Membrane distillation (MD) is a thermally driven process that removes volatile compounds from a heated solution due to a difference in vapor pressure across a porous, typically hydrophobic membrane1. MD is a versatile separation technique that can be integrated with waste heat and/or solar power for renewable desalination at moderate temperatures2. Applications of MD include desalination, treatment of pharmaceuticals, resource recovery from desalination brine3, separation in dairy and food industries. As compared to the more established reverse osmosis process for desalination, MD is capable of handling high salinity feeds while retaining benefits of membrane-based processes, such as modularity, ease of operation and compactness. Typically, MD relies on external heating of the bulk feed solution, which is energy-intensive and prone to heat losses outside the module. Heating the bulk feed solution accounts for the largest energy contribution in MD systems. Additionally, the occurrence of temperature polarization due to the temperature difference across the membrane surface being lower than the bulk temperature difference results in reduced driving force and lower vapor flux.

To address these challenges, researchers have adopted techniques for localized heating near the membrane-feed interface, where vaporization takes place4,5. Most studies assume a membrane-based approach in which the membrane is fabricated or modified to allow for alternative direct heating techniques of its surface through Joule heating6,7,8, photothermal heating9,10,11,12, microwave heating13,14,15 and induction heating16,17. The advantages, limitations and recent developments of each of these techniques are discussed elsewhere5. Joule heating, also known as electrothermal heating, is a simple form of direct heating in which a current passing through a conducting material leads to an increase in temperature due to its electrical resistance. For localized heating using the Joule effect, a few studies demonstrate the use of metallic membranes such as stainless-steel hollow fiber membranes. While metallic membranes have high mechanical, chemical and thermal stability, low permeate flux and liquid entry pressure make them unattractive substitutes for polymer membranes in most membrane separation applications18. Furthermore, tuning membrane hydrophobicity can be challenging with metallic membranes18 as metal surfaces are usually hydrophilic due to their high surface energy19,20,21. One expanding area of research in membrane separation processes is the use of functional spacers. While feed channel spacers are commonly used as turbulence promoters to improve mass and heat transfer22,23, the use of functional spacers goes beyond and can be aimed at achieving fouling control, anti-scaling and/or localized heating by focusing on channel spacer design and modification rather than the membrane itself, hence improving performance characteristics without influencing membrane properties and separation characteristics. To date, studies demonstrating localized heating of the feed spacer have been limited to photothermal heating24,25 and induction heating26,27. Joule heating has not yet been introduced to feed channel spacers in MD systems.

In this work, we modify Ni-Cr based metallic net-type spacers via electrolytic coating of MgO and study their stability in seawater. We optimize spacer geometry and coating parameters and then apply these spacers to electrothermal surface heating to assist in direct contact membrane (DCMD) distillation with low-temperature bulk feed heating (Fig. 1). We study the effect of passing a current through the spacer in situ on permeate flux and energy consumption, and compare MD performance for continuous and periodic application of electric current.

Fig. 1
figure 1

Schematic of spacer-based approach for localized Joule heating in MD described in this study.

Results and discussion

Ceramic coatings on Ni-Cr spacers: mechanism and surface characterization

Ceramic coatings are commonly used as thermal barriers and as natural corrosion protection on metal surfaces. MgO in particular provides the combination of electrical insulation with high thermal conductivity28,29, which is desirable as a coating on heating elements exposed to saline water. We used electrolytic deposition followed by calcination to coat Ni-Cr spacers with MgO. Electrolytic deposition was carried out using 0.5 M Mg(NO3)2 in ethanol and water, according to a method developed by Hashaikeh and Szpunar30. When an adequately high potential field is applied across two electrodes in an aqueous solution of Mg(NO3)2, the dissociation of Mg(NO3)2 into ions (Mg2+ and NO3-) will initiate chemical reactions at the electrode-electrolyte interfaces. These reactions generate hydroxide ions through the following cathodic reactions30:

$$2{{\rm{H}}}_{2}{\rm{O}}+2{{\rm{e}}}^{-}\to {{\rm{H}}}_{2}+2{{\rm{OH}}}^{-}$$
$${{\rm{O}}}_{2}+2{{\rm{H}}}_{2}{\rm{O}}+{4{\rm{e}}}^{-}\to {4{\rm{OH}}}^{-}$$
$${{\rm{NO}}}_{{3}^{-}}+{{\rm{H}}}_{2}{\rm{O}}+{2{\rm{e}}}^{-}\to {{\rm{NO}}}_{{2}^{-}}+{2{\rm{OH}}}^{-}$$
$${{\rm{NO}}}_{{3}^{-}}+6{{\rm{H}}}_{2}{\rm{O}}+{8{\rm{e}}}^{-}\to {{\rm{NH}}}_{3}+{9{\rm{OH}}}^{-}$$

Generated hydroxide ions then hydrolyze Mg2+ ions in the electrolyte to form a cathodic deposit of Mg(OH)2 as: Mg2+(aq) + 2OH(aq) → Mg(OH)2(s). During heat treatment, dehydration of Mg(OH)2 causes the formation of MgO through both crystallization and sintering30. MgO is sensitive to moisture31, but their hydration reactivity is strongly dependent on the size of MgO grains and the temperature at which heat treatment is carried out32. MgO crystallite size increases with calcination temperature, and MgO formed at a higher calcination temperature (>1000 °C) has a very low dissolving rate resulting in retardation of hydration32, compared to a calcination temperature of 700 °C. Since feed channel spacers will be used in direct contact with aqueous systems, a higher calcination temperature 1100 °C was chosen for calcination and concurrent sintering of MgO on the Ni-Cr spacer.

Figure 2 shows the surface of uncoated and coated Ni-Cr spacers at different electrolytic processing times and magnifications, along with energy dispersive X-ray spectroscopy (EDS) images of uncoated and coated spacers. Crack formation is a well-known challenge in ceramic coatings that occurs due to shrinkage during drying33,34, although it may be overcome through appropriate selection of substrate geometry and coating thickness. Figure 2c, f show coated spacers when electrolytic processing was carried out for 20 min on wire diameter of 0.2 mm and 0.1 mm, respectively. In the same amount of time, the spacer with smaller wire diameter undergoes significant cracking, resulting in damaged and non-uniform coating. The coating formed is thicker when the wire diameter is smaller, which results in severe crack formation, as has also been noted by Kozuka et al.35. Optimization of the coating layer to minimize cracks is crucial in determining performance, as the stability of ceramic coatings in corrosive environments such as seawater is inversely proportional to the number of cracks across the coating36. Figure 2d–f, j–l shows the effect of electrolytic deposition time on the resulting morphology of MgO-coated Ni-Cr spacers of wire diameter 0.1 mm. For this wire diameter, a smooth, crack-free coating was obtained when electrolysis was carried out for 5 min. As electrolysis time was increased to 10 min, the thicker coating resulted in visible crack formation, as seen in Fig. 2k. Interestingly, as electrolysis time was further increased to 20 min, nanoparticlesof MgO can be observed however low magnification images confirm that the coating is not uniform. EDS spectra (Fig. 2 m, n) confirm presence of Mg and O after the two-step coating process is completed. Further characterization was carried out on the Ni-Cr spacer of diameter 0.1 mm with an electrolytic deposition time of 5 min.

Fig. 2: Morphological examination of uncoated and coated NiCr spacers.
figure 2

SEM images of Ni-Cr spacers; a wire diameter 0.2 mm, uncoated, b 0.1 mm wire diameter, uncoated; c 0.2 mm wire diameter coated with MgO, t = 20 min; df 0.1 mm wire diameter coated with MgO for 5 min, 10 min and 20 min respectively. gl higher magnification images of Ni-Cr spacers with g 0.2 mm wire diameter, uncoated, h 0.1 mm wire diameter, uncoated; i 0.2 mm wire diameter, coated for t = 20 min; jl 0.1 mm wire coated with electrolytic deposition time of 5 min, 10 min and 20 min respectively. m, n energy dispersive X-ray spectroscopy (EDS) images of uncoated and coated spacers, respectively.

