fouling experiments were performed with di erent 513 silica concentrations (0 :03g=Lto 0:60g=L) and sev- 514 eral twisted tapes as well as a standard ﬁltration system 515 without any fouling mitigation measure. In Fig. 8, the 516 total resistance is shown for the applied ﬂux steps. For 517 the lowest silica concentration of 0 :03g=L, the ﬁltra- 518 tion resistance of the membrane without static mixer 519 increased rapidly from the beginning. This increase 520 became even stronger for ﬂuxes exceeding 200 LMH . 521 At the highest analyzed ﬂux of 248 LMH , the ﬁltra- 522 tion resistance reached 5 :271012m1which is almost 523 ﬁve times the intrinsic membrane resistance. If a static 524 mixer is applied during ﬁltration, the resistance is sub- 525 stantially lower and reached less than 2 1012m1for the 526 highest investigated ﬂux of around 320 LMH . Hence, 527 fouling was signiﬁcantly reduced compared to the sys- 528 tem without a mixer. From Fig. 8a, it can be con- 529 cluded that the di erences within the full-length, short 530 and spaced twisted tapes which have been investigated, 531 are negligible for a silica concentration of 0 :03g=L. 532 The silica concentration was step-wise increased to 533 further investigate the di erences in fouling mitigation 534 capabilities of the di erent twisted tapes. When using 535 a four times higher concentration of 0 :12g=Lsilica, the 536resistance of the full-length twisted tape was the lowest 537 of the analyzed twisted tapes for all ﬂuxes. The di er- 538 ence between full-length tape and twisted tape modiﬁ- 539 cations became signiﬁcant at ﬂuxes above 235 LMH as 540 Fig. 8b shows. For the highest ﬂux of 328 LMH , the 541 resistance of the 150 mmlong twisted tape was lower 542 than the resistance of the system with spaced twisted 543 tape. This result indicates that the short twisted tape in- 544 duces a higher wall shear rate and a ﬂow pattern which 545 is better suited to mitigate fouling. The three 25 mm 546 long elements of the spaced twisted tape led to a lower 547 increase in wall shear rate. Therefore, the increase in 548 silica concentration from 0 :03g=Lto 0:12g=Lalready 549 led to distinct di erences in the fouling mitigation of the 550 di erent twisted tapes. 551 The same trend continued for higher silica concen- 552 trations. At 0 :24g=L, the ﬁltration resistance of the sys- 553 tem with inserted 250 mmtwisted tape signiﬁcantly in- 554 creased to 16 :1310121=mat 326 LMH , see Fig. 8c. 555 Under these conditions, the 150 mmand spaced twisted 556 tape mitigated fouling to the same extent, reaching a ﬁl- 557 tration resistance of about 19 10121=m. The di erence 558 in performance seen at 0 :12g=Lsilica concentration did 559 not get larger with increasing concentration. 560 At the highest silica concentration of 0 :60g=L, foul- 561 ing became even more severe in all systems, see Fig. 8. 562 The ﬁltration resistance at low ﬂuxes is comparable for 563 all twisted tapes and also comparable to the experiments 564 with lower silica concentration. As soon as ﬂuxes over 565 200 LMH were applied, the ﬁltration resistance rose 566 exponentially for all investigated systems, see Fig. 8d. 567 For the short and the spaced twisted tape, ﬂux steps 568 above 236 LMH had to be aborted due to the over- 569 shooting TMP, rapidly reaching more than 17 bar. For 570 the system with full-length twisted tape, it was possible 571 to apply a higher ﬂux of 281 LMH . However, Fig. 8d 572 clearly shows that the resistance was with 21 1012m1573 extremely high. Di erent from the lower silica con- 574 centrations, the system with full-length twisted tape 575 showed an exponential increase in ﬁltration resistance 576 at 0:60g=Lsilica. Still, inserting a full-length twisted 577 tape can increase the range of operating conditions up 578 to 242 LMH in the tested system. 