Mechanical Stirring (Rheocasting).

Mechanical stirring is the earliest and simplest technique for generating semi-solid slurries and forms the basis of the original rheocasting process (Spencer et al., 1972). In this method, a rotating impeller or stirrer is immersed in the partially solidified melt to impose shear within the mushy region. Continuous shearing fragments dendrites and promotes their transformation into rosette and near-spherical globular morphologies through ripening and coarsening. The process is applicable to a wide range of Al, Mg, Cu and Sn-Pb alloys. Its main advantages include simple implementation, low capital cost, scalability and compatibility with conventional casting systems (Li et al., 2002). However, the process may suffer from non-uniform shear distribution, temperature inhomogeneity and gas entrapment under excessive turbulence (Brabazon et al., 2002). Mechanical stirring is generally effective at solid fractions below ~0.5, beyond which the resistance of the solid network hinders stirrer rotation (Kirkwood et al., 2010).

Electromagnetic Stirring.

Electromagnetic stirring (EMS) uses a time-varying magnetic field to generate Lorentz forces within the electrically conducting melt, producing rotational or axial convective flow without mechanical contact. The induced flow shears the mushy zone, fragments dendrites, homogenises temperature and solute fields, and promotes the formation of fine globular microstructures (Bai et al., 2009). The process offers contactless operation, reduced contamination, controllable stirring intensity, and improved grain refinement and macrosegregation control. Despite its advantages over mechanical stirring, EMS remains associated with several challenges, including the formation of partially spheroidised rosette structures and microstructural inhomogeneity across the billet cross-section, both of which may increase reheating times. Production costs are further elevated by the additional stages required for feedstock preparation, reheating before forming and recycling of non-dendritic scrap material (Mohammed et al., 2013). Stirring efficiency also decreases at higher solid fractions (~0.3-0.4) due to increased slurry viscosity and the development of a solid network. Additionally, non-uniform magnetic field distribution in complex mould geometries may result in heterogeneous microstructures (Bai et al., 2009).

Magnetohydrodynamic Stirring.

Magnetohydrodynamic (MHD) stirring is an advanced form of EMS that employs combined electric and magnetic fields to generate controlled three-dimensional flow within the solidifying melt. Unlike conventional EMS, MHD systems may use superimposed DC and AC fields, pulsed magnetic fields or multi-frequency coil arrangements to produce complex flow patterns (Vives, 1992). The induced Lorentz forces promote dendrite fragmentation, enhance temperature and solute homogenisation, and improve grain refinement. MHD provides a more uniform solid fraction distribution than conventional EMS. The technique offers contactless operation, programmable flow control, and improved thermal and compositional homogenisation. However, it involves significantly greater equipment complexity and a higher capital cost. MHD-cast alloys in the semi-solid state exhibit significant liquid-phase segregation and extensive agglomeration of solid grains compared with strain-induced melt activation (SIMA) and spray-cast alloys. Microstructures remain comparatively less equiaxed and display high rosette growth rates. These characteristics are attributed to differences in grain misorientation distribution introduced during processing (Tzimas & Zavaliangos, 2000).

Cooling Slope Method.

Cooling slope (CS) casting is a simple and low-cost semi-solid slurry preparation technique in which superheated molten metal flows over an inclined, cooled plate before solidifying in a mould (Haga & Kapranos, 2002). Rapid heat extraction at the slope surface promotes nucleation, while gravity-driven flow generates shear that detaches nuclei and transports them into the bulk melt, producing fine, near-spherical primary particles (Haga & Suzuki, 2001). Key process parameters include channel inclination, slope length, surface temperature and alloy superheat (Birol, 2009). The technique has been successfully applied to various magnesium and aluminium alloys. Major advantages include simple operation, low equipment cost and the ability to generate spheroidal primary phases. However, the process may suffer from porosity, oxide formation and solidified shell formation along the slope surface, which can affect slurry quality and microstructural uniformity (Deepak Kumar et al., 2014). Excessive superheat may remelt nuclei formed on the slope, whereas insufficient superheat can cause premature solidification. The method is therefore most suitable for high-fluidity alloys with relatively wide solidification ranges.

Spray Casting/Spray Deposition.

