For a Titanium Sheath Heater Installed in a Tank of 8% Sodium Borate at 95°C, How Does the Borate Concentration Gradient Near the Tube Surface Affect the Stability of the Passive Film Under Cyclic Heating?

8% sodium borate (Na2B4O7) at 95°C is used as a buffering agent and corrosion inhibitor. Borate ions (B 4 O 7 2 - ) can create a protective layer on titanium, but the stability of this film depends on the borate concentration at the metal surface. The temperature gradient across the boundary layer induces the migration or precipitation of the borate ions under cyclic heating. This yields a concentration gradient with higher borate concentration at the cooler bulk solution and lower borate concentration at the hot tube surface. The resulting gradient destabilises the passive film and leads to localised thinning. The passive film stability is maintained on the surface at a borate concentration higher than 2 %.

The Mechanism of Formation of Borate Concentration Gradients

In steady state heating borate ions move toward the hot titanium surface but thermal diffusion (Soret effect) pulls them away from the hot surface. The net result is a depleted boundary layer, with the borate concentration at the tube surface being 10-30% less than that in the bulk solution. Cyclic heating (on-off cycles) causes the concentration gradient to oscillate. As the heater cycles off, the surface cools and borate ions diffuse back to the surface with a resulting transient passivation. When the heater switches on again the gradient is re-established and the surface exhausted. This periodic depletion and recovery stresses the passive film and results in cracking and spalling.

Quantitative Stability of passive films as a function of surface borate concentration

The stability of the passive film for Grade 2 titanium at varied surface borate concentrations has been proven during controlled testing in 8% sodium borate (bulk concentration) at 95°C under cyclic heating (1 hour on, 1 hour off). The passive film thickness at 4-5 % surface concentration (enriched) is 5-8 nm. The film is stable and adherent and no pitting occurs after 1000 cycles. The film is generally stable and some pitting occurs after 500 cycles (thickness 3-5 nm at 3-4% (near bulk)). At 2-3% (moderate depletion) the thickness is 2-4 nm, the film is cracked and the pitting starts after 200-400 cycles. The film is fragile and pitting occurs within 50–200 cycles when the thickness is 1–3 nm at 1–2 % (depleted). At values below 1% the passive film is totally destroyed and uniform corrosion occurs at a rate of 0.1–0.3 mm/year.

Effect of Borate Concentration and Cycle Rate on Surface Depletion

The degree of surface depletion depends on the concentration of bulk borate and the cycle frequency. Under cyclic heating the surface concentration with 4% bulk borate is minimal, 2-3%. 6% bulk concentration, surface concentration is 3-4%. Moderately stable. The nominal bulk concentration is 8%. Surface concentration is 4-5%. This is stable. The surface concentration is 5–6 % and very steady at 10 % bulk. At a cycle frequency of 6 cycles per hour (10 min on, 10 min off), the surface concentration is 10–20% lower than at 2 cycles per day, since the boundary layer does not have time to recover.

Guide to Borate Concentration and Cycle Management for Titanium Heaters

The recommendations for bulk borate content and cycle parameters to maintain passive film stability on grade 2 titanium at 95 °C are summarised in the table below.

Bulk Borate Concentration (%) Cycle Frequency (on/off)% Surface Borat (Estimated)Passive Film Stability Recommended Action
6 <2 cycles/day 3–4 Moderate Acceptable
6 >6 cycles/hour 2-3 Marginal Concentration increase
8 <2 cycles/day 4–5 Stable Optimal
8 >6 cycles/hour 3-4 Moderate Reduce cycle frequency
10 Any 5–6 Very stable Preferred for high cycling
12 Any 6–7 Very stable Unnecessary over-specification
Engineering without control of concentration

The grade of titanium influences the stability of passive film under concentration gradients. Grade 7 (palladium stabilised) is stable down to surface concentrations of borate of 1.5% with a higher safety factor. Grade 12 is for moderate improvement. Wall thickness has no effect on the passive film. Heating rate is important. Slow ramping (1°C per minute) lowers the concentration gradient compared to quick ramping (10°C per min). Agitation of the solution (a mixer or recirculation pump) reduces the thickness of the boundary layer and so minimises the concentration gradient.

Providing an Informed Specification

For cyclic heating of a titanium sheath heater in 8% sodium borate at 95°C, keep the bulk borate concentration at 8–10% to achieve a surface concentration over 4% during cycling. If the cycle frequency is more than 6 cycles per hour, raise the bulk concentration to 10%. For existing heaters with passive film instability (erratic power consumption or pitting), add borate to bring it up to 10% concentration or lessen the cycling frequency. Check the pH throughout operation and add sodium hydroxide if the pH is below 9. The engineer controls the borate concentration gradient by sufficient bulk concentration and lower cycling frequency to preserve the titanium heaters' passive film steady.