T-Junction Device Overview

• T-junction devices are geometric structures where three channels meet, enabling controlled redistribution of mass flow, momentum, or electrical current.
• They are applied across diverse fields such as fluid dynamics, microfluidics, pedestrian dynamics, and quantum electronics to manage splitting, merging, and routing phenomena.
• Recent studies highlight their role in superconducting trijunctions and quantum routing, demonstrating programmable coupling and efficient low-loss transport.

A T-junction device, in the cited literature, is a structure in which three channels, leads, streams, or branches meet in a T-shaped geometry. The same geometry appears in branched hydraulic networks, dividing and impinging microflows, pedestrian merges, ballistic and van der Waals transport structures, and multiterminal quantum devices. Across these realizations, the T-shape is not merely descriptive: it determines how dissipation, work exchange, vorticity, transmission, superconducting phase, or particle occupancy are partitioned among three connected arms (Soto-Francés et al., 2021, Spånslätt et al., 2016, Beer et al., 7 Jan 2026).

1. Geometry and scope

In the surveyed work, the T-junction is used in at least three recurrent ways. First, it is a branched or dividing flow junction, where one conduit feeds two outlets or two inlets merge into one channel. Second, it is a three-terminal conductor, where source, drain, and a third lead meet at a node. Third, it is a trijunction weak link in hybrid superconducting or quantum-dot architectures, where routing or phase control must be exercised across three connected branches.

Domain	Representative T-junction realization	Reported phenomena
Fluid networks	branched junction, dividing T-junction, micromixer	head loss, vortex breakdown, turbulent oscillation
Crowd and microfluidics	pedestrian merge, droplet generator, capsule sorter	merging effects, dripping or jetting, stiffness sorting
Electronic and quantum systems	ballistic junction, graphene edge contact, trijunction device	Wigner threshold effect, contact resistance, braiding, routing

This range of usage suggests that “T-junction device” is best understood as a geometric and topological class rather than a single material platform or operating principle. A plausible implication is that comparison across fields is most informative when centered on what the junction redistributes—mass flow, momentum, current, phase, or discrete particles—rather than on fabrication alone.

2. Hydraulic energetics and flow partition in classical T-junctions

In hydraulic network analysis, the T-junction has long been associated with the controversy of negative head loss coefficients. For branched junctions, the conventional or external model uses two experimentally derived coefficients, $C_r$ and $C_b$, for the straight and side branch. The internal model separates true dissipation from work exchange and therefore requires three quantities: two pure head loss coefficients, $C_{\varphi,r}$ and $C_{\varphi,b}$, and a work exchange coefficient. The relations are expressed as

$$C_r(x)=C_{\varphi,r}(x)-C_{d,r}(x), \qquad C_b(x)=C_{\varphi,b}(x)-C_{d,b}(x),$$

with balanced work exchange

$C_{d,r}(1-x)+C_{d,b}x=0,$

where $x=\frac{\dot V_b}{\dot V_c}$ is the side-branch flow ratio (Soto-Francés et al., 2021).

The missing relation needed to infer the internal model from the measurable external coefficients is obtained from the Minimum Energy Dissipation Principle. The resulting characteristic differential equation,

$$-2C_{\varphi,b}+x\frac{dC_{\varphi,b}}{dx} +2C_{\varphi,r}+(1-x)\frac{dC_{\varphi,r}}{dx}=0,$$

links the two pure head loss coefficients. The paper applies this framework to Zhu’s measurements and Herwig’s CFD computations for the same branched junction and reports very good agreement between the derived internal coefficients and the CFD-based ones. It further shows, in a shaped exhaust return duct example, that traditional analysis can misleadingly attribute reduced apparent drag to reduced dissipation when altered internal work exchange is a major contributor.

At higher Reynolds number and under inlet imbalance, the T-junction supports additional mechanisms. High-fidelity numerical simulations of unbalanced turbulent T-junction flows report a new oscillatory behavior between the two inlet streams, distinct from the symmetric paired-vortex mechanism familiar from balanced flows (Jia et al., 12 May 2026). In the unbalanced case, a single strong vortex forms on the high-flow-rate side, periodically detaches, and collides with the opposite wall, producing rapid turbulence generation at the junction. The oscillatory mode persists over $479 \leq Re \leq 7658$, with an approximately constant Strouhal number $St \approx 0.42$, which the paper interprets as a self-similar phenomenon. Many turbulence and mixing parameters then follow power-law relations with Reynolds number.

Dividing T-junctions also exhibit vortex breakdown that is highly sensitive to outlet asymmetry. In a 3D-printed microfluidic device with one inflow and two independently controlled outflows, the inlet Reynolds number and outflow imbalance are written as

$C_b$0

Even slight outflow imbalances greatly alter the structure of vortex breakdown by creating a net pressure difference across the junction (Chan et al., 2018). The reported dimensionless phase diagram separates regimes with breakdown in both outlets, in only one outlet, or in neither outlet. In this setting, the T-junction functions as a controllable flow-manipulation element rather than as a passive splitter.