Surface wettability of Ni-Cr and Ni-Cr-MgO spacers was characterized by static water contact angle tests on spacers with different wire diameters and coating times (Fig. 3). Typically, Nickel-based alloys are hydrophilic with water contact angles between 40 and 80 °C due to their low interfacial solid-liquid energy which enhances spreading37. However, the as-received Ni-Cr spacers had relatively higher contact angles and were not as readily wetted, due to exposure to air and possible contamination, as wettability of hydrophilic metal surfaces is inversely related to surface contamination38. Coating with MgO increased the wettability of Ni-Cr spacers as the water contact angle dropped to 16° after coating for 5 min. The enhanced hydrophilicity of MgO is attributed to the surface polarity of the Mg2+ ion/O2− ion which leads to high surface energy and explains the instrinsic hydrophiliciy of metal oxide surfaces39,40,41. However, we observed that upon increasing coating time, water contact angle increased again and the surface became less hydrophilic. This is in agreement with SEM images, that show an intact MgO coating at 5 min coating time, but with an increase in deposition time, the MgO coating becomes non-uniform and cracked, with visible areas of bare Ni-Cr, causing the water contact angle to rise again.

Fig. 3: Surface wettability characterization.
figure 3

Apparent water contact angle on the surface of MgO-coated Ni-Cr spacers with different wire diameters and coating times. Error bars represent the standard deviations.

Electrochemical characterization and stability in seawater

Electrochemical impedance spectrometry was employed to study interfacial processes and electrochemical stability of Ni-Cr and Ni-Cr-MgO upon exposure to 3.5% aqueous NaCl. Figure 4a–c shows Nyquist and Bode plots for Ni-Cr and Ni-Cr coated with MgO after immersion in 3.5% NaCl for 2 hours and for 3 days. The semi-circle shown in the Nyquist plots for Ni-Cr-3d, Ni-Cr-MgO-2h and Ni-Cr-MgO-3days is due to direct charge transport at the electrode-electrolyte interface42. At the highest frequency of 105 Hz, the real component of impedance is approximately the same (6.7 + 1.6 Ωcm2) for both uncoated and coated spacers immersed for 2 h and for 3 days, and corresponds to the electrolyte and cell internal resistance RS. The electrolyte and cell resistance RS corresponds to the left-most (high-frequency) value of real impedance in the Nyquist plots, and stays approximately constant (6.7 ± 1.6 Ωcm2).

Fig. 4: Electrochemical characterization.
figure 4

a Nyquist impedance spectra of Ni-Cr with and without MgO coating after varying immersion times of 2 h and 3 days; b, c Bode impedance spectra of Ni-Cr and Ni-Cr-MgO immersed in seawater for 2 h and 3 days. d Impedance values at 0.1 Hz for Ni-Cr and Ni-Cr-MgO with immersion time; e Equivalent circuit for Ni-Cr immersed in seawater; f Equivalent circuit of Ni-Cr coated with MgO immersed in seawater. Lines in ac show fitting of the equivalent circuit models to impedance spectra.