579 All in all, the full-length twisted tape reduced foul- 580 ing to the greatest extent for all investigated ﬂuxes and 581 silica concentrations. The short twisted tape with a 582 length of 150 mmand the spaced twisted tape (combi- 583 nation 25 /50) showed similar behavior but led to higher 584 ﬁltration resistances than the full-length twisted tape. 585 At the lowest silica concentration of 0 :03g=L, how- 586 ever, the modiﬁed twisted tape reduced fouling as well 587 as the full-length twisted tape. Therefore, it could be 588 9 /s49/s48/s48 /s49/s53/s48 /s50/s48/s48 /s50/s53/s48 /s51/s48/s48 /s51/s53/s48/s49/s50/s51/s52/s53/s54/s82/s101/s115/s105/s115/s116/s97/s110/s99/s101/s32/s91/s49/s48/s49/s50 /s47/s109/s93 /s70/s108/s117/s120/s32/s91/s76/s77/s72/s93/s110/s111/s32/s109/s105/s120/s101/s114 /s119/s105/s116/s104/s32/s109/s105/s120/s101/s114(a) 0:03g=Lsilica /s49/s48/s48 /s49/s53/s48 /s50/s48/s48 /s50/s53/s48 /s51/s48/s48 /s51/s53/s48/s48/s50/s52/s54/s56 /s50/s53/s48/s82/s101/s115/s105/s115/s116/s97/s110/s99/s101/s32/s91/s49/s48/s49/s50 /s47/s109/s93 /s70/s108/s117/s120/s32/s91/s76/s77/s72/s93/s50/s53/s47/s53/s48 /s49/s53/s48 (b) 0:12g=Lsilica /s49/s48/s48 /s49/s53/s48 /s50/s48/s48 /s50/s53/s48 /s51/s48/s48 /s51/s53/s48/s48/s53/s49/s48/s49/s53/s50/s48/s50/s53/s82/s101/s115/s105/s115/s116/s97/s110/s99/s101/s32/s91/s49/s48/s49/s50 /s47/s109/s93 /s70/s108/s117/s120/s32/s91/s76/s77/s72/s93/s50/s53/s47/s53/s48 /s49/s53/s48 /s50/s53/s48 (c) 0:24g=Lsilica /s49/s48/s48 /s49/s53/s48 /s50/s48/s48 /s50/s53/s48 /s51/s48/s48 /s51/s53/s48/s48/s53/s49/s48/s49/s53/s50/s48/s50/s53/s82/s101/s115/s105/s115/s116/s97/s110/s99/s101/s32/s91/s49/s48/s49/s50 /s47/s109/s93 /s70/s108/s117/s120/s32/s91/s76/s77/s72/s93/s50/s53/s47/s53/s48 /s49/s53/s48/s50/s53/s48 (d) 0:60g=Lsilica Figure 8: Filtration resistance vs ﬂux for all systems with mixer and four di erent silica concentrations. Error bars are standard error of triplicate measurements. Note the di erent y-scales. 10 proven that shortening the twisted tape and using spaced 589 twisted tapes can be su cient in terms of fouling reduc- 590 tion. Additionally, it was shown that it depends on the 591 ﬁltration conditions if the shear rate enhancement and 592 swirl ﬂow induced by the modiﬁed twisted tapes su ce 593 or not to keep the ﬁltration resistance at a viable level. 594 To further assess the process e ciency of static inserts, 595 their inﬂuence on energy demand for ﬁltration needs to 596 be quantiﬁed. 597 4.4. Speciﬁc Dissipated Energy 598 To analyze the energy e ciency of the twisted tape 599 inserts, the speciﬁc dissipated energy was determined. 600 It relates the energy dissipated by pumping and ﬁltra- 601 tion to the obtained amount of permeate, see Eq. 5 and 602 Eq. 6. Figs. 9 and 10 show the speciﬁc energy vs. ﬂux 603 for all experiments. When considering the lowest silica 604 concentration of 0 :03g=L, the empty membrane with no 605 turbulence promoter showed the lowest speciﬁc energy 606 consumption at a ﬂux of 185 LMH , Fig. 9. However, the 607 speciﬁc energy increases exponentially with increasing 608 ﬂux. As fouling increases with rising ﬂux, the ﬁltra- 609 tion resistance increases as well and the TMP has to be 610 raised to maintain the desired ﬂux. Therefore also the 611 speciﬁc dissipated energy increases. 612 Fig. 9 shows that all energy curves posses a mini- 613 mum. The minima result from competing e ects con- 614 tributing to the speciﬁc energy. On the one hand, the 615 pressure drop along the membrane decreases slightly 616 with increasing ﬂux since the average crossﬂow veloc- 617 ity is reduced by the higher stage-cut. Additionally, the 618 pressure drop is divided by the permeate ﬂow rate to 619 obtain the speciﬁc dissipated energy due to crossﬂow. 