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Why does the concentration gradient point towards the area of lowest concentration?
The 2019 Stack Overflow Developer Survey Results Are InWhy isn't the gradient vector of a parametric curve parallel to the tangent vector?Why the gradient vector gives the direction of maximum increase of a function?Direction of Gradient of a scalar functionDoes the gradient of a gradient exist?Proof of the gradient of the inverse of the magnitude of a vector?Why is the dotproduct of direction and gradient the directional derivative? ($nabla_hatv f = nabla f bullet hatv$)$;u_partial Omega =0;$ implies $; fracpartial upartial τ=0;$How is directional derivative at a point on a multi-variable function the projection of the gradient vector at that point?What is the intuition behind the gravitational field having zero divergence?Including rotational motion into a reaction-diffusion model
$begingroup$
This might be a silly question because I don't even know if this is really a point where biology and maths intersect, but after studying Calcalus I'm confused about why do we say that motion ‘with the concentration gradient’ is from the area of high concentration to the area of low concentration. When, we draw the concentration gradient, we draw an arrow pointing towards the area of lowest concentration.
But, if we define a scalar function $C(x,y)$ that gives the concentration of the solute in every point $(x,y)$ of a solution, then logically, the concentration gradient should be $nabla C = leftlangle fracpartial Cpartial x, fracpartial Cpartial y rightrangle$ which gives the direction of maximum increase in the concentration and hence points toward the area of greatest concentration.
However, it seems that the concentration gradient is defined more like $-nabla C$. What is going on here? Is there really any correlation between biology and maths here? Why is the concentration gradient defined like so?
vector-analysis mathematical-modeling
asked Mar 24 at 7:53
Stefan OctavianStefan Octavian
1987
$endgroup$
add a comment |
$begingroup$
This might be a silly question because I don't even know if this is really a point where biology and maths intersect, but after studying Calcalus I'm confused about why do we say that motion ‘with the concentration gradient’ is from the area of high concentration to the area of low concentration. When, we draw the concentration gradient, we draw an arrow pointing towards the area of lowest concentration.
But, if we define a scalar function $C(x,y)$ that gives the concentration of the solute in every point $(x,y)$ of a solution, then logically, the concentration gradient should be $nabla C = leftlangle fracpartial Cpartial x, fracpartial Cpartial y rightrangle$ which gives the direction of maximum increase in the concentration and hence points toward the area of greatest concentration.
However, it seems that the concentration gradient is defined more like $-nabla C$. What is going on here? Is there really any correlation between biology and maths here? Why is the concentration gradient defined like so?
vector-analysis mathematical-modeling
asked Mar 24 at 7:53
Stefan OctavianStefan Octavian
1987
$endgroup$
$begingroup$
Not particularly well versed in this, but this does seem to have a more convenient physical interpretation, since particles go from regions of high concentration to low concentration, so the 'gradient' in this case might give the direction that particles will travel in.
$endgroup$
– Sean Lee
Mar 24 at 7:58
add a comment |
$begingroup$
This might be a silly question because I don't even know if this is really a point where biology and maths intersect, but after studying Calcalus I'm confused about why do we say that motion ‘with the concentration gradient’ is from the area of high concentration to the area of low concentration. When, we draw the concentration gradient, we draw an arrow pointing towards the area of lowest concentration.
But, if we define a scalar function $C(x,y)$ that gives the concentration of the solute in every point $(x,y)$ of a solution, then logically, the concentration gradient should be $nabla C = leftlangle fracpartial Cpartial x, fracpartial Cpartial y rightrangle$ which gives the direction of maximum increase in the concentration and hence points toward the area of greatest concentration.
However, it seems that the concentration gradient is defined more like $-nabla C$. What is going on here? Is there really any correlation between biology and maths here? Why is the concentration gradient defined like so?
vector-analysis mathematical-modeling
asked Mar 24 at 7:53
Stefan OctavianStefan Octavian
1987
$endgroup$
This might be a silly question because I don't even know if this is really a point where biology and maths intersect, but after studying Calcalus I'm confused about why do we say that motion ‘with the concentration gradient’ is from the area of high concentration to the area of low concentration. When, we draw the concentration gradient, we draw an arrow pointing towards the area of lowest concentration.
But, if we define a scalar function $C(x,y)$ that gives the concentration of the solute in every point $(x,y)$ of a solution, then logically, the concentration gradient should be $nabla C = leftlangle fracpartial Cpartial x, fracpartial Cpartial y rightrangle$ which gives the direction of maximum increase in the concentration and hence points toward the area of greatest concentration.
However, it seems that the concentration gradient is defined more like $-nabla C$. What is going on here? Is there really any correlation between biology and maths here? Why is the concentration gradient defined like so?
vector-analysis mathematical-modeling
vector-analysis mathematical-modeling
asked Mar 24 at 7:53
Stefan OctavianStefan Octavian
1987
asked Mar 24 at 7:53
Stefan OctavianStefan Octavian
1987
asked Mar 24 at 7:53
Stefan OctavianStefan Octavian
1987
asked Mar 24 at 7:53
Stefan OctavianStefan Octavian
1987
asked Mar 24 at 7:53
Stefan OctavianStefan Octavian
1987
1987
$begingroup$
Not particularly well versed in this, but this does seem to have a more convenient physical interpretation, since particles go from regions of high concentration to low concentration, so the 'gradient' in this case might give the direction that particles will travel in.
$endgroup$
– Sean Lee
Mar 24 at 7:58
add a comment |
$begingroup$
Not particularly well versed in this, but this does seem to have a more convenient physical interpretation, since particles go from regions of high concentration to low concentration, so the 'gradient' in this case might give the direction that particles will travel in.
$endgroup$
– Sean Lee
Mar 24 at 7:58
$begingroup$
Not particularly well versed in this, but this does seem to have a more convenient physical interpretation, since particles go from regions of high concentration to low concentration, so the 'gradient' in this case might give the direction that particles will travel in.
$endgroup$
– Sean Lee
Mar 24 at 7:58
$begingroup$
Not particularly well versed in this, but this does seem to have a more convenient physical interpretation, since particles go from regions of high concentration to low concentration, so the 'gradient' in this case might give the direction that particles will travel in.
$endgroup$
– Sean Lee
Mar 24 at 7:58
add a comment |
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$begingroup$
Not particularly well versed in this, but this does seem to have a more convenient physical interpretation, since particles go from regions of high concentration to low concentration, so the 'gradient' in this case might give the direction that particles will travel in.
$endgroup$
– Sean Lee
Mar 24 at 7:58