3D Injection Module

• 3D injection modules are subsystems that introduce materials, energy, or signals into spatially resolved 3D environments across a range of scientific and engineering domains.
• They integrate diverse methodologies such as PDE modeling, finite-element analysis, and motion control for precise and adaptive material delivery.
• Key applications include modulating plasma dynamics in tokamaks, enhancing additive manufacturing accuracy, simulating spin transport in spintronics, and enabling targeted neural probe functionalities.

A 3D injection module is a hardware or software subsystem designed to introduce materials, energy, or signals into spatially resolved three-dimensional environments across diverse scientific and engineering domains. Such modules are essential in magnetic confinement fusion, additive manufacturing, spintronics, neural engineering, computational fluid dynamics, computer vision, and medical imaging. Below, six representative implementations are surveyed, each substantiated by published technical workflows, parameterizations, mathematical formulations, and benchmarking evidence.

1. Neutral Material Injection in Tokamak Plasmas

The 3D D₂ neutral injection module for JET H-mode plasmas is realized as a transient neutral source in the JOREK fluid-neutral MHD code (Kong et al., 2024). The neutral density field $n_n(R, Z, \phi, t)$ is evolved by a continuity equation: $$\frac{\partial n_n}{\partial t} + \nabla \cdot (n_n v_n) = S_n(R, Z, \phi, t) - \text{ionization\_loss} - \text{recombination}$$ where $S_n(R, Z, \phi, t)$ is a prescribed 3D Gaussian in $(R, Z, \phi)$ multiplied by a square-pulse Heaviside in time: $$S_n(R, Z, \phi, t) = S_0 \cdot \exp\left[ -\left( \frac{R-R_0}{\Delta r} \right)^2 - \left( \frac{Z-Z_0}{L_\theta} \right)^2 - \left( \frac{\phi-\phi_0}{\Delta \phi} \right)^2 \right] \cdot [H(t) - H(t-\tau)]$$ Key settings:

• Spatial center: $R_0 = 3.482$ m, $Z_0 = 0$, $\phi_0 = 0$
• Widths: $\Delta r = 4$ cm, $L_\theta = 4$ cm, $\Delta \phi = 0.5$ rad (up to 2 rad in scans)
• Pulse duration: $\tau = 0.05$ μs
• Source normalization: $S_0$ set via $\int S_n dV dt$ equals total D₂ atoms injected

Neutral ionization is coupled into plasma mass, momentum, and energy equations as localized source terms, with time-steps $\mathcal{O}(0.01~\mu\mathrm{s})$ required to resolve the injection. Grid refinement is applied around the LFS midplane for adequate resolution of the spatial extent. The source amplitude and toroidal width directly influence the onset of Pegourié-braking and the subsequent resistive current evolution. This module enables direct study of SAW braking ($\mathbf{E}\times\mathbf{B}$-limited plasmoid drift), charge separation constraints, and the effect of flow-region size on drift velocities (Kong et al., 2024).

2. Syringe-Based Fluid Injection for Additive Manufacturing

A 3D injection module for FDM printers enables deposition of functional fluids (e.g., oil–iron mixtures) into printed objects for magnetophoretic display applications (Yan et al., 2023). A secondary syringe extruder equipped with a NEMA 17 stepper drives precise volumetric injection via lead-screw actuation, calibrated as: $$V_\text{step} = A \cdot \frac{\text{pitch}}{\text{steps per rev}}$$ with $A$ the syringe bore cross-section. The module interfaces with Marlin firmware:

• Tool selection: $\text{T0}$ for filament, $\text{T1}$ for syringe
• G-code programming: custom $G1~E1$ microstep motions
• Print–inject sequence: plastic wall formation $\rightarrow$ cell-center movement $\rightarrow$ injection and retraction

Process parameters (injection speed, dwell time, retraction steps) are tuned for droplet accuracy $<$3%, and troubleshooting protocols address needle clogging, cell misalignment, shell leakage, and fluid migration. Slicing and injection scheduling are scripted for arbitrary voxel geometries, and the injector supports continuous customizability for large-scale multi-cell patterns.

3. Three-Dimensional Spin Injection for Spintronics

The 3D spin drift diffusion module models spin injection from a ferromagnet to a semiconductor or normal metal by solving coupled PDEs for spin and charge accumulation, incorporating Ohmic transport, spin-flip relaxation, and interface boundary conditions (Thingna et al., 2011): $\nabla^2 \zeta = \frac{\zeta}{\lambda^2}$ where $\zeta(\mathbf{r})$ is the spin accumulation and $\lambda$ the spin diffusion length. The injection ratio $\gamma$ at interfaces is computed as: $$\gamma = \frac{(\mathbf{j}_\uparrow - \mathbf{j}_\downarrow) \cdot \hat{n}_1}{(\mathbf{j}_\uparrow + \mathbf{j}_\downarrow) \cdot \hat{n}_1}$$ Parameterization spans contact area, slab thickness, and optional buffer/tunnel barriers. Computational realization employs finite-element tetrahedral-mesh discretization, with fictitious-domain carving for pinhole defects and iterative boundary-coupling to resolve $\gamma$ to $10^{-6}$ accuracy. Design guidance includes minimizing conductivity mismatch, avoiding pinhole defect channels, and choosing geometric modulators for efficient spin transport.

