Preprint Article Version 2 Preserved in Portico This version is not peer-reviewed

# Correct Expression of the Material Derivative in Continuum Physics

Version 1 : Received: 1 March 2020 / Approved: 2 March 2020 / Online: 2 March 2020 (15:39:55 CET)
Version 2 : Received: 19 April 2020 / Approved: 22 April 2020 / Online: 22 April 2020 (09:51:56 CEST)
Version 3 : Received: 27 April 2020 / Approved: 28 April 2020 / Online: 28 April 2020 (09:40:46 CEST)
Version 4 : Received: 14 June 2020 / Approved: 15 June 2020 / Online: 15 June 2020 (09:55:06 CEST)

How to cite: Sun, B. Correct Expression of the Material Derivative in Continuum Physics. Preprints 2020, 2020030030 (doi: 10.20944/preprints202003.0030.v2). Sun, B. Correct Expression of the Material Derivative in Continuum Physics. Preprints 2020, 2020030030 (doi: 10.20944/preprints202003.0030.v2).

## Abstract

The material derivative is important in continuum physics. This Letter shows that the expression $\frac{d }{dt}=\frac{\partial }{\partial t}$+ (v • ∇), used in most literature and textbooks, is incorrect. The correct expression $\frac{d (:)}{dt} = \frac{\partial }{\partial t}$(:) + v · [∇(:)] is formulated.

## Subject Areas

material derivative; continuum physics

Comment 1
Commenter: Bohua Sun
Commenter's Conflict of Interests: Author
Comment: Some typos are corrected and more contents were added
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