Perturbation Solution for Pulsatile Flow of a Non-Newtonian Fluid in a Rock Fracture: A Logarithmic Model

The purpose of this work is to study the motion of a non-Newtonian fluid in a rock fracture, generated by a constant pressure gradient to which a pulsating component is superposed. The momentum equation is faced analytically by adopting a logarithmic constitutive law; the velocity is expressed as a...

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Main Authors:	Irene Daprà, Giambattista Scarpi
Format:	Article
Language:	English
Published:	MDPI AG 2020-05-01
Series:	Water
Subjects:	non-Newtonian fluid pulsatile flow rock fracture analytical solution Williamson model
Online Access:	https://www.mdpi.com/2073-4441/12/5/1341

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spelling	doaj-48be8be213584d5fa15dae9ae4b946b32020-11-25T03:26:44ZengMDPI AGWater2073-44412020-05-01121341134110.3390/w12051341Perturbation Solution for Pulsatile Flow of a Non-Newtonian Fluid in a Rock Fracture: A Logarithmic ModelIrene Daprà0Giambattista Scarpi1DICAM, University of Bologna, 40136 Bologna, ItalyDICAM, University of Bologna, 40136 Bologna, ItalyThe purpose of this work is to study the motion of a non-Newtonian fluid in a rock fracture, generated by a constant pressure gradient to which a pulsating component is superposed. The momentum equation is faced analytically by adopting a logarithmic constitutive law; the velocity is expressed as a power series of the amplitude of the pulsating component, up to the second order, easily usable for numerical calculations. The results obtained are compared with those provided in the past by the authors, using a three-parameter Williamson model. The comparison highlights that the value of the mean flow rate in a period differs by less than 10% even if the velocity profiles look quite different.https://www.mdpi.com/2073-4441/12/5/1341non-Newtonian fluidpulsatile flowrock fractureanalytical solutionWilliamson model
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Irene Daprà Giambattista Scarpi
spellingShingle	Irene Daprà Giambattista Scarpi Perturbation Solution for Pulsatile Flow of a Non-Newtonian Fluid in a Rock Fracture: A Logarithmic Model Water non-Newtonian fluid pulsatile flow rock fracture analytical solution Williamson model
author_facet	Irene Daprà Giambattista Scarpi
author_sort	Irene Daprà
title	Perturbation Solution for Pulsatile Flow of a Non-Newtonian Fluid in a Rock Fracture: A Logarithmic Model
title_short	Perturbation Solution for Pulsatile Flow of a Non-Newtonian Fluid in a Rock Fracture: A Logarithmic Model
title_full	Perturbation Solution for Pulsatile Flow of a Non-Newtonian Fluid in a Rock Fracture: A Logarithmic Model
title_fullStr	Perturbation Solution for Pulsatile Flow of a Non-Newtonian Fluid in a Rock Fracture: A Logarithmic Model
title_full_unstemmed	Perturbation Solution for Pulsatile Flow of a Non-Newtonian Fluid in a Rock Fracture: A Logarithmic Model
title_sort	perturbation solution for pulsatile flow of a non-newtonian fluid in a rock fracture: a logarithmic model
publisher	MDPI AG
series	Water
issn	2073-4441
publishDate	2020-05-01
description	The purpose of this work is to study the motion of a non-Newtonian fluid in a rock fracture, generated by a constant pressure gradient to which a pulsating component is superposed. The momentum equation is faced analytically by adopting a logarithmic constitutive law; the velocity is expressed as a power series of the amplitude of the pulsating component, up to the second order, easily usable for numerical calculations. The results obtained are compared with those provided in the past by the authors, using a three-parameter Williamson model. The comparison highlights that the value of the mean flow rate in a period differs by less than 10% even if the velocity profiles look quite different.
topic	non-Newtonian fluid pulsatile flow rock fracture analytical solution Williamson model
url	https://www.mdpi.com/2073-4441/12/5/1341
work_keys_str_mv	AT irenedapra perturbationsolutionforpulsatileflowofanonnewtonianfluidinarockfracturealogarithmicmodel AT giambattistascarpi perturbationsolutionforpulsatileflowofanonnewtonianfluidinarockfracturealogarithmicmodel
_version_	1724590843234353152

Perturbation Solution for Pulsatile Flow of a Non-Newtonian Fluid in a Rock Fracture: A Logarithmic Model

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