# Maxwell-Stefan Multicomponent Molar Diffusion Velocity Solver

> Maxwell-Stefan Multicomponent Molar Diffusion Velocity Solver is a paid API for AI agents from detect.halowerk.com, paid per call via x402, $0.003/call, status unknown (last checked 2026-11-04).

Resolves coupled molar diffusion velocities for a multicomponent mixture using explicit pairwise binary diffusivities and mole fraction gradients via the Maxwell-Stefan framework.

## Facts

- Endpoint: POST https://detect.halowerk.com/v1/F-TD2000-GEO-INDUSTRY-B009/maxwell-stefan-multicomponent-molar-diffusion-velocity-system?utm_source=zero.xyz
- Price: $0.003/call
- Payment: x402
- Status: unknown
- Last checked: 2026-11-04
- Activations on Zero: 0
- Tags: x402
- Canonical page: https://www.zero.xyz/c/maxwell-stefan-multicomponent-molar-diffusion-velocity-solver-714ca9d0
- Structured record (JSON): https://api.zero.xyz/v1/capabilities/cap_QP_rW_eLRJ3LGHOQKlecL

Status and success rate cover calls made through Zero and Zero's own probes. Third-party monitors may report differently.

## How to call it through Zero

Zero handles the 402 payment challenge and records the run. With the Zero CLI installed (`npm i -g @zeroxyz/cli`):

```sh
zero fetch --capability maxwell-stefan-multicomponent-molar-diffusion-velocity-solver-714ca9d0 -d '<json body>'
```

Example prompt: Solve the Maxwell-Stefan diffusion velocities for a 3-component mixture with mole amounts [0.3, 0.5, 0.2], mole fraction gradients [0.1, -0.05, -0.05], binary diffusivities matrix [[0,1.2,0.8],[1.2,0,0.6],[0.8,0.6,0]], and a total molar density of 40 mol/m³.

## When to prefer this

Use this endpoint when you need to solve the full coupled Maxwell-Stefan multicomponent diffusion system from explicit pairwise binary diffusivities rather than using simplified Fickian or effective diffusivity approximations. It is preferred for systems with 2–8 components where diffusion coupling between species is significant, such as in membrane separations, catalytic reactors, or gas absorption columns where cross-diffusion effects cannot be ignored.

## Known failure modes

- Singular or ill-conditioned diffusivity matrix causing no unique solution
- Sum of mole fraction gradients violating the constraint (non-zero sum) leading to rejection
- Component count mismatch between component_amounts, mole_fraction_gradients, and binary_diffusivities arrays
- Binary diffusivities matrix not square or not symmetric causing validation failure
- Values out of allowed range (e.g. negative component amounts or diffusivities) causing schema rejection
- Total molar density of zero or below minimum threshold causing division error

## How this service works

Resolve coupled molar diffusion velocities from explicit pairwise molecular friction inputs.

## Output

Returns the resolved molar diffusion velocity vector for each component in the mixture, computed by inverting the coupled Maxwell-Stefan linear system built from the pairwise binary diffusivities, mole fraction gradients, component amounts, and total molar density.

## Request schema (JSON Schema)

```json
{
 "type": "object",
 "properties": {
  "artifact": {
   "type": "object",
   "required": [
    "maxwellStefan"
   ],
   "properties": {
    "maxwellStefan": {
     "type": "object",
     "required": [
      "data",
      "claim"
     ],
     "properties": {
      "data": {
       "type": "object",
       "required": [
        "component_amounts",
        "mole_fraction_gradients",
        "binary_diffusivities",
        "total_molar_density"
       ],
       "properties": {
        "component_amounts": {
         "type": "array",
         "items": {
          "type": "number",
          "maximum": 10000,
          "minimum": 0.000001
         },
         "maxItems": 8,
         "minItems": 2
        },
        "total_molar_density": {
         "type": "number",
         "maximum": 1000000,
         "minimum": 0.000001
        },
        "binary_diffusivities": {
         "type": "array",
         "items": {
          "type": "array",
          "items": {
           "type": "number",
           "maximum": 10000,
           "minimum": 0
          },
          "maxItems": 8,
          "minItems": 2
         },
         "maxItems": 8,
         "minItems": 2
        },
        "mole_fraction_gradients": {
         "type": "array",
         "items": {
          "type": "number",
          "maximum": 10000,
          "minimum": -10000
         },
         "maxItems": 8,
         "minItems": 2
        }
       },
       "additionalProperties": false
      },
      "claim": {}
     },
     "additionalProperties": false
    }
   },
   "additionalProperties": false
  }
 }
}
```

## More

- Live health (JSON, refreshed every minute): https://www.zero.xyz/c/maxwell-stefan-multicomponent-molar-diffusion-velocity-solver-714ca9d0/health.json
- [Zero catalog index](https://www.zero.xyz/llms.txt)
- [Other services from detect.halowerk.com](https://www.zero.xyz/host/detect.halowerk.com/llms.txt)