Spray casting or spray forming is a non-agitation feedstock production process in which liquid metal is atomised into fine droplets using high-velocity gas jets and deposited onto a cooled substrate (Grant et al., 2017). During atomisation, small droplets solidify rapidly, while larger droplets remain liquid, and intermediate droplets are deposited in a semi-solid state. The process has been applied to aluminium, magnesium, copper alloys, nickel superalloys and metal matrix composites. Major advantages include fine non-dendritic microstructures without mechanical stirring, low macrosegregation and the ability to produce near-net-shape preforms. However, the process involves high equipment and operating costs, overspray losses and challenges related to porosity and oxide control (Mohammed et al., 2013).

Swirled Enthalpy Equilibration Device Process.

The Swirled Enthalpy Equilibration Device (SEED) process is a semi-solid feedstock preparation technique based on eccentric swirling of molten metal within a metallic vessel to promote uniform heat extraction and non-dendritic slurry formation (Doutre et al., 2004). Initially, molten metal with low superheat is poured into a rotating vessel, where swirling flow promotes nucleation at the vessel surface while suppressing dendritic growth. The remaining liquid is subsequently drained, leaving a self-supporting semi-solid slug suitable for pressure forming. The enthalpy equilibration approach relies on controlled heat removal, primarily through the cooled crucible wall, and fluid motion through swirling to produce a fine, rosette-to-globular primary phase within a narrow solid fraction window (Gu et al., 2023). The SEED process has been applied commercially to the high-pressure die casting of automotive Al-alloy components. Dendrite fragmentation and controlled cooling during swirling promote the formation of globular microstructures. Stirring intensity and pouring temperature are the key parameters controlling the transition from dendritic to globular structures and the overall microstructural evolution (Doutre et al., 2004). The SEED process enables the on-demand production of semi-solid slurry with precise solid fraction control and low rotational speeds, thereby minimising gas entrapment. Its crucible-based configuration is also compatible with conventional die-casting systems. However, the process requires careful control of pouring temperature, swirling speed, superheat and cooling conditions to ensure consistent slurry quality. Radial temperature gradients within the crucible may lead to microstructural heterogeneity, while the liquid-draining step increases process complexity (Luo et al., 2019). The method is most effective for near-eutectic aluminium alloys with moderate solidification ranges, whereas alloys with high solidus temperatures or wide freezing ranges are more difficult to process reproducibly.

Strain-induced Melt Activation Process.

The SIMA process is a solid-state deformation route for producing non-dendritic feedstock suitable for thixoforming (Wang et al., 2011). In the SIMA process, a cast alloy billet is first subjected to heavy plastic deformation to introduce a high density of dislocations and stored strain energy. The deformed billet is then reheated into the semi-solid temperature range, where partial melting promotes recrystallisation and liquid penetration along high-energy grain boundaries (Bolouri et al., 2010). This isolates the recrystallised grains and produces a fine, near-spherical primary phase surrounded by liquid, making the microstructure suitable for thixocasting and thixoforging. However, the process requires an additional deformation step before reheating, increasing processing complexity and cost. Careful control of deformation and reheating conditions is necessary to ensure uniform recrystallisation and grain separation. The method is most suitable for wrought aluminium and magnesium alloys and is less effective for alloys with wide solidification ranges or poor workability (Czerwinski, 2020).

Recrystallisation and Partial Melting Process.

The recrystallisation and partial melting (RAP) process is similar to SIMA but employs warm or hot working to introduce stored deformation energy before reheating into the semi-solid range. During partial remelting, recrystallisation and liquid penetration along grain boundaries produce fine, near-spherical grains surrounded by liquid (Jiang et al., 2016). Compared with SIMA, RAP generally provides faster recrystallisation kinetics and more uniform microstructures, particularly in larger billets. The process reduces the risk of deformation-induced cracking and is suitable for alloys with limited cold workability. However, it requires controlled warm working conditions and careful regulation of deformation and temperature to retain sufficient stored energy for recrystallisation. RAP is most effective for wrought aluminium and is less suitable for brittle cast alloys that cannot undergo substantial solid-state deformation. Also, non-uniform strain in large billets leads to a heterogeneous semi-solid microstructure (Wang et al., 2017).

Direct Partial Remelting.

Direct partial remelting (DPRM) is a thixo-route process in which a grain-refined cast billet is reheated directly into the semi-solid temperature range without prior deformation. During isothermal holding, partial melting promotes spheroidisation through Ostwald ripening and grain boundary migration, producing near-spherical solid grains suitable for thixoforming (Omar et al., 2011). The process typically operates at solid fractions of 0.4-0.6, and the final microstructure strongly depends on the initial grain size and morphology of the feedstock. In this method, the as-received material is reheated directly into the semi-solid range without requiring conventional feedstock preparation routes such as SIMA or RAP (Mohammed et al., 2013). This simplifies processing and broadens the range of materials and processing pathways available for producing thixoformable microstructures. However, precise temperature control and uniform heating are essential to avoid excessive grain coarsening, while the process remains highly dependent on the quality of the initial grain-refined billet. Coarse- or columnar-grained feedstocks are generally unsuitable for this method (Ji et al., 2022).