3. Microfluidic droplet generation and capsule sorting

A standard microfluidic T-junction is often used for controlled droplet generation. Its baseline operating map is organized by the Capillary number and the velocity ratio,

$C_b$1

with reported regimes including Blocking, Squeezing, Dripping, Jetting, and Parallel Flow (Viswanathan, 2022). The introduction of rib-like “Junction Gutters” (JGs) modifies this map. The paper finds that JGs can favourably alter the formation frequency and morphology of drops and promote upscaling significantly for hydrodynamic conditions associated with low $C_b$2. It also reports that certain gutter configurations are unfavourable for generating monodisperse droplets. Under conditions that would otherwise signify a jetting regime in a standard junction, specific combinations of dimensionless gutter length and depth can instead produce uniform dripping.

The T-junction is also used as a deformability-sensitive sorting element for capsules. In low-Reynolds-number experiments with ovalbumin-alginate capsules, the relevant control parameter is an elastic capillary number defined as

$C_b$3

where $C_b$4 is the force required to compress the capsule to $C_b$5 of its initial height (Häner et al., 2019). Centered capsules travel at constant velocity in the straight channel, decelerate and expand in the spanwise direction near the T-junction, then turn into one daughter channel. The reported maximum extension collapses onto a master curve in $C_b$6, and the position in the junction from which the capsule is entrained into the daughter channel depends uniquely on $C_b$7. On that basis, the authors demonstrate that a T-junction can sort fixed-size capsules according to stiffness, and that a downstream diffuser enhances the initial separation produced at the junction.

Taken together, these studies treat the T-junction as a passive hydrodynamic processor. It can trigger breakup, shift dripping and jetting boundaries, or convert stiffness differences into spatial separation without requiring active components inside the junction itself.

4. Pedestrian-flow T-junctions as merging devices

In pedestrian dynamics, the T-junction is a merging geometry rather than a mechanical device in the narrow sense, but it is analyzed with the same attention to local flux partition and state-dependent transport. Laboratory experiments with a T-junction and a $C_b$8 corner use the Voronoi method for high-resolution measurement of density, velocity, and specific flow (Zhang et al., 2011). For any point $C_b$9 inside the Voronoi cell $C_{\varphi,r}$0 of pedestrian $C_{\varphi,r}$1,

$C_{\varphi,r}$2

and area-averaged specific flow is

$C_{\varphi,r}$3

The main empirical result is that the fundamental diagrams of pedestrian flow in a T-junction are not the same before and after merging. At the same density, velocities before merging are smaller than those after merging; behind merging, specific flow increases continuously with density up to about $C_{\varphi,r}$4, whereas in the branches it is almost constant for densities between $C_{\varphi,r}$5 and $C_{\varphi,r}$6 (Zhang et al., 2012). Comparison with a single corner shows that the discrepancy is not explained by turning alone. The experiments conclude that the merging process, and the associated congestion before the merge, is responsible for the non-unique fundamental diagrams.

The space-resolved profiles obtained with Voronoi analysis show that the highest densities occur near the merging area, that density is typically higher on the inner sides of the branches, and that velocities increase noticeably after merging. These maps are described as informative for identifying dangerous spots and improving egress management and facility design. In this literature, the T-junction is therefore a calibrated merging unit whose transport law is region-dependent rather than universal.

5. Electronic and mesoscopic transport devices

In mesoscopic transport, the T-junction is a three-terminal conductor in which the third terminal can act as a side branch, scatterer, or floating probe. A T-shaped ballistic junction is modeled with the Landauer–Büttiker formalism. At zero temperature,

$C_{\varphi,r}$7

and if lead $C_{\varphi,r}$8 is floating, the effective two-terminal conductance is

$C_{\varphi,r}$9

The floating-electrode voltage is

$C_{\varphi,b}$0

Within this framework, the low-voltage conductance shows the Wigner threshold effect and bend resistance, the system exhibits filtering properties with current distribution between different modes, and the nonlinear regime reveals back action of direct-channel current on the floating electrode voltage (Bek et al., 2011).

At the atomic scale, all-graphene T-junctions have been investigated as three-terminal edge contacts. Ab-initio calculations report that these structures are energetically feasible when the one-dimensional interface is free from foreign atoms (Jacobsen et al., 2016). The most symmetric structures have significant binding energy, and the calculated contact resistances are in the range of $C_{\varphi,b}$1 kOhm, comparable to the best contact resistance reported for edge-contacted graphene-metal contacts. The reported transport is obtained from three-terminal equilibrium Green’s functions, with transmission between terminals $C_{\varphi,b}$2 and $C_{\varphi,b}$3 written as

$C_{\varphi,b}$4

T-junction geometry also appears in van der Waals active devices. An asymmetrically designed 1T-TaS$C_{\varphi,b}$5/2H-MoS$C_{\varphi,b}$6 T-junction implements negative differential resistance through an electrically driven charge-density-wave phase transition (Mahajan et al., 2020). The operating principle is stated to be governed by majority carrier transport and to be distinct from tunneling-based NDR devices. The reported peak current density is in excess of $C_{\varphi,b}$7 nA$C_{\varphi,b}$8m$C_{\varphi,b}$9, about two orders of magnitude higher than typical layered-material-based NDR implementations, and the peak current density can be tuned by an external gate voltage as well as photo-gating. The device characteristics reportedly repeat in multiple measurements over a period of more than a month.