Real impedance (x-axis of the Nyquist plots) refers to the resistive components while the imaginary component of the impedance (y-axis) corresponds to capacitative elements. The Armstrong equivalent model43 has been used to fit EIS spectra (Fig. 4e) obtained for the Ni-Cr electrodes with an additional Warburg diffusion element for the coated spacers (Fig. 4f) to analyze impedance data. A non-linear least squares fitting was used to fit experimental data to the models and the fitting lines are in good agreement with experimental data, as shown in Fig. 4a–c, are in good agreement with experimental data. The equivalent circuit consists of solution resistance, constant phase elements (CPEs), resistance RP and a charge transfer resistance RCT. RP is associated with hydrogen adsorption on the electrode surface due to intrinsic activity of the electrode44. CPEs were used to model the system as opposed to ideal capacitors as interfaces do not behave as an ideal frequency-independent capacitors in real systems45,46. CPEDL is attributed to the double layer capacitance between the electrode and the electrolyte solution, while CPEP is a result of surface homogeneity. Typically, this CPE element is seen in equivalent circuits modeling coated materials, however its presence in the uncoated Ni-Cr spacer arises from current and potential distributions associated with electrode geometry47, as the electrode is a net-type mesh. In the coated spacer, CPEP represents both variations in electrode geometry and the coating capacitance due to MgO. In the coated spacers, an additional Warburg diffusion impedance element is found as the result of ion diffusion through micro-pores in the coating as conductive paths on the surface48. RCT, qualitatively assessed from the diameter of the semicircles in the Nyquist plot, decreases with immersion in NaCl for both the coated and uncoated spacers, however after 3 days of exposure to NaCl, the charge transfer resistance of the coated spacer is slightly higher than that of uncoated Ni-Cr, indicating better barrier characteristics. This is also confirmed through impedance values at low frequency, |Z | 0.1Hz, as shown in Fig. 4d. This value, obtained from the Bode plot, is used as a measure of corrosion resistance in electrodes49,50,51,52. Early on (≤6 hours), impedance is higher for uncoated Ni-Cr, but after exposure for 3 days, impedance for the coated spacer is 1060 Ω cm2, as compared to 816 Ω cm2 for the uncoated spacer, indicating a 30% increase in corrosion protection in seawater due to the ceramic coating. Furthermore, the decrease in imaginary component (depicted by the y-axis) of impedance in the Nyquist plots indicates a decrease in double layer capacitance upon exposure to aqueous NaCl. Upon coating, the shape of the Nyquist plot is also altered, towards a skewed semicircle, which can be attributed to non-uniform coating thickness53. Phase angle Bode plots (Fig. 4c) show that Ni-Cr at 2 h exhibits capacitative behavior at low frequencies which shifts to slightly higher frequencies upon coating. This corresponds to the double-layer capacitance discussed earlier. Capacitative behavior from the CPEs is depicted as phase angles between 0 and 90°, while resistive behavior is shown by a phase angle of 0°.

Joule heating and membrane distillation

Ni-Cr spacers with 0.1 mm wire diameter were chosen for Joule heated membrane distillation based on their electrothermal heating effect. When surface temperature was measured in air upon application of 500 mA cm−2, the temperature of 0.1 mm wire diameter spacer reached 63 ± 2 °C, while that with the larger wire diameter (0.2 mm) only reached 36 ± 1 °C. This is because Joule heating relies on resistance through the material, and resistance is related to cross-sectional area, and hence wire diameter, according to Pouillet’s Law:

$$R=\rho \frac{l}{A}$$

where R [Ω] is the resistance of the sample, \(\rho\) [Ωm] is material resistivity, \(l\) is the length of the sample and A is cross-sectional area.

As the change in resistivity of Nichrome is negligible in this temperature range54,55, and length remain the same, resistance is higher when the wire diameter is smaller, leading to more improved surface heating. For this reason, MgO-coated Ni-Cr spacers with 0.1 mm diameter and coating time of 5 min were chosen for MD tests.

