*3.2. Two-Step Method*

Unlike the one-step method, the two-step approach is a top-down process that uses dried nanoparticles that were initially prepared, through physical or chemical processes, after which these particles get dispersed in a base fluid through ultrasonic agitation [125–128], magnetic stirring [129–132], homogenizing [131,133,134], or ball milling (least commonly used) [16,135,136] with or without adding surfactant(s) to the mixture. Other less common dispersion routes can also be used, such as dissolver, kneader, three roller mill, stirred media mill, and disc mill [137]. Figure 11 demonstrates an example of the two-step method, where a bath type ultrasonic device is used to form the suspension. In addition to the bath type sonicators, some researchers have employed the probe/horn type sonicators to fabricate their nanofluids. They have reported higher particles dispersion capability and enhanced suspensions thermal properties using this type of device compared to the bath type dispersers [138]. The reason behind the previously achieved improvements in the suspension is that the probe device provides focused and intense ultrasonication effects, reaching up to 20 kW/L, to the mixture in an evenly distributed manner [139]. This is something that the bath type sonicators cannot provide due to its low relative intensity (i.e., 20–40 W/L) and non-uniform distribution of the ultrasonication effect on the fabricated nanofluid. It is important to note that the bath type ultrasonicator is more applicable for commercial scale production of nanofluids. In contrast, the probe type is better suited for synthesis at the lab scale. Regardless of the type of two-step mixing approach used, this method is still considered as a cost-effective process that is appropriate for both small- and large-scale production of any type of nanofluids, which is seen as a favorable approach to many researchers in the field [140]. However, some of the critical issues associated with this method during nanofluids fabrication are the agglomeration of the nanoparticles due to the very high surface energy between the particles, and the notable increase in the process temperature with fabrication time when using some of the mixing devices (e.g., bath type ultrasonic device) [8,13]. The first obstacle causes the suspension to be in a weak physical stability state that results from the nanoparticles undergoing agglomeration, which is followed by separation of the particles from the base fluid in the form of sediments. Thus, the nanofluid thermophysical properties degrade with time. As for the raise in fabrication process temperature problem, the reproducibility of similar nanofluids (i.e., obtaining suspensions with the same thermophysical properties) would be impossible to achieve. This is because different bath type ultrasonic devices and/or surrounding atmospheric conditions lead to varying the thermophysical properties and physical stability of the fabricated colloidal [8,38]. There are several ways to overcome the aforementioned limitations in the two-step method. For example, surfactants can be added to the mixture to reduce the level of particles agglomeration, and the sonicator bath temperature could be controlled throughout the fabrication process by equipping the device with a temperature regulator. Other approaches used to physically stabilize the as-prepared dispersions are mentioned afterward in the nanofluid stability enhancement section (Section 4.2). When preparing nanofluids, the nanoparticles and surfactants (if required) are added to the base fluid with respect to either volume (vol.) or weight (wt.) percentage (%). Most researchers tend to use the vol. % to calculate the added nanopowder to the base fluid, which can be estimated through the appropriate formulae presented in Table 1.

**Table 1.** Fraction calculation Formulae for different forms of nanofluids.



**Table 1.** *Cont*. or ( )+ ( 

( )

 ) × 100

*Nanomaterials* **2021**, *11*, x FOR PEER REVIEW 15 of 79

Where *V*, *m*, *ρ*, *np*, *np*1, *np*2, *b f* , *b f* 1, and *b f* 2 represent the volume, mass, density, single type of nanoparticles, first type of nanoparticles, second type of nanoparticles, single type of base fluid, first type of base fluid, and second type of base fluid, respectively. In addition to the equations shown in Table 1, one can use the following three equations to determine the vol. % for their nanofluids when having two different particles and/or two base fluids concentration ratio(s). Where , , , , 1, 2, , 1, and 2 represent the volume, mass, density, single type of nanoparticles, first type of nanoparticles, second type of nanoparticles, single type of base fluid, first type of base fluid, and second type of base fluid, respectively. In addition to the equations shown in Table 1, one can use the following three equations to determine the vol. % for their nanofluids when having two different particles and/or two base fluids concentration ratio(s).

**Figure 11. Figure 11** Example of nanofluids two-step preparation using a bath type ultrasonic device. *.* Example of nanofluids two-step preparation using a bath type ultrasonic device.

For single type of nanoparticles and two different types of base fluids:

$$\frac{\left(\frac{m}{\rho}\right)\_{np}}{\left(\frac{m}{\rho}\right)\_{np} + \left[\left(\frac{m}{\rho}\right)\_{bf1} \times \frac{A}{A+B} + \left(\frac{m}{\rho}\right)\_{bf2} \times \frac{B}{A+B}\right]} \times 100\tag{5}$$

where the ratio of *b f* 1 : *b f* 2 is equal to *A* : *B*.

For two different types of nanoparticles and single type of base fluid:

$$\frac{\left(\frac{m}{\rho}\right)\_{np1} \times \frac{A}{A+B} + \left(\frac{m}{\rho}\right)\_{np2} \times \frac{B}{A+B}}{\left[\left(\frac{m}{\rho}\right)\_{np1} \times \frac{C}{C+D} + \left(\frac{m}{\rho}\right)\_{np2} \times \frac{D}{C+D}\right] + \left(\frac{m}{\rho}\right)\_{bf}} \times 100\tag{6}$$

where the ratio of *np*1 : *np*2 is equal to *C* : *D*.

For two different types of nanoparticles and two types of base fluid:

$$\frac{\left(\frac{m}{\rho}\right)\_{np1} + \left(\frac{m}{\rho}\right)\_{np2}}{\left[\left(\frac{m}{\rho}\right)\_{np1} \times \frac{\mathbb{C}}{\mathbb{C} + D} + \left(\frac{m}{\rho}\right)\_{np2} \times \frac{D}{\mathbb{C} + D}\right] + \left[\left(\frac{m}{\rho}\right)\_{bf1} \times \frac{A}{A+B} + \left(\frac{m}{\rho}\right)\_{bf2} \times \frac{B}{A+B}\right]} \times 100\tag{7}$$

where the ratio of *np*1 : *np*2 and *b f* 1 : *b f* 2 are equal to *C* : *D* and *A* : *B*, respectively.