These electronic realizations show three distinct roles for the T-shape: a quantum scattering node, a covalent three-terminal contact, and an active heterostructure whose asymmetry redistributes current during a phase transition.

6. Superconducting, topological, and quantum-routing trijunctions

In topological superconductivity, the T-junction is a standard trijunction geometry for controlling pairwise couplings and phase-dependent zero modes. A three-terminal Josephson T-junction composed of topologically superconducting wires connected by a normal metal region hosts zero-energy Andreev bound states of self-conjugate Majorana nature (Spånslätt et al., 2016). The bound-state condition is

$$C_r(x)=C_{\varphi,r}(x)-C_{d,r}(x), \qquad C_b(x)=C_{\varphi,b}(x)-C_{d,b}(x),$$0

and the zero-mode existence follows from $$C_r(x)=C_{\varphi,r}(x)-C_{d,r}(x), \qquad C_b(x)=C_{\varphi,b}(x)-C_{d,b}(x),$$1. The paper shows that at least one Majorana zero mode always resides in the normal metal region for any choice of superconducting phases. If the junction respects pseudo time-reversal symmetry and two superconducting phases are equal while one differs, the extended Majorana zero mode is distributed only in the two equal-phase arms. If all three phases are equal, three orthogonal extended Majorana zero modes exist. Tunneling conductance is proposed as the experimental diagnostic,

$$C_r(x)=C_{\varphi,r}(x)-C_{d,r}(x), \qquad C_b(x)=C_{\varphi,b}(x)-C_{d,b}(x),$$2

A related line of work treats the T-junction as a braiding platform. In a two-dimensional electron gas trijunction device, optimization in multidimensional voltage space is used to identify regimes in which one desired Majorana pair coupling is large while undesired couplings are suppressed (Luna et al., 2023). The reported operational criteria are

$$C_r(x)=C_{\varphi,r}(x)-C_{d,r}(x), \qquad C_b(x)=C_{\varphi,b}(x)-C_{d,b}(x),$$3

The simulated braiding path preserves a finite topological gap, but electrostatic disorder strongly degrades performance and can render the device inoperable at state-of-the-art disorder levels.

Multiterminal Josephson transport in more conventional hybrid systems is also organized by T-junction topology. A gate-tunable three-terminal Josephson device based on an InAs 2DEG proximitized by epitaxial Al exhibits a central region in the $$C_r(x)=C_{\varphi,r}(x)-C_{d,r}(x), \qquad C_b(x)=C_{\varphi,b}(x)-C_{d,b}(x),$$4 plane where both voltages vanish and several arms in which only some leads remain superconducting (Graziano et al., 2019). The zero-field experimental phase diagram agrees very well with a resistively and capacitively shunted junction model, written for each arm as

$$C_r(x)=C_{\varphi,r}(x)-C_{d,r}(x), \qquad C_b(x)=C_{\varphi,b}(x)-C_{d,b}(x),$$5

No explicit topological phase transition is observed in that multimode regime. More recently, InAsSb-Al hybrid nanocrosses have enabled multiterminal Josephson junction devices in which supercurrent through each terminal combination is measured as a function of junction density and relative phase controlled by magnetic field; the extracted critical currents are $$C_r(x)=C_{\varphi,r}(x)-C_{d,r}(x), \qquad C_b(x)=C_{\varphi,b}(x)-C_{d,b}(x),$$6 nA, $$C_r(x)=C_{\varphi,r}(x)-C_{d,r}(x), \qquad C_b(x)=C_{\varphi,b}(x)-C_{d,b}(x),$$7 nA, and $$C_r(x)=C_{\varphi,r}(x)-C_{d,r}(x), \qquad C_b(x)=C_{\varphi,b}(x)-C_{d,b}(x),$$8 nA (Kahn et al., 6 Nov 2025).

The T-junction has also become a routing primitive in semiconductor spin-qubit architectures. In Si/SiGe, a T-junction device linking two independently driven shuttle lanes enables conveyor-mode electron transfer between perpendicular lanes with no extra control lines beyond the four channels per conveyor belt (Beer et al., 7 Jan 2026). The reported inter-lane charge-transfer fidelity is

$$C_r(x)=C_{\varphi,r}(x)-C_{d,r}(x), \qquad C_b(x)=C_{\varphi,b}(x)-C_{d,b}(x),$$9

at an instantaneous electron velocity of $C_{d,r}(1-x)+C_{d,b}x=0,$0. The filling of 54 quantum dots is controlled by simple atomic pulses, and electron patterns can be swapped through the junction. This suggests that, in quantum-information hardware, the T-junction is evolving from a merely local coupler into a routing element for two-dimensional architectures.

Across these superconducting and quantum realizations, the common requirement is selective control over coupling between three arms without losing coherence. The specific observables differ—zero-bias peaks, critical-current manifolds, or shuttling fidelity—but the governing problem is the same: the T-junction must redistribute amplitude, phase, or occupancy in a programmable and low-loss manner.