MgO-coated Ni-Cr spacers were applied to DCMD for desalination using 10000 mg L−1 NaCl as feed; the feed was heated to 45 °C. The effect of applying a current density of 0.2 A cm−2 continuously or periodically on MD performance characteristics, namely average permeate flux and average SEC was analyzed to determine optimum Joule heating cycle. A detailed description of the MD setup is given in the Methods section. An AC voltage was applied to minimize cathodic and anodic reactions at the terminals of the spacer. In the case of Joule heated spacers, a current was applied either continuously, or intermittently every 20 min for a duration of 10 min. Variation in permeate flux, salt rejection and SEC with and without applied current are shown in Fig. 5a, b. Average permeate flux increased by 15%, from 19.0 kg m−2 h−1 to 22 kg m−2 h−1. This increase in flux is due to internal heat generation within the feed channel spacer, which is in close proximity to the membrane. Localized Joule heating close to the membrane surface increases the effective driving force across the membrane for mass transfer to occur. Interestingly, improvement in flux was similar whether the applied field was continuous or intermittent. This may be attributed to the relatively high specific heat of Ni-Cr (480 J kg−1 K−1), as compared to carbon nanotubes previously used for Joule heating56. High density of metals combined with relatively high specific heat capacity together lead to a high thermal mass, which translates into slow thermal cycling between heated and cooled states56,57. Ni-Cr spacers should be able to retain the driving force obtained from Joule heating during OFF cycles. Salt rejection was maintained at ≥99.5% and remained unaffected by applied current. Membrane properties remain uncompromised as our work relies on localized electrothermal heating through a spacer-heating approach as opposed to membrane-heating. In previous studies incorporating electrothermal heating, coating a CNT film directly on the membrane surface allowed surface heating, but led to undesirable changes in membrane hydrophobicity, pore size distribution and porosity56.

Fig. 5: Membrane distillation performance.
figure 5

a Permeate vapor flux and salt rejection during DCMD with no spacer, and with spacer and varying applied current; b specific energy consumption for varying applied current. Error bars represent the standard deviations.

SEC for water production with no applied current is 6.01 ×103 kWh/m3. We note that this value increased only slightly, by 4% when an intermittent current was applied, and by 8% when a continuous current was applied. This increase is due to the electrical energy added for localized Joule heating of the spacer, which is greater when current is passed continuously during the test. Nevertheless, the increase in average permeate flux surpasses the proportional increase in SEC, indicating the potential viability of applying Joule heated spacers in MD systems. Our results show that a continuous electric field is not needed, as similar performance enhancement can be achieved with lower energy consumption using periodic application of an electric field. Since heating efficiency depends strongly on material properties, SEC should be optimized in terms of duration, frequency and magnitude of applied current for any given material.

MD is a promising desalination technique that is yet to reach its full potential due to low flux, high energy systems. Although MD research is largely focused on membrane development, the role of feed channel spacers is often underrepresented in system performance. We report a spacer-based approach for localized Joule heating in MD systems via ceramic-coated metallic spacers. We demonstrate the role of ceramic MgO coatings as a barrier layer under corrosive environments such as seawater, and control of film uniformity via electrolytic deposition time of MgO and spacer geometry. Electrolytic deposition for 5 min is suitable to generate uniform, crack-free coatings and the wire diameter of the Ni-Cr mesh is inversely related to the maximum surface temperature achieved via Joule heating. For wire diameters of 0.1 mm and 0.2 mm, the maximum surface temperature is 63 ± 2 °C and 36 ± 1 °C, explained by Pouillet’s law.

We apply Ni-Cr net-type feed spacers coated with MgO for surface heating via the Joule effect for brackish water desalination. Electrically induced spacer surface heating in combination with low-temperature bulk feed heating at 45 °C results in a flux enhancement of 15% with an associated increase in SEC of only 4% when an alternating electric field of 0.2 A cm−2 is passed through the spacer periodically. The advantage of combining Joule heating with low temperature heating is that waste heat and/or solar power may still be exploited along with high grade electrical energy. We find that both periodic and continuous application of electric current lead to similar improvement in flux when compared to 0 A cm−2. Our work demonstrates a proof-of-concept study of electrolytically deposited ceramic coatings on metallic spacers, and the control of electrically assisted performance enhancement in MD systems through the use of low-resistivity metallic spacers and optimization of applied current duration and frequency. By implementing functional feed channel spacers instead of modifying the membrane itself, we retain membrane properties and performance characteristics while enhancing overall performance. Future work involves exploring materials for both the barrier coating and for the spacer, and overcoming challenges associated with spacer fabrication and/or modification of functional materials. We believe periodic heating of the feed spacer via the Joule effect is a unique approach to enhancing the performance of MD systems, and will help direct MD towards commercial viability.



