{"id":{"repo_id":"strathclyde","oai_identifier":"oai:strathclyde:q524jn78d"},"canonical_url":"https://search.dev.ndltd.org/etd/strathclyde/oai:strathclyde:q524jn78d","repository":{"repo_id":"strathclyde","name":"University of Strathclyde","base_url":"https://stax.strath.ac.uk/catalog/oai"},"display":{"title":"Non-Newtonian effects and Taylor-Aris despersion in rivulet flow","abstract":"In this thesis we use a combination of analytical and numerical methods to analyse two aspects of the steady flow of rivulets of fluid, namely the effects of non-Newtonian rheology, and the transport of a passive solute in a rivulet of Newtonian fluid. In Chapters 2-4 we consider rivulet flow of non-Newtonian fluids. Firstly, we obtain the solution for unidirectional gravity-driven flow of a uniform thin rivulet of a power-law fluid down a planar substrate, and then we use this solution to describe the flow of a rivulet with prescribed constant contact angle but slowly varying semi-width down a slowly varying substrate, specifically the flow in the azimuthal direction around the outside of a large horizontal circular cylinder. Secondly, we use the solution for unidirectional flow to describe the flow of arivulet with prescribed constant semi-width but slowly varying contact angledown a slowly varying substrate. Thirdly, we consider rivulet flow of generalised Newtonian fluids down a vertical planar substrate. In particular, we obtain the solutions for rivulet flow of a Carreau fluid and of an Ellis fluid, highlighting their similarities and differences. In Chapters 5 and 6 we investigate both the short-time advection and the long-time Taylor-Aris dispersion of a passive solute in uniform non-thin and thin rivulets, respectively, of a Newtonian fluid undergoing steady unidirectional flow driven by gravity and/or a prescribed uniform surface shear stress on a verticalplanar substrate. In particular, we obtain an explicit expression for the effective diffusivity of the solute in a thin rivulet as a function of the surface shear stress, the volume flux along the rivulet, and either the semi-width or the contact angle of the rivulet.","abstract_html":"In this thesis we use a combination of analytical and numerical methods to analyse two aspects of the steady flow of rivulets of fluid, namely the effects of non-Newtonian rheology, and the transport of a passive solute in a rivulet of Newtonian fluid. In Chapters 2-4 we consider rivulet flow of non-Newtonian fluids. Firstly, we obtain the solution for unidirectional gravity-driven flow of a uniform thin rivulet of a power-law fluid down a planar substrate, and then we use this solution to describe the flow of a rivulet with prescribed constant contact angle but slowly varying semi-width down a slowly varying substrate, specifically the flow in the azimuthal direction around the outside of a large horizontal circular cylinder. Secondly, we use the solution for unidirectional flow to describe the flow of arivulet with prescribed constant semi-width but slowly varying contact angledown a slowly varying substrate. Thirdly, we consider rivulet flow of generalised Newtonian fluids down a vertical planar substrate. In particular, we obtain the solutions for rivulet flow of a Carreau fluid and of an Ellis fluid, highlighting their similarities and differences. In Chapters 5 and 6 we investigate both the short-time advection and the long-time Taylor-Aris dispersion of a passive solute in uniform non-thin and thin rivulets, respectively, of a Newtonian fluid undergoing steady unidirectional flow driven by gravity and/or a prescribed uniform surface shear stress on a verticalplanar substrate. In particular, we obtain an explicit expression for the effective diffusivity of the solute in a thin rivulet as a function of the surface shear stress, the volume flux along the rivulet, and either the semi-width or the contact angle of the rivulet.","abstract_has_math":false,"creators":["Al Mukahal, Fatemah Hussain Habib"],"institution":"University of Strathclyde","degree_name":"phd","degree_level":"doctoral-pg","degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2017,"date_issued":"2017","date_published":"2017","updated_at":"2026-07-24T04:42:25Z","subjects":[],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier.doi","label":"DOI","values":["10.48730/7k31-7q27"],"render_values":[{"text":"10.48730/7k31-7q27","href":"https://doi.org/10.48730/7k31-7q27","code":true}]},{"key":"dc:identifier","label":"Identifier","values":["T14778"],"render_values":[{"text":"T14778","href":null,"code":true}]},{"key":"dc:creator.authoridentifier","label":"Author