An Experimental Validation Study on Ferrofluid Evaporation

The current research on the evaporation of ferrofluids mainly focuses on the characterization of ultra-low vapor pressure ferrofluids in vacuum and the theoretical analysis of the evaporation process. Few studies have focused on the experimental validation of the proposed evaporation rate equations and on the comparison of the differences in ferrofluid evaporation. In this study, based on the Bolotov’s model, an evaporation rate equation is deduced from the experimental model. The experimental study included a comparison of the evaporation, magnetic particle volume fraction, temperature, height of the fluid surface from the outlet, and magnetic field of a kerosene-based ferrofluid and its base carrier liquid. The prepared sample was evaporated in a test tube, and the evaporation rate was calculated by measuring the weight loss of the sample. The experimental results show that the evaporation rate of the base carrier liquid is higher than that of the ferrofluid. The smaller the volume fraction of the magnetic particles, the greater the evaporation rate. The magnetic particles play a key role in preventing evaporation of the base liquid. The higher the temperature, the smaller the deviation of the evaporation rate from the predicted value. The evaporation rates obtained by the two control groups at the height of the fluid surface from the outlet were lower than the predict value. The magnetic field had a certain promotional effect on the evaporation of the ferrofluid. The experimental results were consistent with the results obtained using Bolotov’s model. This research validates Bolotov’s model and shows that the model is somewhat biased but still responds well to different variables.


Introduction
A ferrofluid, also known as a magnetic fluid, is a nanoscale functional material, usually prepared via the coprecipitation method [1]. It is a colloidal suspension of single-domain magnetic particles, which is composed of three parts-the magnetic particles, surfactant, and base carrier liquid [2,3]. The diameters of the magnetic particles range from 8 to 10 nm, and the particles are coated with surfactant to prevent agglomeration of the liquid and are dispersed in a base liquid. Ferrofluids have both the magnetic properties of a solid and the fluidity of a liquid. When no external magnetic field is applied, the ferrofluid acts as a Newtonian fluid. When a magnetic field is applied, the magnetic particles recombine, so that the entire ferrofluid becomes strongly magnetized and exhibits magnetism, showing non-Newtonian fluid behavior [4].
Since Stephen [5] first synthesized a ferrofluid in 1965, it has been applied in numerous industries including [6] dynamic sealing [7], heat conduction, damping [8], and drug targeting [9]. Magnetic fluid sealing is a new type of sealing method, which is different from the traditional sealing methods employed in the past. The magnetic fluid seal has the advantages of zero leakage, a long life, and high reliability [10][11][12]. For the practical application of magnetic fluid sealing devices, a magnetic fluid must exist in the gap between the pole tooth and the rotating shaft, forming several "O"-shaped sealing rings, which are responsible for the sealing effect [13][14][15]. However, under the action of a magnetic field and a temperature field, the ferrofluid will evaporate, causing changes in the properties of the magnetic fluid and resulting in failure of the seal. To satisfy the high quality requirements and the harsh practical conditions-for example, for applications like monocrystalline silicon furnaces and optical devices-it is necessary to further study the evaporation of ferrofluids. Numerous studies have focused on this aspect. Some researchers started with a focus on the preparation of new ferrofluids with low evaporation rates. For example, Bottenberg and Chagnon [16] prepared a polyphenylene ether-based ferrofluid. Compared with hydrocarbonbased ferrofluids, this ferrofluid has a lower saturated vapor pressure, which can reach 10 -5 Pa at 20 °C. It is especially suitable for sealing under high vacuum environments. Black et al. [17] prepared and characterized a Perfluoropolyether (PFPE)-based ferrofluid and found that it showed low volatility at high temperatures. Li and Raj [18] calculated the evaporation rate of hydrocarbonbased and fluorocarbon-based ferrofluids under four different vacuum levels. It was found that under higher vacuum levels the evaporation rate of two ferrofluids were significantly higher than under atmospheric conditions, and the fluorocarbon-based magnetic fluids are more suitable for ultra-high-vacuum applications. The preparation of ferrofluids with low saturated vapor pressure, which is very important for the selection of the base carrier liquid and surfactant, is a challenging task under research settings. Although the evaporation rate of ferrofluids with low saturated vapor pressure has been significantly improved, the stability of ferrofluids remains unsatisfactory. Some researchers have used the evaporation of droplets to study the evaporation mechanism of ferrofluids. Cristaldo et al. [19,20] numerically analyzed the heating process of a ferrofluid droplet under an alternating magnetic field with a thermal boundary layer model and showed that because of the alternating magnetic field, the interior of the thermal boundary could layer rapidly reach the boiling point, thereby increasing the droplet evaporation rate. Bolotov et al. [21,22] derived equations of the evaporation rate to estimate the life of a tribounit with ferrofluid under a vacuum and gas atmosphere, but scarely any experiments were performed to verify it. Jaiswal et al. [23] and Chattopadhyay et al. [24] studied the evaporation kinetics of a magnetic salt solution pendant droplet under a horizontal magnetic field. Their experimental observations revealed that the evaporation rate was enhanced with a magnetic field, and magneto-solutal advection was thought to be the controlling factor for the augmented evaporation rate. Jadav et al. [25] placed water-based magnetic droplets on a flat glass substrate and studied the influence of a magnetic field on the evaporation rate and contact angle. The results showed that in the dry droplets, the structure and distribution of the nanomagnetic particles were related to the direction and magnitude of the applied field. Harikrishnan et al. [26] distinguished individual surfactants, particles, and the combined role of surfactants and particles in regulating evaporation kinetics, showing that the combined colloidal system of nanoparticles and surfactants exhibited the largest evaporation rate. This rate is a strong function of particle and surfactant concentration, revealing the role of surfactant in regulating the evaporation rate of colloidal solutions. Shyam et al. [27] studied the evaporation kinetics of a fixed ferromagnetic droplet placed on a soft substrate under the action of a time-dependent magnetic field. The time-varying magnetic field can effectively control the evaporation time of the ferromagnetic droplets; they also determined the critical frequency of the applied magnetic field strength, which makes the droplets encounter the minimum lifetime. At the critical frequency, the advection time scale of the magnetic nanoparticles is balanced by the magnetic disturbance time scale. Karapetsas calculations showed that the droplet lifetime was significantly affected by the balance between surfactantenhancing diffusivity, inhibiting thermal Marangoni stress-induced motion and impeding the evaporative flux by reducing the effective interfacial area. Saroj and Panigrah [29] studied the evaporation of immobilized ferrofluid droplets on PDMS substrates and showed that the evaporation rate of the droplets increased with an increase in the ferrofluid concentration. In addition, they studied the "coffee-ring effect [30]" of the ferrofluid; it is believed that the magnetic field leads to a uniform deposition pattern of dry droplets. Previous studies mainly focused on the characterization of an ultra-low vapor pressure ferrofluid in a vacuum and theoretical analysis of its evaporation process. However, there is a lack of studies on the verification of the proposed equations and the comparison of the differences between ferrofluid evaporation with and without a magnetic field in an experimental manner. In this study, we analyzed the evaporation rate of a kerosenebased ferrofluid under normal pressure with and without