Ultrasonic Vibration Treatment.

Ultrasonic vibration treatment introduces high-frequency acoustic waves into the solidifying melt through a sonotrode, generating acoustic cavitation and acoustic streaming (Jian et al., 2005). Cavitation causes the formation and collapse of microbubbles, producing intense localised pressure pulses and microjets that fragment dendrite arms, while acoustic streaming enhances convective mixing, homogenises temperature and solute fields, and distributes the fragments throughout the melt. The process provides effective grain refinement, promotes degassing and oxide removal, and can be applied without major modifications to existing equipment. However, sonotrode erosion, limited acoustic penetration depth and sensitivity to probe positioning restrict large-scale application (Jiang et al., 2014). Ultrasonic treatment is most effective during the early stages of solidification at low solid fractions, as the developing solid network rapidly attenuates acoustic propagation and reduces cavitation activity.

Gas-induced Semi-solid Process.

The gas-induced semi-solid (GISS) process produces a semi-solid slurry by injecting inert gas through a porous graphite diffuser immersed in the melt near the liquidus temperature (Wannasin et al., 2010). Rising gas bubbles generate localised shear and convective flow that fragment dendrites and distribute the fragments throughout the melt, while simultaneous heat extraction from the injected gas promotes undercooling and nucleation. The GISS route is suitable for processing different types of alloys, such as zinc alloys, cast aluminium alloys, wrought aluminium alloys and die casting aluminium alloys (Mohammed et al., 2013). The process integrates stirring and cooling in a compact, low-cost setup compatible with conventional casting systems, while the inert atmosphere also helps reduce oxidation. However, gas entrapment, non-uniform shear distribution and graphite tip erosion remain important challenges. The method is most effective at low-to-moderate solid fractions, as increasing solid content reduces bubble mobility and convective efficiency. Techniques such as ultrasonic vibration, SIMA and inert gas purging are not industrially viable at high solid fractions, further highlighting the processing niche of GISS (Gautam et al., 2025).

Closure Laws and Inter-phase Exchange Terms

The key inter-phase exchange terms in the two-phase globular equiaxed model are the solidification rate $\dot{M}$ (kg m^-3 s^-1), the inter-phase momentum drag $M_{a,\beta }$ (N m^-3), the inter-phase heat transfer $Q_{\alpha ,\beta }$ (W m^-3) and the solute exchange $C_{\alpha ,\beta }$ (kg m^-3 s^-1 of solute). These terms couple the solid and liquid phase conservation equations. The solidification rate $\dot{M}$ is the crucial quantity from which all other solidification-induced exchange terms are derived. It is evaluated from the solid-liquid interfacial energy balance:

where $f_s$ is the solid volume fraction, ${\rho }_s$ the solid density, L the latent heat, $h_{sl}$ the inter-phase heat transfer coefficient per unit interfacial area and $Q_n$ the external thermal source. Once $\dot{M}$ is known, the inter-phase solute exchange C is obtained from the lever rule or Scheil-type conditions applied at the solid-liquid interface, accounting for the impingement factor ${\text{Ω}}_{imp}$ that reduces the effective interfacial area at high solid fractions:

where $C^{\ast }$ is the solute concentration at the solid-liquid interface. The impingement factor ${\text{Ω}}_{imp}$ accounts for the overlap of diffusion fields between neighbouring grains and can be treated as a function of solid fraction $f_s$ or approximated as ${\text{Ω}}_{imp}\approx f_s$ (Wu et al., 2013, 2014).

The equiaxed grain radius $R_s$ is related to the grain number density n by the geometric relation: $R_s=\sqrt[3]{3f_s/4\pi n_s}$. The system of four transport equations (mass, momentum, energy and species for each phase) contains four primary unknowns: the phase volume fractions $f_s$, the phase velocities uα, the temperature T (assuming local thermal equilibrium between phases: $T_s=T_l=T$) and the solute concentrations. The assumption of local thermal equilibrium $\left(T_l\approx T_s\right)$ is standard in most two-phase models for alloys with moderate cooling rates, as the inter-phase heat transfer is rapid relative to the solidification timescale. Under this assumption, the energy equations for both phases can be combined into a single mixture enthalpy equation, reducing the number of unknowns. Once T is known from the mixture energy equation, the remaining inter-phase exchange terms M, Q and C are computed using the known solidification rate $\dot{M}$ and the grain evolution equation. If the effect of turbulent flow must be accounted for, the diffusion length scale used in computing Q and C must be adjusted using turbulent diffusivity correlations (Ni & Beckermann, 1993).