Identifier","values":["201390916"],"render_values":[{"text":"201390916","href":null,"code":true}]}]},"links":{"outbound_url":"https://stax.strath.ac.uk/concern/theses/q524jn78d","outbound_label":"Repository record","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Al Mukahal, Fatemah Hussain Habib"]},{"key":"dc:creator.authoridentifier","label":"Author Identifier","values":["201390916"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2017"]},{"key":"dc:date.issued","label":"Date","values":["2017"]},{"key":"dc:publisher.department","label":"Dc Publisher Department","values":["Department of Mathematics and Statistics"]},{"key":"dc:publisher.institution","label":"Dc Publisher Institution","values":["University of Strathclyde"]},{"key":"dc:type.qualificationlevel","label":"Dc Type Qualificationlevel","values":["doctoral-pg"]},{"key":"dc:type.qualificationname","label":"Dc Type Qualificationname","values":["phd"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["T14778"]},{"key":"dc:identifier.doi","label":"DOI","values":["10.48730/7k31-7q27"]},{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://stax.strath.ac.uk/concern/theses/q524jn78d"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["In this thesis we use a combination of analytical and numerical methods to analyse two aspects of the steady flow of rivulets of fluid, namely the effects of non-Newtonian rheology, and the transport of a passive solute in a rivulet of Newtonian fluid. In Chapters 2-4 we consider rivulet flow of non-Newtonian fluids. Firstly, we obtain the solution for unidirectional gravity-driven flow of a uniform thin rivulet of a power-law fluid down a planar substrate, and then we use this solution to describe the flow of a rivulet with prescribed constant contact angle but slowly varying semi-width down a slowly varying substrate, specifically the flow in the azimuthal direction around the outside of a large horizontal circular cylinder. Secondly, we use the solution for unidirectional flow to describe the flow of arivulet with prescribed constant semi-width but slowly varying contact angledown a slowly varying substrate. Thirdly, we consider rivulet flow of generalised Newtonian fluids down a vertical planar substrate. In particular, we obtain the solutions for rivulet flow of a Carreau fluid and of an Ellis fluid, highlighting their similarities and differences. In Chapters 5 and 6 we investigate both the short-time advection and the long-time Taylor-Aris dispersion of a passive solute in uniform non-thin and thin rivulets, respectively, of a Newtonian fluid undergoing steady unidirectional flow driven by gravity and/or a prescribed uniform surface shear stress on a verticalplanar substrate. In particular, we obtain an explicit expression for the effective diffusivity of the solute in a thin rivulet as a function of the surface shear stress, the volume flux along the rivulet, and either the semi-width or the contact angle of the rivulet."]},{"key":"dc:description.abstract","label":"Abstract","values":["In this thesis we use a combination of analytical and numerical methods to analyse two aspects of the steady flow of rivulets of fluid, namely the effects of non-Newtonian rheology, and the transport of a passive solute in a rivulet of Newtonian fluid. In Chapters 2-4 we consider rivulet flow of non-Newtonian fluids. Firstly, we obtain the solution for unidirectional gravity-driven flow of a uniform thin rivulet of a power-law fluid down a planar substrate, and then we use this solution to describe the flow of a rivulet with prescribed constant contact angle but slowly varying semi-width down a slowly varying substrate, specifically the flow in the azimuthal direction around the outside of a large horizontal circular cylinder. Secondly, we use the solution for unidirectional flow to describe the flow of arivulet with prescribed constant semi-width but slowly varying contact angledown a slowly varying substrate. Thirdly, we consider rivulet flow of generalised Newtonian fluids down a vertical planar substrate. In particular, we obtain the solutions for rivulet flow of a Carreau fluid and of an Ellis fluid, highlighting their similarities and differences. In Chapters 5 and 6 we investigate both the short-time advection and the long-time Taylor-Aris dispersion of a passive solute in uniform non-thin and thin rivulets, respectively, of a Newtonian fluid undergoing steady unidirectional flow driven by gravity and/or a prescribed uniform surface shear stress on a verticalplanar substrate. In particular, we obtain an explicit expression for the effective diffusivity of the solute in a thin rivulet as a function of the surface shear stress, the volume flux along the rivulet, and either the semi-width or the contact angle of the rivulet."]