Questions tagged [transport-phenomena]

Transport phenomenon are mechanisms by which particles or quantities move from one place to another. For example, this could be electrical transport (where electrical charge moves), thermal transport (where thermal energy moves), or molecular diffusion (where mass moves).

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Convective heat transfer using a small parameter expansion of the heat equation

I'm trying to follow along with this paper on perturbative transport analysis. The section I'm stuck on analyzes the heat equation in 1D slab geometry. To get a diffusion-only solution is relatively ...
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12 views

Moment transport in fluid, when $(v_x,v_y,v_z) = (by,0,0)$

Consider a fluid, where the velocity of the fluid has components $$(v_x,v_y,v_z) = (by,0,0)$$ where $b$ is a constant. We can use Newton's law of viscosity to determine the flux of momentum in this ...
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How to determine qualitatively the metallic/semimetallic conduction behaviour by comparing chemical potential and thermal energy?

Suppose a material has a semi-metallic dispersion and we want to study electronic transport with small applied electric and magnetic field. Let the chemical potential be positive-valued (i.e. the ...
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61 views

Molecular explanation for pressure

According to this post, viscous stress is the result of molecular diffusion. More specifically, it's a transfer of momentum in a direction perpendicular to the direction of a velocity gradient. This ...
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50 views

Is momentum flux scalar or vector?

I'm trying to derive Navier Stokes equation and stacked the linear momentum equation below. The second term is momentum flux, but it seems scalar value for me because it is vector times vector. How ...
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29 views

Modelling electrical conductivity in low-dimensional nanostructures

I know that the Boltzmann transport equation can be solved under the Relaxation Time Approximation (RTA) to obtain the electrical properties of materials. However, the parameter that I am interested ...
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41 views

Is my understanding of Seebeck effect correct?

I'm not sure whether I understand thermoelectric voltages (Seebeck effect). In the following image I show a simple thermo-couple consisting of materials A and B. On the left side there is a ...
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29 views

Derivation of the advection equation

In this Wikipedia article, specifically in the section "Mathematics of advection", the following general equation for advection is given as: \begin{equation} \dfrac{\partial\psi}{\partial t}+...
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29 views

Transition from local equilibrium to global equilibrium in Boltzmann's equation

My question is about the evolution of a system from local equilibrium to global equilibrium. The system is described by a Boltzmann transport equation $$ \dfrac{\partial f}{\partial t}+\mathbf{v}\cdot\...
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1D flow equation with source inside the medium

How do I set up and solve a 1D flow problem which looks like this - i.e There is a source of water injecting directly into the medium at a point $a$ distance away from the origin. The source is time-...
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45 views

Is there an intuitive understanding about why chemical potential is the good quantity to think about for transport?

I need to understand some very basic behavior of electron transport. The question I have is about why we need to look at chemical potential, rather than energy, to deduce if electron will move from ...
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57 views

Groundwater flow with external forcing

I want to solve the diffusion equation in porous media with some external forcing at the origin. The regular diffusion equation- $$ \frac{\partial h}{\partial t}=D\nabla^2h $$ But I want to solve for ...
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Book recommendation for hydrodynamics of bubbles, drops, and particles

I am wondering if someone could please recommend to me some references on the topic of hydrodynamics of bubbles, drops, and particles, preferably in the context of complex and bio fluids. I am ...
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56 views

Momentum-derivative of energy when mass is not constant

We know by multivariable calculus, that a scalar multivariable function such the energy function $E=E(\vec{P},\vec{L},X_{0},X_{1},...,X_{n})$, using the chain rule, can be expanded as follows: $\frac{...
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98 views

Boltzmann Law in moving fluids?

In my research, I am concerned with the analysis of systems which operate essential like this: There is a tube, say of radius $r$. In this simplification in can be infinitely long. Air moves along it ...
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What does a voltmeter real measure in case of a pn junction?

I recently learned, that a voltmeter doesn't measure difference of electrical potential but difference of electrochemical potential $\tilde{\mu} = \mu/e + \Phi$. My original question was about ...
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Understanding $D \partial^2 P(x,v,t)/\partial x^2$ as a type of collision term

Using conservation of particles in a control volume in phase space (in one dimension with no sources of particles or external forces), one can derive the formal transport equation $$ \partial_t P(x,v,...
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Question on the calculation of the flux of a subtance at a point across any surface

How would one notate the operation leading to Eqn(1)? The flux of a substance at a point $P$ is represented by the vector $f_i$, and its vector components ($\vec f_x,\vec f_y,\vec f_z$) are the fluxes ...
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104 views

If there is no limit to $ZT$, why are there no materials with $ZT>3$?

It is well understood that the thermoelectric performance of a material (described by the parameter $ZT $ ) has no transport related upper theoretical bound. This means a material can exist that can ...
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73 views

Group Velocity Formalism vs. Current Operator Formalism in band theory

There are at least two ways to argue about the velocity (or current) in band theory. The first one is the group-velocity formalism $$\mathbf v_g = \frac{1}{\hbar} \nabla_{\mathbf k} \epsilon_{\mathbf ...
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130 views

What's the equivalent of the resistance for steady stokes flow? Inverse of the viscosity tensor?

it is well known that we describe electrical propagation in a conductor using the conductivity matrix $A$, through the following laplace equation: $$div(A(x) \nabla u(x))=f(x)$$ where $u$ is the ...