620 Hence, the speciﬁc dissipated energy for pumping de- 621 creases at higher ﬂuxes. This e ect is even more promi- 622 nent if a twisted tape is inserted, because of a higher 623 pressure loss. 624 On the other hand, the speciﬁc energy consumption in- 625 creases with higer transmembrane pressure needed to 626 obtain higher ﬂuxes. This inﬂuence gets more promi- 627 nent with rising ﬂux. 628 Altogether, these e ects lead to a minimum in energy 629 consumption for all systems with twisted tapes. The 630 minimum is not as visible for the system without twisted 631 tape since the necessary low ﬂuxes were not measured 632 in this study. However, Fig. 9 clearly shows that up to 633 a ﬂux of around 235 LMH , the ﬁltration in the systems 634 with a mixer is dominated by pressure drop, whereas, 635 for higher ﬂuxes, the e ect of TMP is dominating. In 636 conclusion, the application of static mixers is particu- 637 larly interesting in the TMP-dominated region. Addi- 638 tionally, the insertion of twisted tapes shifts the opti- 639mum operating conditions, deﬁned as the minimum spe- 640 ciﬁc energy consumption, to higher ﬂuxes. The higher 641 speciﬁc dissipated energy of the system with a 25 /25- 642 spaced twisted tape in comparison to the full-length 643 tape, in Fig. 9b, indicates that the introduced wall shear 644 rate is too low for e cient fouling prevention. 645 Experiments with higher silica concentration were 646 only possible by use of twisted tapes due to severe foul- 647 ing. Fig. 10 shows the speciﬁc energy consumption for 648 0:12g=L, 0:24g=Land 0:60g=Lsilica concentration. 649 At 0:12g=L, see Fig. 10a, the full-length twisted tape 650 introduces the highest speciﬁc energy consumption in 651 the pressure drop dominated regime. When reaching 652 the TMP-dominated regime, the modiﬁed twisted tapes 653 exhibit a faster increase in speciﬁc energy consump- 654 tion breaking even with the full-length tape at a ﬂux of 655 280 LMH . Hence, it depends on the ﬂux region and 656 the extent of fouling if the application of a full-length 657 twisted tape or a short or spaced twisted tape is more 658 energy-e cient. 659 For 0:24g=Land 0:60g=Lsilica, all types of ana- 660 lyzed twisted tapes start with the same speciﬁc energy 661 consumption for the lowest ﬂux step as Fig. 10b and 662 Fig. 10c show. The speciﬁc energy consumption of the 663 full-length twisted tape always stays equal or below the 664 modiﬁed versions. For 0 :60g=Lsilica, high ﬂux exper- 665 iments needed to be skipped due to overshooting TMP. 666 Only the full-length twisted tape allowed for a higher 667 ﬂux. These experiments reinforce the assumption of a 668 TMP-dominated regime where better fouling mitigation 669 results in lower speciﬁc energy consumption. The op- 670 timum operating condition also shifts to higher ﬂuxes 671 depending on the fouling potential. 672 5. Conclusion 673 The present study investigated the e ect of short and 674 spaced twisted tapes on fouling mitigation in tubular ce- 675 ramic membranes. CFD simulations of the ﬂow ﬁeld, 676 shear rate and pressure drop for di erent short and 677 spaced twisted tapes were performed to reduce the ex- 678 perimental e ort and gain additional data. The length of 679 the short tapes, as well as the length of the twisted parts 680 and the free space in case of the spaced twisted tapes, 681 were varied. Comparing the simulated with experimen- 682 tally measured pressure drop along the ﬂow channel, the 683 simulation model could be successfully validated. In 684 the simulations, the short tape with a length of 150 mm 685 (instead of 250 mm) and the spaced twisted tapes with 686 25mmtwisted tape and 25 mmor 50 mmfree space gave 687 similar ﬂow pattern