Moving straight over a surface does not always produce a force aligned with the motion. I wanted to test a narrower question: if the directions in which fluid flows most easily stay fixed, can changing speed reverse the sideways component of a contact force?
I kept the material properties and indentation depth fixed while comparing slow and fast translation. In the specified poroelastic layer, the computed sideways force changed from negative to positive, and the two signs survived small, one-at-a-time changes around the baseline. I released the computational data and code on Zenodo on October 19, 2026.
A deforming solid with fluid inside
A wet sponge offers a limited starting analogy: pressing it deforms the solid framework while moving the water inside. Poroelasticity treats those two responses together. My calculation uses a synthetic thin layer, not a measured sponge. Its top and bottom faces are sealed, but fluid can redistribute sideways beneath a bonded elastic cover.
Fluid transport also depends on direction. In the baseline, the two principal in-plane directions lie at ±45° to the direction of motion, with a fourfold permeability difference. I kept that orientation fixed while translating a smooth curved indenter at a prescribed depth. There is no interfacial shear friction in the model; pressure acting on the sloping surface supplies both longitudinal and transverse force components.
The reference lateral scale is 1 mm, the layer is 1 μm thick, and the indentation is 10 nm. The elastic cover is 3 μm thick, with a modulus of 2.1 GPa and tension of 30 N/m. These are constructed model inputs, not jointly measured properties of a specimen. Fixed indentation also means the normal load is allowed to change with speed. A fixed-load test would require a different calculation.
The pressure centroid changed sides
Speeds 1 and 80 are dimensionless, not metres per second. The scale v = Va/D₀ combines physical speed V, reference length a, and reference fluid diffusivity D₀. It compares translation with internal fluid redistribution. For these particular material inputs, the endpoints correspond to about 1.001 and 80.067 μm/s.
On a 256 × 256 grid, the transverse force was approximately −8.10 nN at v = 1 and +135.03 nN at v = 80. Repeating the baseline on a 512 × 512 grid gave −8.07 and +132.36 nN. The signs follow the stated pressure-slope force convention; the force on the opposite body has the opposite sign.
For this curved surface, the transverse force is proportional to the sideways pressure centroid. Saving the pressure field therefore lets a reader trace the force back to its distribution rather than trust a final number alone. Six additional interior speeds sample the change, but do not establish an exact crossing speed or the number of crossings.
Checking more than one successful run
I varied one factor at a time: permeability coupling, fluid–skeleton coupling, cover thickness, tension, or translation speed. All 11 low–high pairs, including the baseline, retained negative low-speed and positive high-speed forces. Refining the two cases selected for their weakest signs changed their force magnitudes by about 0.53% and 1.83%. This tests a local neighbourhood of one parameter set, not an entire material range.
Two direction checks ask whether the calculation respects the expected symmetries. Removing in-plane transport anisotropy makes the transverse force nearly zero; reflecting the tilted permeability direction reverses the transverse force while preserving the longitudinal component. I also checked nonnegative contact pressure, separation outside contact, and agreement between saved pressure moments and the force tables.
The archive contains 38 contact cases: 28 frozen primary checks, two selected fine sensitivity cases, six interior baseline speeds, and two fine baseline endpoints. These are related model calculations, not 38 independent experiments. The later additions remain distinguishable from the original sensitivity plan.
How speed can change the balance
Internal fluid needs time to respond to a changing pressure, and the response times differ with transport direction. A calculation using two reflected pressure components shows how speed can change which supplies the larger transverse contribution. That sign exchange can occur with passive transport and a symmetric permeability law.
The two-component calculation explains a possibility; it is not a theorem for the entire contact. In the full calculation, pressure and contact extent change with speed, while the finite layer and cover alter the response. I solved those contacts separately to obtain the integrated force signs.
What the public package supports
The numerical method combines an open-x thin-layer response with a periodic finite-depth and cover correction; the y direction is periodic too. It is not an independently discretized solution over a fully infinite plane. At the coarse high-speed baseline, a work-rate-versus-dissipation diagnostic differs by about 5.6%. That is not a certified error bar for the transverse force, so I used pressure readback, grid comparisons, and symmetry checks alongside it.
The supported conclusion is model-specific: the fixed permeability orientation did not fix the direction of the transverse force. The force values do not predict a measurable signal for a particular gel or sensor. Extending the result to a material would require jointly characterized properties and further checks, including fixed-load control.
The public package contains complete inputs, 38 pressure fields, per-case diagnostics, force tables, source code, and reproduction instructions. The default commands reuse existing outputs; a fresh rerun requires preserving those originals separately before comparison. Data and documentation use CC BY 4.0, and source code uses MIT.
I directed the research scope and verification workflow. OpenAI Codex assisted with implementation, numerical and algebraic checks, literature screening, and manuscript preparation. This release is computational data and code, not journal acceptance or experimental validation of a material.