4. 3D Injection in Thermally-Coupled Two-Phase Flow Simulations

For mold-filling simulations, a 3D injection-molding module models non-Newtonian two-phase flow (Carreau–WLF viscosity) with adaptive simplex space–time discretization (Karyofylli et al., 2019). The governing system includes incompressible Navier–Stokes, energy, and level-set interface evolution: $$\begin{align*} \nabla \cdot \mathbf{u} &= 0 \ \rho \left( \frac{\partial \mathbf{u}}{\partial t} + \mathbf{u} \cdot \nabla \mathbf{u} - \mathbf{f} \right) - \nabla \cdot \sigma &= 0 \ \rho C_p \left( \frac{\partial T}{\partial t} + \mathbf{u} \cdot \nabla T \right) = k \nabla^2 T + \Phi(\mathbf{u}) \end{align*}$$ with local temporal refinement near the melt front via partitioned 4D simplex mesh slabs. Strongly coupled block-Newton–GMRES solves are employed, with performance optimizations for MPI-based parallel assembly and local refinement. The module achieves sub-1 s fill times in coated benchmark domains and scalability to $>$1 million elements on multi-core clusters.

5. Advanced Microfluidic Injection in Neural Engineering

Microfluidic injection modules fabricated by two-photon polymerization are integrated onto implantable photonic neural probes to enable neurochemical delivery and localized uncaging (Mu et al., 2023). Key characteristics:

• 4.3 mm channel length, 70 × 18 μm cross-section, conformal adhesion to probe shank
• Resin: IP-S polymerized by 780 nm femtosecond laser, with silanization for enhanced SiN adhesion
• Fluidic connectivity: stainless/PTFE adaptors, UV-cured epoxy sealing
• Injection protocols: dye delivery at $Q=10~\mu$L/min, localized photolysis via on-probe emitters (15 μW @ 405 nm)
• Laminar flow validated by linear pressure-flow dependence, diffusion control to sub-100 μm

Modules are designed for immediate geometric customizability and direct conformal printing onto advanced optoelectronic devices without process modifications.

6. Volumetric Conditioning Module for 3D Diffusion Models

In generative medical imaging, the injection module is a "Volumetric Conditioning Module" (VCM, Editor's term) based on an asymmetric, FiLM-modulated 3D U-Net for control of pretrained diffusion models (Ahn et al., 2024). Operational sequence:

• Input: multi-channel volumetric conditions ($3\times20\times28\times20$), noisy latent $z_t$, and predicted noise $\epsilon_t$
• Encoder: six-stage, deep, residual blocks with time-embedding
• FiLM injection: output modulation parameters ($\gamma_t$, $\beta_t$) applied via

$$\epsilon'_t = \epsilon_t \odot (1 + \gamma_t) \oplus \beta_t$$

at each diffusion step, without touching pretrained weights

• Training: MSE on noise prediction plus $\ell_1$ regularization, with AdamW, modality dropout for robustness
• Benchmarks: Dice$>0.89$, ASSD$<0.79$ mm on single/multimodal input, performance superior/competitive to ControlNet with far fewer trainable parameters, efficient VRAM usage

Applications span axial super-resolution, image-to-image translation, and semantic synthesis, with extensibility to volumetric non-medical domains.

Comparison of Key Characteristics

Domain	Spatial Injection Mechanism	Mathematical Framework
Tokamak MHD	3D Gaussian + square pulse neutral source in JOREK	PDEs: fluid continuity, coupled to MHD
Additive Mfg.	Syringe-based stepper-driven volumetric injection	Motion control, G-code, fluid dynamics
Spintronics	FEM discretized drift-diffusion for spin injection	Coupled PDEs for charge, spin, BCs
Mold-Filling	Adaptive 4D simplex ST mesh, melt/air interface	Navier-Stokes, heat, level-set
Neural Probes	Two-photon printed microfluidic, conformal geometry	Laminar flow (Poiseuille), diffusion
Diffusion Models	Asymmetric 3D U-Net, FiLM-modulated latent injection	FiLM-modulated noise prediction, diffusion loss

Future Directions and Generalization

The paradigm of spatially resolved 3D injection is increasingly converging across physical, hardware, and computational contexts. Future modules are likely to incorporate real-time feedback, adaptive condition encoding, and multi-modal inputs for enhanced control and efficiency. Key developments will leverage mesh refinement, programmable hardware, and plug-in architectures to extend injection functionality into new regimes such as dynamic control of medical imaging, multi-material manufacturing, and tightly integrated quantum-classical devices.

This synthesis draws exclusively on published workflows, architectures, and quantitative parameters from referenced works, including modular MHD injection (Kong et al., 2024), syringe-based FDM printing (Yan et al., 2023), spin-drift simulation (Thingna et al., 2011), simplex-based mold simulation (Karyofylli et al., 2019), microfluidic neural probes (Mu et al., 2023), and volumetric conditioning modules for diffusion synthesis (Ahn et al., 2024).