Ni-Cr (80:20 nickel chromium alloy) net-type square-shaped spacer sheets were obtained from Anping County Longyi Mesh Manufacture Co., Ltd. (Hebei, China). A commercial polytetrafluoroethylene (PTFE) filter (mean pore size 0.2 µm) on a laminated polypropylene (PP) support was purchased from Sterlitech (Auburn, USA). Mg(NO3)2 ∙ 6H2O (ACS reagent, 99%), absolute ethanol EMSURE® were obtained from Sigma-Aldrich, USA.

MgO coating deposition

A facile method of electrochemically processed MgO coatings was adopted from Hashaikeh and Szpunar30. Briefly, Ni-Cr spacers of two wire diameter (0.1 mm and 0.2 mm) were used as cathode while graphite sheets of the same dimensions (14.5 cm × 4 cm) was used as the anode. The electrodes were kept at a distance of 2 cm from each other and the electrolyte consisted of 0.5 M aqueous Mg(NO3)2 in a binary mixture of CH3CH2OH and H2O (1:1 ratio). A current of 5 mA cm−2 was passed through the electrolytic cell for t = 0 min, 5 min, 10 min and 20 min. Following electrolytic processing of Mg(OH)2 coatings, the spacers were first air dried at room temperature and then subjected to heat treatment at 1100 °C to obtain MgO-coated spacers by removal of hydroxide groups through thermal decomposition. Altering electrolytic deposition time led to final coatings of different thicknesses and morphologies, as discussed in the previous section.

Surface characterization

Morphology of pristine Ni-Cr and MgO-coated Ni-Cr spacers of the two wire diameters was examined using high-resolution scanning electron microscopy (FEI Quanta 450 FEG, Netherlands) under high vacuum, along with energy-dispersive X-ray spectroscopy (EDS) analysis. Prior to imaging, MgO-coated spacers first coated with a thin layer of Au using the 108 Auto Sputter Coater (Ted Pella, USA). The effect of MgO coating on the wettability was investigated via water contact angle measurements using an EasyDrop Standard drop shape analysis (DSA100, Krüss GmbH, Germany) A 2 μL droplet of DI water was produced on the spacer surface using a syringe with needle diameter 0.51 mm, and a digital image was acquired and analyzed. The software was used to determine the contact angle using the sessile drop method and the average of three measurements was recorded for the uncoated and coated spacers. This was carried out for at least two uncoated and two coated samples.

Electrochemical characterization

Electrochemical Impedance Spectroscopy (EIS) was carried out on the Metrohm Autolab PGSTAT 302 fitted with FRA32M using a three-electrode setup. Ni-Cr and MgO-Ni-Cr spacers acted as the working electrode and a platinum wire was used as the counter electrode in 3.5% NaCl as electrolyte. A potential of 50 mV was applied at frequencies ranging from from 0.1 to 105 Hz and the current response was recorded. Nyquist and Bode plots were generated from impedance data, and equivalent circuits were used to model the coated spacer. All spacers were immersed in 3.5% NaCl for 30 min prior analysis, and EIS spectra were recorded at t = 2 h and 3 days. Impedance values were multiplied by the geometrical area of the electrode (2 cm2) for normalization of data. At least two samples were run for each measurement.

Joule heating and membrane distillation

Each of the NiCr spacers (wire diameters 0.1 mm and 0.2 mm) were connected to a DC power source at room temperature, and a current of 500 mA cm−2 was passed through them and the final surface temperature was measured at three different points. The average of the three temperatures was reported.