Theoretical Research
Bolotov et al. [22] derived the evaporation rate equation of a ferrofluid from Fick's first law under several conditions. When the ferrofluid is in a vessel enclosed in a shell with a hole, as shown in Figure 1, the equation can be written as follows: where W is evaporation rate of the ferrofluid, g/s; D is diffusion coefficient of the vapor molecules, m 2 /s; S h is surface area of the hole, m 2 ; P s is saturated vapor pressure of the base fluid, Pa; μ is molar mass of the base fluid, g/mol; R 0 is universal gas constant, J/(mol·K); T is absolute temperature of the ferrofluid, K; h is thickness of the hole, m; S is surface area of the ferrofluid, m 2 ; α is evaporation coefficient of the ferrofluid; ω s is volume fraction of the magnetic particles. (1) According to Eq. (1), for the condition in which the ferrofluid is in a vessel like a test tube, as shown in Figure 2, S = S h , where h is the height from the surface of ferrofluid to the mouth of test tube. The equation can be written as follows: To predict the evaporation rate using Eq. (2), the coefficients α and D must be determined. In certain cases, coefficient α can be less than 1, but for most substances, α ≈ 1 [21]. Coefficient D can be calculated in reverse from the evaporation rate of the base fluid under a certain temperature and atmospheric pressure. The following equation can be used to obtain the D under other conditions: where D 0 is the known diffusion coefficient at temperature T 0 and atmospheric pressure p A0 , and D is the unknown diffusion coefficient at temperature T and atmospheric pressure p A .
(2) Figure 5 Prediction of the evaporation rate of a ferrofluid at different temperatures

Experimental Materials and Devices
The materials used in the experiment were kerosene and kerosene-based ferrofluids with different volume fractions. The magnets used were N35 NdFeB cylindrical permanent magnets, which manufactured by Shanghai Siyuan Magnetic Industry, with a diameter of 16 mm, a thickness of 10 mm, a remanence B r of 1.2 T, a coercive force H c of 880 kA/m, and the maximum magnetic energy product (BH)max of 270 kJ/m 3 . The device used in the experiment was the Hefei Anke Environmental Testing Equipment, and a GDJS-1000L high and low temperature alternating damp heat test box with a temperature range of − 70 °C to + 150 °C, and a temperature error of ± 0.5 ℃. A cylindrical flat-bottomed transparent borosilicate glass test tube with a total height of 76 mm and an inner diameter of 10 mm was used. An ME55 balance (METTLER TOLEDO), with a division value of 0.01 mg was also used.

