---
title: "Active Nematic Flow Interactive Lab | Sandbox Physics"
description: "Why do differently shaped defects stir a fluid differently? Active rods exert stress along their local orientation."
canonical_url: "https://sandboxphysics.com/labs/active-nematic-flow/"
language: "en"
page_type: "lab"
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  zh-CN: "https://sandboxphysics.com/zh/labs/active-nematic-flow/"
last_modified: "2026-10-28"
---

FR22 · Orientations push a fluid

# Active Nematic Flow

**Why do differently shaped defects stir a fluid differently?** Active rods exert stress along their local orientation. Where that orientation bends, the stress pushes the fluid unevenly. A positive half defect has a polar shape; a negative half defect has threefold symmetry, so their surrounding flows differ.

Watch a field of rods drive a moving sea of tracers. Reverse the active stress, add an orientational anchoring island or stripe, and follow the defects detected in the evolving field.

> Interactive simulation: open this page in a web browser to change the parameters and run the model.

Model assumptions

A small periodic two-dimensional Q-tensor model evolves with relaxation, advection, rotation and alignment. The same field drives an incompressible screened Stokes flow through its active stress. The anchoring pattern is permeable to fluid. Passive elastic stress, thermal noise and material calibration are omitted.

Positive half defect Negative half defect Passive fluid tracers

Lengths and times use model units; hue shows direction. Anchoring lets fluid through.

Positive half defects $2$

Negative half defects $2$

RMS fluid speed $0.2$

Half-section flux $0.951$

### A flow that changes with its texture

Cyan is RMS speed; amber is signed horizontal flux through the lower half of the central vertical section. A complete periodic section has zero net flux. Both curves come from the evolving velocity field.

Equations, approximations and sources

The two-component alignment tensor relaxes, moves and rotates with a periodic incompressible flow. A spectral projection solves the centered-difference screened Stokes equation with active stress from the same tensor. Local anchoring is an orientation potential, not a solid boundary.

The coarse browser model isolates coupling and sampling. It omits passive elastic stress and material calibration; its trajectories are numerical examples. Export includes raw tensor samples, velocity samples, seeds, parameters and tracked charges.

[Giomi (2015), active nematodynamics, equations 1–2 and Figure 1](https://arxiv.org/html/1409.1555v2)

[Continue through the active-matter course](https://sandboxphysics.com/stories/active-matter/)

[Read the active matter course: from persistent motion to defects and flow](https://sandboxphysics.com/stories/active-matter/)

Physics tutorial

## Active Nematic Flow

**Background** Watch a field of rods drive a moving sea of tracers. Reverse the active stress, add an orientational anchoring island or stripe, and follow the defects detected in the evolving field.

**Why it matters** A fluid can keep swirling when inertia is negligible, because the rods continually supply energy.

Start with the essentials

- **Focus question**: Why do differently shaped defects stir a fluid differently?
- **One-sentence intuition**: The divergence of the active stress drives the flow; the flow then transports and rotates the same orientation field.

### Core mathematical model

#### Active stress drives screened Stokes flow

$$
0=-\nabla p+\nabla^2\mathbf v-\xi\mathbf v-\zeta\nabla\cdot Q,\qquad\nabla\cdot\mathbf v=0
$$

Viscosity is one in the chosen units. Positive activity is extensile in this sign convention. Pressure removes the compressible part of the force.

#### Relaxation and anchoring

$$
H=0.12\nabla^2Q+(1-2\operatorname{tr}Q^2)Q+Ww(\mathbf r)(Q_{\rm a}-Q)
$$

Relaxation smooths the field and restores order. The last term turns rods toward a prescribed orientation near a permeable island or stripe.

### Common difficulties

#### Two meanings of motion

**Typical misconception** A bright marker is a particle with a prescribed speed.

**Better mental model** Markers follow zeros detected in the evolving tensor field. Tracers are separate passive points carried by the computed fluid velocity.

#### Model scale

**Typical misconception** The grid is a calibrated sample of a biological material.

**Better mental model** A small periodic two-dimensional Q-tensor model evolves with relaxation, advection, rotation and alignment. The same field drives an incompressible screened Stokes flow through its active stress. The anchoring pattern is permeable to fluid. Passive elastic stress, thermal noise and material calibration are omitted.

### Run the experiment

1. 01

   #### Reverse the stress

   Compare Defects drive the flow and Reverse the stress immediately after preparation.

   **What to observe:** The initial tensor field is the same. Changing the stress sign reverses its instantaneous velocity; later the fields evolve differently.

2. 02

   #### Add an anchoring pattern

   Choose An anchoring island or Guide with a stripe. Drag the pattern across the field.

   **What to observe:** The rods turn near the pattern, which changes the active force and the detected defect paths. The pattern is permeable.

3. 03

   #### Compare screening and size

   Increase Friction screening. In Numerical settings, change the box size and repeat the same preset.

   **What to observe:** Friction weakens long-range flow. Changing the periodic box also changes the neighboring images of every defect.

Physical conclusion

A small periodic two-dimensional Q-tensor model evolves with relaxation, advection, rotation and alignment. The same field drives an incompressible screened Stokes flow through its active stress. The anchoring pattern is permeable to fluid. Passive elastic stress, thermal noise and material calibration are omitted.

## Related experiments and articles

Active matter · Reading path

### Active matter from swimming particles to moving defects

Articles on this path that use this experiment, followed by the other experiments they suggest.

1. [Article **Turn an orientation field into a flow**](https://sandboxphysics.com/stories/active-matter/stress-drives-flow/)
2. [Article **Guide defects by choosing where rods prefer to point**](https://sandboxphysics.com/stories/active-matter/anchoring-and-confinement/)
3. [Lab **Nematic Defect Microscope** Find half-turn defects](https://sandboxphysics.com/labs/nematic-defect-microscope/)
4. [Article **Read active turbulence through a spectrum and a material path**](https://sandboxphysics.com/stories/active-matter/reading-active-turbulence/)

Fields & matter · Starter path

## From a field to an electron microscope

Map an electric field and steer a charged particle. Then find the electron's wavelength and use electron beams to see a crystal and a surface.

[Start here → **Make an Electric Field Visible** Move the probe around a dipole and check that the field always points downhill on the potential landscape. Observe · 8 min](https://sandboxphysics.com/labs/electric-field/)

1. [1 Make an Electric Field Visible](https://sandboxphysics.com/labs/electric-field/)
2. [2 A Charge Bending through Fields](https://sandboxphysics.com/labs/charged-particle/)
3. [3 Electron Wavelength & Voltage](https://sandboxphysics.com/labs/electron-wavelength/)
4. [4 Electron Diffraction & Reciprocal Space](https://sandboxphysics.com/labs/electron-diffraction/)
5. [5 TEM Bright Field, Dark Field & SAED](https://sandboxphysics.com/labs/tem-mode-selector/)
6. [6 SEM Secondary-Electron Topography](https://sandboxphysics.com/labs/sem-topography/)

[View the full path →](https://sandboxphysics.com/topics/fields-and-matter/#starter-path)