Kinematics of surface growth
Related Experiment Video
Updated: Oct 31, 2026

Visually Based Characterization of the Incipient Particle Motion in Regular Substrates: From Laminar to Turbulent Conditions
Published on: February 22, 2018
R Skalak1, D A Farrow, A Hoger
1Department of Bioengineering-0412, University of California, San Diego, La Jolla 92093-0412, USA. rskalak@ucsd.edu
Abstract:
In this paper a general mathematical framework is developed to describe cases of fixed and moving growth surfaces. This formulation has the mathematical structure suggested by Skalak (1981), but is extended herein to include discussion of possible singularities, incompatibilities, residual stresses and moving growth surfaces. Further, the general theoretical equations necessary for the computation of the final form of a structure from the distribution of growth velocities on a growth surface are presented and applied in a number of examples. It is shown that although assuming growth is always in a direction normal to the current growth surface is generally sufficient, growth at an angle to the growth surface may represent the biological reality more fully in some respects. From a theoretical viewpoint, growth at an angle to a growth surface is necessary in some situations to avoid postulating singularities in the growth velocity field. Examples of growth on fixed and moving surfaces are developed to simulate the generation of horns, seashells, antlers, teeth and similar biological structures.
More Related Videos
11:47Characterization of Surface Modifications by White Light Interferometry: Applications in Ion Sputtering, Laser Ablation, and Tribology Experiments
Published on: February 27, 2013
05:50Measuring Cell-Edge Protrusion Dynamics during Spreading using Live-Cell Microscopy
Published on: November 1, 2021
Related Concept Videos
Surface Tension
Mechanism of Lamellipodia Formation
Surface Tension and Surface Energy
Consider a beaker filled with liquid. The bulk molecules in the liquid experience equal attractive forces on all sides with the surrounding molecules. However, the surface molecules experience a net attractive force downward due to the bulk molecules. The surface of the liquid behaves like a stretched membrane,...
Surface Tension of Fluid
Surface tension varies with...
Hydrostatic Pressure Force on a Curved Surface
Hydrostatic Pressure Force on a Plane Surface