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物質収支（Mass Balance）の一般化

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1. README（理論背景・数式の意味）

物質収支（Mass Balance）の一般化

希釈や混合の問題を解く際、最も確実な「正攻法」は、系（システム）に含まれる溶質の質量保存に注目することです。これを「物質収支」と呼びます。

支配方程式 (Governing Equations)

2つの溶液を混ぜる場合、以下の等式が成立します。

  1. 全質量の保存 (Total Mass Balance):

  2. 溶質の質量保存 (Solute Mass Balance):

ここで：

  • : 加える溶液1の質量 [g]
  • : 溶液1の濃度（比率）
  • : 用意した溶液2（または水）の質量 [g]
  • : 溶液2の濃度（比率、水なら0）
  • : 目標濃度

一般解の導出

上記2式から混合後の質量 を消去し、求める質量 について解くと、以下の「てんびんの公式」が導かれます。

ご提示の式 は、（水）の場合のこの一般式を簡略化したものです。

体積換算と工学的解釈

求まった質量 を、比体積（1gあたりの体積） を用いて体積 に変換します。

このモデルを用いることで、濃度誤差が最終的な体積決定に与える影響（感度）を解析することが可能になります。

# ==========================================================
# 2. Setup Code (import)
# ==========================================================
import numpy as np
import matplotlib.pyplot as plt
import ipywidgets as widgets
from IPython.display import display, clear_output

# Set plot style / プロットスタイルの設定
plt.style.use('seaborn-v0_8-muted')

# ==========================================================
# 3. TheoreticalModel
# ==========================================================
class TheoreticalModel:
    """
    Handles HCl dilution math using solute mass conservation.
    溶質の質量保存則に基づき塩酸希釈の計算を行うクラス。
    """
    def __init__(self):
        self.m_a = 0.0  # Mass of added acid [g] / 加える塩酸の質量
        self.V_a = 0.0  # Volume of added acid [cm^3] / 加える塩酸の体積

    def validate(self, C_a, C_t, m_w):
        """Validates physical constraints. / 物理的制約の検証"""
        if not (0 < C_t < C_a):
            return False, "Error: Target conc (C_t) must be between 0 and Source conc (C_a)."
        if m_w <= 0:
            return False, "Error: Water mass (m_w) must be positive."
        return True, ""

    def solve(self, m_w, C_a, C_t, v_s):
        """
        Step-by-step solution derivation.
        計算過程をステップバイステップで導出。
        """
        # Step 1: Calculate Mass m_a = (m_w * C_t) / (C_a - C_t)
        numerator = m_w * C_t
        denominator = C_a - C_t
        self.m_a = numerator / denominator
        
        # Step 2: Convert to Volume V_a = m_a * v_s
        self.V_a = self.m_a * v_s

        # Transparency Output / 計算の透明性表示
        print("--- Calculation Process (計算過程の透明性) ---")
        print(f"1. Solute Balance Equation (質量収支式): m_a * C_a = (m_a + m_w) * C_t")
        print(f"2. Rearranged for m_a (m_aの導出式): m_a = (m_w * C_t) / (C_a - C_t)")
        print(f"   Substitution (数値代入): m_a = ({m_w} * {C_t}) / ({C_a} - {C_t})")
        print(f"   => m_a = {numerator} / {denominator}")
        print(f"   => m_a = {self.m_a:.4f} g")
        print(f"3. Volume Conversion (体積換算): V_a = m_a * v_spec")
        print(f"   Substitution (数値代入): V_a = {self.m_a:.4f} * {v_s}")
        print(f"   => V_a = {self.V_a:.4f} cm^3")
        print("----------------------------------------------")
        
        return self.m_a, self.V_a

# ==========================================================
# 4. Visualizer
# ==========================================================
class Visualizer:
    """
    Plots the Area Diagram for concentration balance.
    濃度のつり合いを示す面積図を描画するクラス。
    """
    def __init__(self):
        self.prev_state = None # To store ghost lines / ゴースト線用の前回データ保存

    def plot_area(self, m_w, C_a, C_t, m_a):
        fig, ax = plt.subplots(figsize=(10, 6))
        
