Short and Spaced Twisted Tapes to Mitigate Fouling in Tubular Membranes

Static mixers are an e ﬃ 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 ﬀ 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 ﬃ 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 ﬀ ect experimentally investigated using silica suspensions. Additionally, the e ﬀ ect of foulant concentration in this system is analyzed. For low silica concentrations (0 . 03 g / L ) the short and spaced twisted tapes mitigate fouling as e ﬃ 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 ﬃ cient up to a certain fouling exposure.


Introduction
Ultrafiltration processes are often affected by membrane fouling.Fouling can be caused by several phenomena, such as foulants adsorbed at the membrane surface or in the membrane pores, foulants forming a gel layer at the membrane surface, particles constricting or blocking the pores, and microorganisms forming a biofilm.Various countermeasures aiming at fouling reduction are applied in industry, and many more have been investigated in research.Mostly, these fouling countermeasures influence the hydrodynamics inside the membrane module, trying to impose fluid instabilities [1] resulting in chaotic and turbulent-like flow tration, static inserts are applied as all these phenomena Similarly, not only the surface of the inserts can 75 be perforated, but also the edges of the twisted tape 76 can be corrugated, notched or serrated [9,25,26,15].
Hence, it is widely acknowledged in the literature to assume the membrane as impermeable for simulation [46].In the system used in this work, the ratio of permeate to feed flow was 4.7 % at maximum allowing for the same assumption.The axial pressure gradient also influences the filtration as the TMP changes along the membrane due to the decreasing feed-side pressure.In our case, the pressure drop along the membrane was less than 15 mbar (both the numerically obtained and the experimentally measured value) which is much smaller than the applied transmembrane pressures.Silica particles were neglected as well since they do not influence Here ρ is the density, v the velocity, p the pressure, 315 η the dynamic viscosity and F is the sum of external 316 forces applied to the fluid.The finite element method 317 with linear shape functions was used in COMSOL for 318 discretization.

319
The meshing was successively refined by increasing the 320 degrees of freedom until a stable result was obtained.

321
The pressure drop along the module was used as a con-322 trol parameter.A number of mesh elements above 3•10 5 323 was found to be sufficient.The viscosity of the silica suspensions was measured 326 in a double gap system at 30 to cross-flow and the energy dissipated due to filtration.

372
Eq. 5 shows the resulting calculation as given by Fane

373
and Chang [48].The energy dissipated due to cross- with permeate flow rate (second term of Eq. 5). 385 Q denotes the volumetric flow rate, TMP the trans- 402

80Figure 1 :Figure 2 :Figure 3 :
Figure1: 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.
the fluid properties at low concentrations, as was shown in rheology experiments.The Reynolds number is Re ≈ 2060 for pure water properties at 30 • C, atmospheric pressure, a tube diameter of 5.5 mm and an inlet velocity of 0.3 m/s.Hence, a stationary laminar flow model with incompressible flow was applied.310 For single phase incompressible laminar flow, COM-311 SOL solves the Navier-Stokes equations.These equa-312 tions describe the conservation of momentum (Eq. 1) 313 and mass (Eq.2). 314

374
flow was calculated by multiplying the pressure drop 375 along the membrane with the feed flow rate (first term 376 in Eq. 5).Theoretically, an average flow rate at the 377 feed side should be used instead of the feed flow rate.378 As, however, the stage-cut in the experiments never ex-379 ceeded 4.7 %, this difference was neglected and the feed 380 flow rate used.Additionally, the hydraulic energy dis-381 sipated by filtration was considered as the second con-382 tribution to the total dissipated energy.The energy dis-383 sipated by filtration was obtained by multiplying TMP 384 386membrane pressure and p the pressure.The subscript F 387 refers to feed, R to retentate and P to permeate.388Thedissipated hydraulic energy describes the energy 389 which is lost as it is converted into friction losses, mix-390 ing and heat.Hence, it can also be considered as the 391 energy that reduces fouling.Static mixers obstruct the 392 flow, induce eddies and vortices.Therefore, they in-393 crease the pressure drop along the membrane.As this 394 pressure drop substantially contributes to the hydraulic 395 dissipated energy, the additional energy required due to 396 the insertion of static mixers is already included in E diss .397 By relating the dissipated energy to the obtained 398 amount of permeate, the specific dissipated energy E sp 399 in kWh per m 3 permeate was received (Eq.6).E diss is 400 divided by the permeate flow rate Q P or by flux J times 401 filtration area A.

TMP, filtration resistance
and specific dissipated en-403 ergy during the flux step experiments were analyzed to 404 compare the fouling mitigation capabilities of the dif-405 ferent mixers.All experiments were carried out in trip-406 licates, and the standard error is indicated as error bars.

1 .Figure 4 :Fig. 5a. 468 469Figure 5 :
Figure4: Flux step method.In a), a fouling experiment for the conventional filtration system without a static mixer is displayed (silica concentration: 0.03 g/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 mm was applied, and 0.03 g/L silica were used.

Figure 6 :Figure 7 :Figure 8 :Figure 9 :
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 mm twisted tape and a 25 mm long twisted tape.

Fig. 10c
Fig.10cshow.The specific energy consumption of the 686

696Figure 10 :
Figure 10: Specific dissipated energy vs flux for the systems with mixer and three different silica concentrations.Error bars display standard error of triplicate measurements. 925

Table 1 :
Measured viscosity η of deionized water and silica suspensions with the indicated concentrations at 30 • C. Given are the viscosity values averaged for shear rates from 10 s −1 to 100 s −1 .The standard error SE of triplicate measurements is stated in addition.
• C using a Discovery Hy-333 pensions.Hence, an average value for the viscosity of 334 each fluid was calculated from the measured values at 335 370 E diss consists of two parts; the energy dissipated due 371