},{"key":"dc:title","label":"Title","values":["Non-Newtonian effects and Taylor-Aris despersion in rivulet flow"]}]}],"canonical_facts":{"dc:creator":["Al Mukahal, Fatemah Hussain Habib"],"dc:creator.authoridentifier":["201390916"],"dc:date":["2017"],"dc:date.issued":["2017"],"dc:description":["In this thesis we use a combination of analytical and numerical methods to analyse two aspects of the steady flow of rivulets of fluid, namely the effects of non-Newtonian rheology, and the transport of a passive solute in a rivulet of Newtonian fluid. In Chapters 2-4 we consider rivulet flow of non-Newtonian fluids. Firstly, we obtain the solution for unidirectional gravity-driven flow of a uniform thin rivulet of a power-law fluid down a planar substrate, and then we use this solution to describe the flow of a rivulet with prescribed constant contact angle but slowly varying semi-width down a slowly varying substrate, specifically the flow in the azimuthal direction around the outside of a large horizontal circular cylinder. Secondly, we use the solution for unidirectional flow to describe the flow of arivulet with prescribed constant semi-width but slowly varying contact angledown a slowly varying substrate. Thirdly, we consider rivulet flow of generalised Newtonian fluids down a vertical planar substrate. In particular, we obtain the solutions for rivulet flow of a Carreau fluid and of an Ellis fluid, highlighting their similarities and differences. In Chapters 5 and 6 we investigate both the short-time advection and the long-time Taylor-Aris dispersion of a passive solute in uniform non-thin and thin rivulets, respectively, of a Newtonian fluid undergoing steady unidirectional flow driven by gravity and/or a prescribed uniform surface shear stress on a verticalplanar substrate. In particular, we obtain an explicit expression for the effective diffusivity of the solute in a thin rivulet as a function of the surface shear stress, the volume flux along the rivulet, and either the semi-width or the contact angle of the rivulet."],"dc:description.abstract":["In this thesis we use a combination of analytical and numerical methods to analyse two aspects of the steady flow of rivulets of fluid, namely the effects of non-Newtonian rheology, and the transport of a passive solute in a rivulet of Newtonian fluid. In Chapters 2-4 we consider rivulet flow of non-Newtonian fluids. Firstly, we obtain the solution for unidirectional gravity-driven flow of a uniform thin rivulet of a power-law fluid down a planar substrate, and then we use this solution to describe the flow of a rivulet with prescribed constant contact angle but slowly varying semi-width down a slowly varying substrate, specifically the flow in the azimuthal direction around the outside of a large horizontal circular cylinder. Secondly, we use the solution for unidirectional flow to describe the flow of arivulet with prescribed constant semi-width but slowly varying contact angledown a slowly varying substrate. Thirdly, we consider rivulet flow of generalised Newtonian fluids down a vertical planar substrate. In particular, we obtain the solutions for rivulet flow of a Carreau fluid and of an Ellis fluid, highlighting their similarities and differences. In Chapters 5 and 6 we investigate both the short-time advection and the long-time Taylor-Aris dispersion of a passive solute in uniform non-thin and thin rivulets, respectively, of a Newtonian fluid undergoing steady unidirectional flow driven by gravity and/or a prescribed uniform surface shear stress on a verticalplanar substrate. In particular, we obtain an explicit expression for the effective diffusivity of the solute in a thin rivulet as a function of the surface shear stress, the volume flux along the rivulet, and either the semi-width or the contact angle of the rivulet."],"dc:identifier":["T14778"],"dc:identifier.doi":["10.48730/7k31-7q27"],"dc:identifier.uri":["https://stax.strath.ac.uk/concern/theses/q524jn78d"],"dc:publisher.department":["Department of Mathematics and Statistics"],"dc:publisher.institution":["University of Strathclyde"],"dc:title":["Non-Newtonian effects and Taylor-Aris despersion in rivulet flow"],"dc:type.qualificationlevel":["doctoral-pg"],"dc:type.qualificationname":["phd"]},"updated_at":"2026-07-24T04:42:25Z"}