Nucleation Model.

For the majority of engineering alloys, heterogeneous nucleation on inoculant particles governs the equiaxed grain population. An initial number density n0 of inoculant particles (embryos) is present in the parent melt; undercooling progressively activates these as equiaxed nuclei. The nucleation rate, which has a Gaussian distribution function of undercooling, can be estimated by the source term $N_{rm}$. The nucleation parameters, $n_{\max }\text{Δ}{T}_N$ and $\text{Δ}{T}_{\sigma }$, can be ascertained through experimentation (Ahmadein et al., 2009; Wang & Beckermann, 1996). Since the solid phase is regarded as a pseudofluid, the associated momentum conservation equation must be solved by defining the solid phase’s viscosity, ${\mu }_s$, which is brought about by interactions between individual equiaxed grains. Ishii and Zuber (1979) demonstrated that the viscosity of a solid/liquid combination is equal to ${\mu }_{mix}={\mu }_l\cdot {\left(1-f_s/f_s^c\right)}^{-2\cdot 5\cdot f_s^c}$. The viscosity of the solid phase is obtained as follows, considering that the mixing rule (Beckermann et al., 1999) ${\mu }_{mix}=f_l{\mu }_l+f_s{\mu }_s$ is applicable here. A packing limit with a significantly smaller solid volume percentage (e.g., 0.2) can be implemented to simulate the coalescence of dendritic crystals (Combeau et al., 2009; Li et al., 2012). Other calculation techniques need to be taken into account for the turbulent flow (Acharya & Moukalled, 1989; Henkes & Hoogendoorn, 1994; Lipton et al., 1984; Ni & Beckermann, 1993).

Boussinesq Approximation and Density Treatment.

Grain sedimentation and thermo-solutal convection are modelled using the Boussinesq approximation (Li et al., 2014; Wu & Ludwig, 2006, 2007) in which the density $\rho$ is treated as constant in all terms of the Navier-Stokes equations except for the gravitational body force term. In the buoyancy term, density variations are linearised as:

where ${\beta }_T$ and ${\beta }_C$ are the thermal and solutal expansion coefficients, respectively, ${\rho }_0$ is the reference density, $T_0$ and $C_0$ are the reference temperature and concentration, respectively. This approximation is valid when density variations are small, a condition generally satisfied in Al-alloy systems over typical solidification temperature ranges. The Oberbeck-Boussinesq approximation decouples the flow equations from the energy and species equations except through the buoyancy source term, greatly simplifying the numerical solution. Because the liquid and solid have different densities, the shrinkage-driven feeding flow is handled separately: in open-domain continuous casting, hot melt enters at the inlet; in closed-domain ingot or form castings, a shrinkage cavity must be fed by an additional gas or slag phase (Wu et al., 2017).

Implementations of the Columnar-to-Equiaxed Transition Model.

The three-phase CET model of Wu and Ludwig (2006, 2007) was first applied in an exploratory simulation of a scaled-down model ingot to demonstrate mixed columnar-equiaxed solidification. Heat transfer controls the overall solidification sequence, but melt convection and grain sedimentation exert a significant influence on the final as-cast structure. When the surface temperature falls below the liquidus temperature, solidification commences with the formation of the columnar phase at the mould wall. Equiaxed grains nucleate in the undercooled melt, and melt convection transports them towards the mould wall, where they sink. Sinking crystals drag the melt downwards along the walls, generating a rising melt flow in the casting centre. Thermal-solutal buoyancy further modifies the overall convection pattern. As solidification proceeds, the columnar phase volume fraction increases at the mould wall, while equiaxed grains continue to nucleate, grow and sink along the columnar tip front until the CET occurs. The model was subsequently extended for industrial ingots (Wu et al., 2017), incorporating the formation of shrinkage cavities and dendritic equiaxed crystal morphology as significant additions. It was noted that the prior assumption of an ideal globular equiaxed grain morphology tends to overestimate macrosegregation (Wu & Ludwig, 2006, 2007), highlighting the importance of morphological fidelity in closure laws.