Experimental Method
To verify the evaporation rate of the ferrofluid using Eq.
(2), a kerosene-based ferrofluid and its base fluid kerosene were tested. A test tube, with a height and inner diameter of 76 mm and 10 mm, respectively, was filled with the sample. In some cases, a magnet was placed under the test tube to form a magnetic field. The test tube was placed in a high temperature test chamber for 12 h, as shown in Figure 3. During the process of evaporation, the sample's weight was measured every 3 h using a precision electronic balance with a resolution of 0.01 mg to obtain the weight loss data. The height h was controlled to ensure that the influence of the magnetic field on the surface area S was as small as possible.
The volume fraction ω s was obtained from the density of sample and was ~ 13%. To prepare ferrofluids with different volume fractions, the samples were diluted with the base fluid and then were subjected to ultrasonic treatment for an hour. Both the saturated vapor pressure p s and molar mass μ were obtained from handbooks [31].

Temperature
To study the influence of temperature on the evaporation process, the ferrofluid and kerosene were placed in the chamber at 50 °C, 70 °C, and 90 °C with a height h = 41 mm and ω s = 13%. Figure 4 presents the weight loss of the samples, which reveals that the evaporation rate of the ferrofluid is lower than that of its base fluid. However, it also shows that the curve of weight loss is nearly a straight line but not strictly a straight line, and the curve's gradient (evaporation rate) shows a reducing trend. According to Eq. (2), this phenomenon can be attributed to the increase of h and ω s in the evaporation process. To make the calculating conditions more consistent with practical conditions, only the dataset of the first three hours was selected to represent the evaporation rate of the samples. Before the calculation using Eq. (2) to predict the evaporation rate of the ferrofluid, the diffusion coefficient D was calculated in reverse using the evaporation rate of kerosene at 70 °C, which D 0 = 1.9964 × 10 −6 m 2 /s. The predicted evaporation rates of the ferrofluid at different temperatures are shown in Figure 5, which indicates that the deviation of the predicted values and the experimental values decreases with increasing temperature.

Volume Fraction
A ferrofluid with different volume fractions was prepared to study the relationship between the evaporation rate and the volume fraction when the sample evaporates with a height h = 41 mm at 70 °C. The ferrofluid was diluted with kerosene in a proportion of 3:1 and 1:1. Figure 6 presents the result of the experiment, which reveals that the evaporation rate of diluted ferrofluid shows an intermediate between those of the undiluted ferrofluid and kerosene. The more dilute the ferrofluid, the faster it evaporates, which clearly proves that the magnetic particles prevent the base fluid from evaporating. Figure 7 shows that the prediction values based on Eq. (2) are overestimated, but still reflect the difference between different dilution rates.

Height
Height h was also investigated as a variable. Undiluted samples with different heights, h = 41 mm and h = 46 mm, were tested at 70 °C. Figure 8 shows the result of the experiment which reveals that the higher the value of h, the slower the evaporation. Because the height changed in the case of h = 46 mm, the diffusion coefficient D had to be recalculated and was found to be D 0 = 1.8941 × 10 −6 m 2 /s. The predicted rates are given in Figure 9, which shows the same overestimated results as Sections 4.1 and 4.2.

Magnetic Field
The most distinguishing feature of a ferrofluid is the response of the magnetic particles dispersed in a base liquid to a magnetic field. Considering that the evaporation process of the base fluid is weakened by the magnetic particles, it is necessary to explore the influence of the magnetic field on the evaporation rate. An explorative experiment was designed to compare the cases with and without a magnetic field applied to the bottom of test tube. Undiluted samples were placed in the chamber with a height h = 41 mm at 70 °C. Figure 10 shows that the evaporation of a ferrofluid to which a magnetic field is applied is intermediate between that of a ferrofluid to which a magnetic field is not applied and that of kerosene. This phenomenon might be attributed to the reduction in the local concentration near the ferrofluid surface, which makes the ferrofluid with a lower volume fraction evaporate.

Conclusions
We analyzed the evaporation rate of a kerosene-based ferrofluid with different variables using experimental studies and predicted the evaporation rate based on Bolotov's model. Our conclusions are listed as follows: (1) Ferrofluids have a lower evaporation rate than the base fluid. The magnetic particles prevent the base fluid from evaporating, and a lower volume fraction leads to a higher evaporation rate. (2) Although the results obtained using Bolotov's model show a certain deviation from the experimental results, the model still responds well to different variables.
(3) The magnetic field promotes the process of evaporation, which might be attributed to the reduction in the local concentration near the ferrofluid surface.
Because Bolotov's model is merely based on the loss of surface area S due to the magnetic particles covering the evaporation surface, it is reasonable to guess that there are other factors that affect the evaporation rate, which needs further study.