        # Current result: Area rectangles / 今回の結果：長方形
        # Rectangle 1: Water Base (m_w)
        ax.add_patch(plt.Rectangle((0, 0), m_w, 0, color='blue', alpha=0.1, label='Water Base (m_w)'))
        # Rectangle 2: Added Acid (m_a)
        ax.add_patch(plt.Rectangle((m_w, 0), m_a, C_a, color='red', alpha=0.4, label='Added Acid (m_a)'))
        
        # Target Concentration line (C_t)
        ax.axhline(y=C_t, color='green', linestyle='-', linewidth=2, label=f'Target Line C_t ({C_t}%)')

        # Ghost line for previous result / ゴースト線（前回の結果）
        if self.prev_state is not None:
            p_mw, p_ma, p_ca, p_ct = self.prev_state
            ax.plot([0, p_mw, p_mw, p_mw + p_ma, p_mw + p_ma], [0, 0, p_ca, p_ca, 0], 
                    color='gray', linestyle='--', alpha=0.4, label='Previous Result (Ghost)')
            ax.axhline(y=p_ct, color='gray', linestyle=':', alpha=0.4)

        # Plot Settings (English Only) / グラフ設定
        ax.set_title("Concentration Area Diagram: Solute Mass Conservation")
        ax.set_xlabel("Cumulative Solution Mass [g]")
        ax.set_ylabel("Concentration [%]")
        ax.set_xlim(0, (m_w + m_a) * 1.2)
        ax.set_ylim(0, C_a * 1.2)
        ax.grid(True, linestyle=':', alpha=0.6)
        ax.legend(loc='upper right')
        
        plt.show()
        
        # Update state for sensitivity analysis
        self.prev_state = (m_w, m_a, C_a, C_t)

# ==========================================================
# 5. UIBuilder
# ==========================================================
class UIBuilder:
    def __init__(self, model, viz):
        self.model = model
        self.viz = viz
        self.output = widgets.Output()

        # [Model Parameters: Solution Constants]
        self.C_a_box = widgets.BoundedFloatText(value=35.0, min=0.1, max=100.0, description='C_a [%]:')
        self.v_s_box = widgets.BoundedFloatText(value=0.85, min=0.01, max=5.0, description='v_spec [cm^3/g]:')

        # [Observed / Input Data: Experimental Setup]
        self.m_w_box = widgets.BoundedFloatText(value=125.0, min=0.1, max=10000.0, description='m_w [g]:')
        self.C_t_box = widgets.BoundedFloatText(value=10.0, min=0.1, max=99.0, description='C_t [%]:')

        # [Run Button]
        self.run_btn = widgets.Button(description='Run Simulation (実行)', button_style='primary', icon='play')
        self.run_btn.on_click(self._on_run)

        # Grouped Layout
        self.ui_layout = widgets.VBox([
            widgets.HTML("<b>[Model Parameters: Physical Properties]</b>"),
            widgets.HBox([self.C_a_box, self.v_s_box]),
            widgets.HTML("<b>[Input Data: Desired Setup]</b>"),
            widgets.HBox([self.m_w_box, self.C_t_box]),
            widgets.HTML("<br>"),
            self.run_btn
        ])

    def _on_run(self, b):
        with self.output:
            clear_output(wait=True)
            # 1. Validate / 検証
            is_valid, msg = self.model.validate(self.C_a_box.value, self.C_t_box.value, self.m_w_box.value)
            if not is_valid:
                print(f"❌ {msg}")
                return
            
            # 2. Calculate / 計算
            ma, _ = self.model.solve(
                self.m_w_box.value, 
                self.C_a_box.value, 
                self.C_t_box.value, 
                self.v_s_box.value
            )
            
            # 3. Visualize / 描画
            self.viz.plot_area(self.m_w_box.value, self.C_a_box.value, self.C_t_box.value, ma)

    def display(self):
        display(self.ui_layout, self.output)

# ==========================================================
# 6. Initialization
# ==========================================================
model_inst = TheoreticalModel()
viz_inst = Visualizer()
ui_inst = UIBuilder(model_inst, viz_inst)
ui_inst.display()
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