Membrane distillation tests were carried out on the Convergence Inspector Membrane Distillation pilot-scale system (DEMCON, Netherlands) in direct contact mode fitted with a PTFE membrane (mean pore size 0.2 µm, Sterlitech, USA). The active area of the membrane was 7.5 cm × 3 cm. An aqueous NaCl solution of 10,000 mg L−1 was used as feed, whereas DI water was circulated as the permeate. The NiCr spacer was placed on the membrane surface facing the feed solution. Both feed and permeate flow rates were kept at 60 L h−1 in counter-current mode. The system is fitted with mass flow meters, pressure sensors, temperature sensors, conductivity meters and permeate weighing scale as shown in Fig. 6. Measurements were taken at 60 s intervals. For all tests, the feed was first heated to 45 °C and MD was operated for 6 h. A step-down transformer with an AC voltage of 24 V and a frequency of 50 Hz was used for electrically assisted heating. The transformer was connected to each side of the feed spacer via copper terminals. Three current programs were run through the spacer, namely 0 A cm−2, 0.2 A cm−2 continuous and 0.2 A cm−2 intermittent. During intermittent application, the power source was turned on every 20 min for 10-min intervals. Current was monitored through a digital multimeter and permeate was kept at a temperature 15 °C. Each test was carried out two times with a fresh sample of NiCr spacer.

Fig. 6: Experimental setup and current density application in MD.
figure 6

a Schematic of MD setup used in this study; b current density applied to conductive spacer in continuous mode, and c periodic current density applied to conductive spacer.

Equation (6) was used to determine permeate vapor flux.

$$J[{\rm{kg}}{{\rm{m}}}^{-2}{{\rm{h}}}^{-1}]=\frac{({\rm{change\; in\; permeate\; mass}})}{A* t}$$

where t is the time, A is the active membrane area (22.5 cm2).

Salt rejection (SR) was calculated from the feed and permeate conductivities according to the following equation:

$${\rm{SR}}[ \% ]=\frac{{k}_{{\rm{feed}}}-{k}_{{\rm{permeate}}}}{{k}_{{\rm{feed}}}}x100$$

where kfeed and kpermeate are feed and permeate conductivities, respectively.

Specific energy consumption (SEC) was calculated as an indicator of operating expenses during MD. SEC has two main contributors: thermal energy input for localized Joule heating at the spacer surface and energy input to heat the bulk feed solution.

By conservation of energy, heat lost by the feed as it passes through the cell is equal to the heat flux through the membrane. The heat flux through the membrane, \({Q}_{m}\), [kW] is then:


where \({\dot{m}}_{f}\) is the mass flow rate in kg s−1, \({{C}_{p}}_{w}\) is the feed water specific heat in kJ kg−1 °C−1, \({T}_{f,{in}}\) and \({T}_{f,{out}}\) are the inlet and outlet feed temperatures.

To determine the energy gained by the feed from Joule heating, \({Q}_{j}\)[kW], the energy consumed for bulk heating the feed \({Q}_{{in}}\) [kW] is first determined as \({Q}_{m}\) when when no current is passed through the spacer. In the case of Joule heated spacer, the overall heat flux \({Q}_{m}\) accounts for both energy input to heat the bulk feed and energy generated from Joule heating. Equation (6) is then used to calculate the energy gained by the feed from Joule heating:


SEC [kWh m−3] is determined from the equation below58,59:

$${\rm{STEC}}=\frac{{(Q}_{{\rm{in}}}+{Q}_{{\rm{j}}})\rho }{J{A}_{{\rm{m}}}}$$

where \(\rho\) is the density of water in kg m−3, \(J\) is the permeate flux through the membrane in kg m−2 h−1, \({A}_{{\rm{m}}}\) is the active area of the membrane in m2.