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joys1995 committed Jun 19, 2024
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159 changes: 108 additions & 51 deletions categories/index.html
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<title>Categories - Joey Blog</title>


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<li><a href="/posts/my-first-post/">混合溶液粘度</a></li>

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<ul>
<li>
<div class="mb:16 py:24 f:fade-30 f:fade-10:hover transition:150ms;ease-in">
<a class="f:24 font:semibold" href="https://joys1995.github.io/posts/my-first-post/">
<div>混合溶液粘度</div>
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<div class="mt:12 f:fade-70"><time>Jun 19, 2024</time></div>
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164 changes: 100 additions & 64 deletions index.html
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<!DOCTYPE html>
<html lang="en-us">
<head>
<html><head>
<meta name="generator" content="Hugo 0.111.3">
<meta charset="UTF-8">
<meta name="viewport" content="width=device-width, initial-scale=1">
<title>Joey Blog</title>


<link rel="stylesheet" href="/css/style.css">
<link rel="alternate" type="application/rss+xml" href="/index.xml" title="Joey Blog">
</head>
<body>
<header>
<a href="https://joys1995.github.io/">Joey Blog</a>

</header>
<meta charset="utf-8" />
<meta http-equiv="X-UA-Compatible" content="IE=edge" />
<meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no" />


<main>


<article>
<h1><a href="https://joys1995.github.io/posts/my-first-post/">混合溶液粘度</a></h1>
<time datetime="2024-06-19T09:00:00">19.06.2024 09:00</time>

<div>
关于混合溶液的粘度预测是一个古老的话题，很朴素的，类似密度等常规物性，我们预计混合溶液的粘度在理想情况下，应该具有线性分布：
以两组分为例：
$$ \eta = x\eta_{\text{1}} + (1-x)\eta_{\text{2}} $$ 但事实上，实际混合溶液的粘度都低于两者的线性叠加
https://pubs.acs.org/doi/epdf/10.1021/ja02254a001
后来，Arrhenius在1887年提出了基于热力学的混合粘度理论公式：
$$ \log\eta = x\log\eta_{\text{1}} + (1-x)\eta_{\text{2}} $$
在1949年，Nature: Mixture Law for Viscosity对参数进行了局部修正 $$ \log\eta = N_1\log\eta_{\text{1}} + N_2\log\eta_{\text{2}}+N_1N_2d $$
这一点推测是由于分子大小和流动性的差异导致混合体系的粘度相较线性值下降更为明显
在溶解溶质的溶液中，对于稀溶液，粘度可以被下述公式计算得到 $$ \frac{\eta_{\text{S}}}{\eta_{\text{O}}} = 1 + A\sqrt{c} $$ 当浓度增加时， $$ \frac{\eta_{\text{S}}}{\eta_{\text{O}}} = 1 + A\sqrt{c} + Bc $$ 当浓度进一步增加时， $$ \frac{\eta_{\text{S}}}{\eta_{\text{O}}} = 1 + A\sqrt{c} + Bc + Cc^2 $$

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<title>Joey Blog</title>


<div>


<meta name="description" content="" />
<meta name="author" content="" />


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<script src="https://unpkg.com/@master/[email protected]"></script>
<script src="https://unpkg.com/master-styles-group"></script>
<script src="https://unpkg.com/themes.js"></script>
<script>window.themes = window.themes || new window.Themes()</script>

</div>

</main>
<aside>
<div>
<div>
<h3>LATEST POSTS</h3>
</div>
<div>
<ul>

<li><a href="/posts/my-first-post/">混合溶液粘度</a></li>

</ul>
</div>
</div>
</aside>


<footer>
<p>&copy; 2024 <a href="https://joys1995.github.io/">Joey Blog</a></p>
</footer>
<style>
:root {
--font-sans: "Inter var", ui-sans-serif, system-ui, -apple-system, BlinkMacSystemFont, Segoe UI, Roboto, Helvetica Neue, Arial, Noto Sans, sans-serif, Apple Color Emoji, Segoe UI Emoji, Segoe UI Symbol, Noto Color Emoji;
}
</style></head>
<body class="bg:fade-84@dark font:fade-16@dark font:sans">
<nav class="w:full h:90 fixed bg:fade-84/.95@dark bg:white z:1000">
<div class="
h:full
w:full
max-w:1200
mx:auto
px:32
d:flex
align-items:center
">
<div>
<a href="/" class="mr-3 font:extralight">

Joey Blog

</a>
</div>

<script type="text/javascript" src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/MathJax.js?config=TeX-AMS-MML_HTMLorMML">
</script>
<div class="ml:auto">



</div>
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<div class="d:flex flex:column@<=sm pt:90 px:24 jc:center gap:44 word-break:break-word">
<div class="max-w:700 w:full box:content-box">
<div class="d:flex flex:col"><div class="
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混合溶液粘度
</a>
<div class="mt:12 f:14 f:fade-60"><time>Jun 19, 2024</time></div>

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