and shear rates as the full-length 688 twisted tape. Therefore, these modiﬁcations of twisted 689 11 /s49/s48/s48 /s49/s53/s48 /s50/s48/s48 /s50/s53/s48 /s51/s48/s48 /s51/s53/s48/s48/s46/s48/s48/s48/s46/s48/s53/s48/s46/s49/s48/s48/s46/s49/s53 /s49/s53/s48/s50/s48/s48/s101/s109/s112/s116/s121/s69 /s115/s112/s32/s91/s107/s87/s104/s47/s109/s179/s93 /s70/s108/s117/s120/s32/s91/s76/s77/s72/s93/s50/s53/s48(a) short twisted tapes /s49/s48/s48 /s49/s53/s48 /s50/s48/s48 /s50/s53/s48 /s51/s48/s48 /s51/s53/s48/s48/s46/s48/s48/s48/s46/s48/s53/s48/s46/s49/s48/s48/s46/s49/s53 /s50/s53/s48/s50/s53/s47/s53/s48/s69 /s115/s112/s32/s91/s107/s87/s104/s47/s109/s179/s93 /s70/s108/s117/s120/s32/s91/s76/s77/s72/s93/s101/s109/s112/s116/s121 /s50/s53/s47/s50/s53 (b) spaced twisted tapes Figure 9: Speciﬁc dissipated energy vs ﬂux for the system without mixer and all systems with mixer at a silica concentration of 0 :03g=L. The speciﬁc energy of the system without tape and the one with full-length twisted tape are shown for comparison. Error bars display standard error of triplicate measurements. tapes were fabricated via 3D printing and intensively in- 690 vestigated in fouling experiments. Four concentrations 691 of colloidal silica suspensions were used. At the low- 692 est investigated concentration of 0 :03g=L, all modiﬁed 693 twisted tapes mitigate fouling as well as the full-length 694 twisted tape. As the pressure drop induced by the mod- 695 iﬁed tapes turned out to be considerably lower than that 696 of the full-length tape, the speciﬁc dissipated energy of 697 all modiﬁed tapes was reduced in the low ﬂux range in 698 comparison to the full-length twisted tape. Compared 699 to the membrane without turbulence promoter, the sys- 700 tems with mixers showed a decreased speciﬁc energy 701 consumption for ﬂuxes above 200 LMH . 702 At higher silica concentrations, the full-length 703 twisted tape led to markedly reduced ﬁltration resis- 704 tances in comparison to the modiﬁed twisted tapes. 705 The di erence was more pronounced the higher the ap- 706 plied ﬂux and the higher the silica concentration. In 707 terms of speciﬁc dissipated energy, however, the mod- 708 iﬁed twisted tapes proﬁt from lower pressure losses. 709 Thus, the modiﬁed tapes have a lower energy consump- 710 tion in the pressure drop-dominated regime. The full- 711 length twisted tape develops an advantage with increas- 712 ing fouling potential. In the TMP-dominated regime, 713 high wall shear rates over the whole membrane length 714 are most e ective. 715 In conclusion the application of twisted tapes is not 716 only possible and proven in heat transfer, but is also suit- 717 able for enhanced mass transfer and improved fouling 718 prevention in membrane processes. A pressure drop- 719and a TMP-dominated regime were also deﬁned with a 720 recommendation of e ective twisted tape designs. Re- 721 ducing the membrane area covered by the twisted tape 722 by using modiﬁed twisted tapes proved to have a posi- 723 tive e ect on speciﬁc dissipated energy in the pressure 724 drop-dominated regime. In the TMP-dominated regime, 725 a full-length twisted tape performed best because of its 726 stronger fouling reduction. Therefore, the aim of reduc- 727 ing the pressure drop of turbulence promoters without 728 losing performance was reached with restriction to the 729 pressure drop-dominated regime. 730 Acknowledgement 731 The authors acknowledge ﬁnancial support from the 732 ERA-NET Susfood-CEREAL project, No. 031A431B, 733 by the German Federal Ministry of Education and Re- 734 search. This project has also received funding from the 735 European Research Council (ERC) under the European 736 Unions Horizon 2020 research and innovation program 737 (grant agreement no. 694946). 738